Daily Papers

Large language models (LLMs) are trained on extensive datasets that encapsulate substantial world knowledge. However, their outputs often include confidently stated inaccuracies. Earlier works suggest that LLMs encode truthfulness as a distinct linear feature, termed the "truth direction", which can classify truthfulness reliably. We address several open questions about the truth direction: (i) whether LLMs universally exhibit consistent truth directions; (ii) whether sophisticated probing techniques are necessary to identify truth directions; and (iii) how the truth direction generalizes across diverse contexts. Our findings reveal that not all LLMs exhibit consistent truth directions, with stronger representations observed in more capable models, particularly in the context of logical negation. Additionally, we demonstrate that truthfulness probes trained on declarative atomic statements can generalize effectively to logical transformations, question-answering tasks, in-context learning, and external knowledge sources. Finally, we explore the practical application of truthfulness probes in selective question-answering, illustrating their potential to improve user trust in LLM outputs. These results advance our understanding of truth directions and provide new insights into the internal representations of LLM beliefs. Our code is public at https://github.com/colored-dye/truthfulness_probe_generalization

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

In the rapidly evolving domain of distributed ledger technology, scalability and interoperability have become paramount challenges for both academic and industry sectors. In this paper, we introduce a comprehensive formal model to address atomic composability across multiple rollups on Ethereum. The proposed model incorporates mechanisms like buffering, dependency management, concurrency control, and the groundbreaking zero-knowledge proofs. Moreover, we evaluate its practical repercussions, strengths, and weaknesses, ensuring resilience against manipulative or erroneous actions. The application of the proposed model to shared sequencers and other existing solutions accentuates its versatility and universality.

Instruction-following has emerged as a crucial capability for large language models (LLMs). However, existing approaches often rely on pre-existing documents or external resources to synthesize instruction-following data, which limits their flexibility and generalizability. In this paper, we introduce DecIF, a fully autonomous, meta-decomposition guided framework that generates diverse and high-quality instruction-following data using only LLMs. DecIF is grounded in the principle of decomposition. For instruction generation, we guide LLMs to iteratively produce various types of meta-information, which are then combined with response constraints to form well-structured and semantically rich instructions. We further utilize LLMs to detect and resolve potential inconsistencies within the generated instructions. Regarding response generation, we decompose each instruction into atomic-level evaluation criteria, enabling rigorous validation and the elimination of inaccurate instruction-response pairs. Extensive experiments across a wide range of scenarios and settings demonstrate DecIF's superior performance on instruction-following tasks. Further analysis highlights its strong flexibility, scalability, and generalizability in automatically synthesizing high-quality instruction data.

The Bernays-Sch\"onfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clause sets over a finite set of first-order constants. For the Horn case, we provide a Datalog hammer preserving validity and satisfiability. A toolchain from the BS(LRA) prover SPASS-SPL to the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. This is exemplified by the verification of supervisor code for a lane change assistant in a car and of an electronic control unit for a supercharged combustion engine.

This paper provides a novel approach to reconciling complex low-level memory model features, such as pointer--integer casts, with desired refinements that are needed to justify the correctness of program transformations. The idea is to use a "two-phased" memory model, one with and unbounded memory and corresponding unbounded integer type, and one with a finite memory; the connection between the two levels is made explicit by our notion of refinement that handles out-of-memory behaviors. This approach allows for more optimizations to be performed and establishes a clear boundary between the idealized semantics of a program and the implementation of that program on finite hardware. To demonstrate the utility of this idea in practice, we instantiate the two-phase memory model in the context of Zakowski et al.'s VIR semantics, yielding infinite and finite memory models of LLVM IR, including low-level features like undef and bitcast. Both the infinite and finite models, which act as specifications, can provably be refined to executable reference interpreters. The semantics justify optimizations, such as dead-alloca-elimination, that were previously impossible or difficult to prove correct.

Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in programming languages, type-and-effect systems did not yet gain widespread adoption. One reason for this is that type-and-effect systems are more complex and the existing inference algorithms make compromises between expressiveness, intuitiveness, and decidability. In this work, we present an effect inference algorithm for a type-and-effect system with subtyping, expressive higher-rank polymorphism, and intuitive set-like semantics of effects. In order to deal with scoping issues of higher-rank polymorphism, we delay solving of effect constraints by transforming them into formulae of propositional logic. We prove soundness and completeness of our algorithm with respect to a declarative type-and-effect system. All the presented results have been formalized in the Rocq proof assistant, and the algorithm has been successfully implemented in a realistic programming language.

In today's rapidly expanding data landscape, knowledge extraction from unstructured text is vital for real-time analytics, temporal inference, and dynamic memory frameworks. However, traditional static knowledge graph (KG) construction often overlooks the dynamic and time-sensitive nature of real-world data, limiting adaptability to continuous changes. Moreover, recent zero- or few-shot approaches that avoid domain-specific fine-tuning or reliance on prebuilt ontologies often suffer from instability across multiple runs, as well as incomplete coverage of key facts. To address these challenges, we introduce ATOM (AdapTive and OptiMized), a few-shot and scalable approach that builds and continuously updates Temporal Knowledge Graphs (TKGs) from unstructured texts. ATOM splits input documents into minimal, self-contained "atomic" facts, improving extraction exhaustivity and stability. Then, it constructs atomic TKGs from these facts while employing a dual-time modeling that distinguishes when information is observed from when it is valid. The resulting atomic TKGs are subsequently merged in parallel. Empirical evaluations demonstrate that ATOM achieves ~18% higher exhaustivity, ~17% better stability, and over 90% latency reduction compared to baseline methods, demonstrating a strong scalability potential for dynamic TKG construction.

We present a machine-checked formalization of structurally governed AI workflow architectures and prove that effect-level governance can be imposed without reducing internal computational expressivity. Using Interaction Trees in Rocq 8.19, we define a governance operator G that mediates all effectful directives, including memory access, external calls, and oracle (LLM) queries. Our development compiles with 0 admitted lemmas and consists of 36 modules, ~12,000 lines of Rocq, and 454 theorems. We establishseven properties: (P1) governed Turing completeness, (P2) governed oracle expressivity, (P3) a decidability boundary in which governance predicates are total and closed under Boolean composition while semantic program properties remain non-trivial and undecidable by governance, (P4) goal preservation for permitted executions, (P5) expressive minimality of primitive capabilities (compute, memory, reasoning, external call, observability), (P6) subsumption asymmetry showing structural governance strictly subsumes content-level filtering, and (P7) semantic transparency: on all executions where governance permits, the governed interpretation is observationally equivalent (modulo governance-only events) to the ungoverned interpretation. Together, these results show that governance and computational expressivity are orthogonal dimensions: governance constrains the effect boundary of programs while remaining semantically transparent to internal computation.

Multi-agent LLM systems share state through memory stores, vector indices, and tool registries. We model such sharing as long-running read-generate-write operations under deterministic-generation semantics -- the regime durable-execution engines enforce by deterministic replay -- and formalize four concurrency anomalies in TLA+: stale-generation, phantom-tool, causal-cascade, and tool-effect reordering, structural analogues of classical isolation anomalies, each with a TLC counter-example. The exclusion lattice over these anomalies is trivial; the contribution is the mechanically verified realizability and strict separation of one maximal chain within it, L_0 subsetneq cdots subsetneq L_4, to our knowledge the first machine-checked consistency hierarchy for such runtimes. A development of 274 Verus obligations (zero assume, zero admit; trust base: two structural axioms and a mutex correspondence) proves the detectors sound and complete against the specifications and each runtime its avoidance set. Three deployed Rust runtimes realize L0-L1 (pessimistic locking, serializable snapshot isolation, default-SI), each verified against stale-generation and refined to its state machine; L2-L4 are exec-mode-verified with dependency-free prevention twins (A3, A6, A2: 0/1000 versus 1000/1000), and L2 is run live across three model families (A3 prevented in all 120 retracted sessions). We reproduce a silent lost update in ByteDance's deer-flow, formalizing its fix as a verified L_0 to L_1 refinement, and exhibit tool-effect reordering in LangGraph's ToolNode on unmodified output, removed by an L3 commit-order sequencer. The verified detector, refinements, and realizability artifacts are the contribution; the phenomena and lattice are classical.

This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC derives from the lambda-calculus by taking the standard operational perspective of a call-by-name stack machine as primary, and introducing two natural generalizations. One, "locations", introduces multiple stacks, which each may represent an effect and so enable effect operators to be encoded into the abstraction and application constructs of the calculus. The second, "sequencing", is known from kappa-calculus and concatenative programming languages, and introduces the imperative notions of "skip" and "sequence". This enables the encoding of reduction strategies, including call-by-value lambda-calculus and monadic constructs. The encoding of effects into generalized abstraction and application means that standard results from the lambda-calculus may carry over to effects. The main result is confluence, which is possible because encoded effects reduce algebraically rather than operationally. Reduction generates the familiar algebraic laws for state, and unlike in the monadic setting, reader/writer effects combine seamlessly. A system of simple types confers termination of the machine.

The popularity of the Rust language continues to explode; yet, many critical codebases remain authored in C, and cannot be realistically rewritten by hand. Automatically translating C to Rust is thus an appealing course of action. Several works have gone down this path, handling an ever-increasing subset of C through a variety of Rust features, such as unsafe. While the prospect of automation is appealing, producing code that relies on unsafe negates the memory safety guarantees offered by Rust, and therefore the main advantages of porting existing codebases to memory-safe languages. We instead explore a different path, and explore what it would take to translate C to safe Rust; that is, to produce code that is trivially memory safe, because it abides by Rust's type system without caveats. Our work sports several original contributions: a type-directed translation from (a subset of) C to safe Rust; a novel static analysis based on "split trees" that allows expressing C's pointer arithmetic using Rust's slices and splitting operations; an analysis that infers exactly which borrows need to be mutable; and a compilation strategy for C's struct types that is compatible with Rust's distinction between non-owned and owned allocations. We apply our methodology to existing formally verified C codebases: the HACL* cryptographic library, and binary parsers and serializers from EverParse, and show that the subset of C we support is sufficient to translate both applications to safe Rust. Our evaluation shows that for the few places that do violate Rust's aliasing discipline, automated, surgical rewrites suffice; and that the few strategic copies we insert have a negligible performance impact. Of particular note, the application of our approach to HACL* results in a 80,000 line verified cryptographic library, written in pure Rust, that implements all modern algorithms - the first of its kind.

As a vital stage of automated rule checking (ARC), rule interpretation of regulatory texts requires considerable effort. However, interpreting regulatory clauses with implicit properties or complex computational logic is still challenging due to the lack of domain knowledge and limited expressibility of conventional logic representations. Thus, LLM-FuncMapper, an approach to identifying predefined functions needed to interpret various regulatory clauses based on the large language model (LLM), is proposed. First, by systematically analysis of building codes, a series of atomic functions are defined to capture shared computational logics of implicit properties and complex constraints, creating a database of common blocks for interpreting regulatory clauses. Then, a prompt template with the chain of thought is developed and further enhanced with a classification-based tuning strategy, to enable common LLMs for effective function identification. Finally, the proposed approach is validated with statistical analysis, experiments, and proof of concept. Statistical analysis reveals a long-tail distribution and high expressibility of the developed function database, with which almost 100% of computer-processible clauses can be interpreted and represented as computer-executable codes. Experiments show that LLM-FuncMapper achieve promising results in identifying relevant predefined functions for rule interpretation. Further proof of concept in automated rule interpretation also demonstrates the possibility of LLM-FuncMapper in interpreting complex regulatory clauses. To the best of our knowledge, this study is the first attempt to introduce LLM for understanding and interpreting complex regulatory clauses, which may shed light on further adoption of LLM in the construction domain.

We introduce k-quantifier logics -- logics with access to k-tuples of elements and very general quantification patterns for transitions between k-tuples. The framework is very expressive and encompasses e.g. the k-variable fragments of first-order logic, modal logic, and monotone neighbourhood semantics. We introduce a corresponding notion of bisimulation and prove variants of the classical Ehrenfeucht-Fraisse and Hennessy-Milner theorem. Finally, we show a Lindstrom-style characterisation for k-quantifier logics that satisfy Los' theorem by proving that they are the unique maximally expressive logics that satisfy Los' theorem and are invariant under the associated bisimulation relations.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as the cornerstone for shaping the remarkable coding abilities of Large Language Models (LLMs). However, the scalability of RLVR is severely constrained by the scarcity of sufficiently challenging verifiable code tasks that target near the model's edge of competence. Prior studies often rely on heuristic seed expansions for data synthesis, which severely limits both novelty and difficulty. Consequently, the training value of such data fails to scale proportionally with the size of its synthesis. To this end, we propose Atomic Decomposition and Recombination (ADR), a novel framework that generates verifiable code tasks via decomposition into atomic elements and controlled recombination, thereby enabling the generation of genuinely novel and challenging verifiable code tasks. Experiments and analysis demonstrate that ADR achieves superior originality, difficulty, diversity, and test quality over existing baselines, and consistently delivers greater improvements in code ability across RLVR in diverse downstream domains, including algorithmic programming, tool usage, and data science. Our work sheds light on a new paradigm for novel code task synthesis and scalable RLVR training.

Large Language Models (LLMs) achieve superior performance through training-time scaling, and test-time scaling further enhances their capabilities by conducting effective reasoning during inference. However, as the scale of reasoning increases, existing test-time scaling methods suffer from accumulated historical information, which not only wastes computational resources but also interferes with effective reasoning. To address this issue, we observe that complex reasoning progress is often achieved by solving a sequence of independent subquestions, each being self-contained and verifiable. These subquestions are essentially atomic questions, relying primarily on their current state rather than accumulated history, similar to the memoryless transitions in a Markov process. Based on this observation, we propose Atom of Thoughts (AoT), where each state transition in the reasoning process consists of decomposing the current question into a dependency-based directed acyclic graph and contracting its subquestions, forming a new atomic question state. This iterative decomposition-contraction process continues until reaching directly solvable atomic questions, naturally realizing Markov transitions between question states. Furthermore, these atomic questions can be seamlessly integrated into existing test-time scaling methods, enabling AoT to serve as a plug-in enhancement for improving reasoning capabilities. Experiments across six benchmarks demonstrate the effectiveness of AoT both as a standalone framework and a plug-in enhancement. Notably, on HotpotQA, when applied to gpt-4o-mini, AoT achieves an 80.6% F1 score, surpassing o3-mini by 3.4% and DeepSeek-R1 by 10.6%. The code will be available at https://github.com/qixucen/atom.

Existing LLM agent frameworks lack formal semantics: there is no principled way to determine whether an agent configuration is well-formed or will terminate. We present λ_A, a typed lambda calculus for agent composition that extends the simply-typed lambda calculus with oracle calls, bounded fixpoints (the ReAct loop), probabilistic choice, and mutable environments. We prove type safety, termination of bounded fixpoints, and soundness of derived lint rules, with partial Coq mechanization (1,567 lines, 43 completed proofs). As a practical application, we derive a lint tool that detects structural configuration errors directly from the operational semantics. An evaluation on 835 real-world GitHub agent configurations shows that 94.1% are structurally incomplete under λ_A, with YAML-only lint precision at 54%, rising to 96--100% under joint YAML+Python AST analysis on 175 samples. This gap quantifies, for the first time, the degree of semantic entanglement between declarative configuration and imperative code in the agent ecosystem. We further show that five mainstream paradigms (LangGraph, CrewAI, AutoGen, OpenAI SDK, Dify) embed as typed λ_A fragments, establishing λ_A as a unifying calculus for LLM agent composition.

Environment, Social, and Governance (ESG) KPIs assess an organization's performance on issues such as climate change, greenhouse gas emissions, water consumption, waste management, human rights, diversity, and policies. ESG reports convey this valuable quantitative information through tables. Unfortunately, extracting this information is difficult due to high variability in the table structure as well as content. We propose Statements, a novel domain agnostic data structure for extracting quantitative facts and related information. We propose translating tables to statements as a new supervised deep-learning universal information extraction task. We introduce SemTabNet - a dataset of over 100K annotated tables. Investigating a family of T5-based Statement Extraction Models, our best model generates statements which are 82% similar to the ground-truth (compared to baseline of 21%). We demonstrate the advantages of statements by applying our model to over 2700 tables from ESG reports. The homogeneous nature of statements permits exploratory data analysis on expansive information found in large collections of ESG reports.

There has recently been considerable interest in incorporating information retrieval into large language models (LLMs). Retrieval from a dynamically expanding external corpus of text allows a model to incorporate current events and can be viewed as a form of episodic memory. Here we demonstrate that pre-processing the external corpus into semi-structured ''atomic facts'' makes retrieval more efficient. More specifically, we demonstrate that our particular form of atomic facts improves performance on various question answering tasks when the amount of retrieved text is limited. Limiting the amount of retrieval reduces the size of the context and improves inference efficiency.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

We introduce refutationally complete superposition calculi for intentional and extensional clausal lambda-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the lambda-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

Reverse-mode differentiation is used for optimization, but it introduces references, which break the purity of the underlying programs, making them notoriously harder to optimize. We present a reverse-mode differentiation on a purely functional language with array operations. It is the first one to deliver a provably efficient, purely functional, and denotationally correct reverse-mode differentiation. We show that our transformation is semantically correct and verifies the cheap gradient principle. Inspired by PROPs and compilation to categories, we introduce a novel intermediate representation that we call 'unary form'. Our reverse-mode transformation is factored as a compilation scheme through this intermediate representation. We obtain provably efficient gradients by performing general partial evaluation optimizations after our reverse-mode transformation, as opposed to manually derived ones. For simple first-order programs, the obtained output programs resemble static-single-assignment (SSA) code. We emphasize the modularity of our approach and show how our language can easily be enriched with more optimized primitives, as required for some speed-ups in practice.

This paper presents a program logic for reasoning about multithreaded Java-like programs with dynamic thread creation, thread joining and reentrant object monitors. The logic is based on concurrent separation logic. It is the first detailed adaptation of concurrent separation logic to a multithreaded Java-like language. The program logic associates a unique static access permission with each heap location, ensuring exclusive write accesses and ruling out data races. Concurrent reads are supported through fractional permissions. Permissions can be transferred between threads upon thread starting, thread joining, initial monitor entrancies and final monitor exits. In order to distinguish between initial monitor entrancies and monitor reentrancies, auxiliary variables keep track of multisets of currently held monitors. Data abstraction and behavioral subtyping are facilitated through abstract predicates, which are also used to represent monitor invariants, preconditions for thread starting and postconditions for thread joining. Value-parametrized types allow to conveniently capture common strong global invariants, like static object ownership relations. The program logic is presented for a model language with Java-like classes and interfaces, the soundness of the program logic is proven, and a number of illustrative examples are presented.

LLM-based agents have recently emerged as promising tools for solving challenging problems without the need for task-specific finetuned models that can be expensive to procure. Currently, the design and implementation of such agents is ad hoc, as the wide variety of tasks that LLM-based agents may be applied to naturally means there can be no one-size-fits-all approach to agent design. In this work we aim to alleviate the difficulty of designing and implementing new agents by proposing a minimalistic, high-level generation framework that simplifies the process of building agents. The framework we introduce allows the user to specify desired agent behaviors in Linear Temporal Logic (LTL). The declarative LTL specification is then used to construct a constrained decoder that guarantees the LLM will produce an output exhibiting the desired behavior. By designing our framework in this way, we obtain several benefits, including the ability to enforce complex agent behavior, the ability to formally validate prompt examples, and the ability to seamlessly incorporate content-focused logical constraints into generation. In particular, our declarative approach, in which the desired behavior is simply described without concern for how it should be implemented or enforced, enables rapid design, implementation and experimentation with different LLM-based agents. We demonstrate how the proposed framework can be used to implement recent LLM-based agents, and show how the guardrails our approach provides can lead to improvements in agent performance. In addition, we release our code for general use.

In this paper, we address the challenging task of multimodal mathematical reasoning by incorporating the ability of "slow thinking" into multimodal large language models (MLLMs). Our core idea is that different levels of reasoning abilities can be combined dynamically to tackle questions with different complexity. To this end, we propose a paradigm of Self-structured Chain of Thought (SCoT), which is composed of minimal semantic atomic steps. Different from existing methods that rely on structured templates or free-form paradigms, our method can not only generate cognitive CoT structures for various complex tasks but also mitigates the phenomenon of overthinking. To introduce structured reasoning capabilities into visual understanding models, we further design a novel AtomThink framework with four key modules, including (i) a data engine to generate high-quality multimodal reasoning paths; (ii) a supervised fine-tuning process with serialized inference data; (iii) a policy-guided multi-turn inference method; and (iv) an atomic capability metric to evaluate the single step utilization rate. We conduct extensive experiments to show that the proposed AtomThink significantly improves the performance of baseline MLLMs, achieving more than 10\% average accuracy gains on MathVista and MathVerse. Compared to state-of-the-art structured CoT approaches, our method not only achieves higher accuracy but also improves data utilization by 5 times and boosts inference efficiency by 85.3\%. Our code is now public available in https://github.com/Quinn777/AtomThink.

The fundamental units of internal representations in large language models (LLMs) remain undefined, limiting further understanding of their mechanisms. Neurons or features are often regarded as such units, yet neurons suffer from polysemy, while features face concerns of unreliable reconstruction and instability. To address this issue, we propose the Atoms Theory, which defines such units as atoms. We introduce the atomic inner product (AIP) to correct representation shifting, formally define atoms, and prove the conditions that atoms satisfy the Restricted Isometry Property (RIP), ensuring stable sparse representations over atom set and linking to compressed sensing. Under stronger conditions, we further establish the uniqueness and exact ell_1 recoverability of the sparse representations, and provide guarantees that single-layer sparse autoencoders (SAEs) with threshold activations can reliably identify the atoms. To validate the Atoms Theory, we train threshold-activated SAEs on Gemma2-2B, Gemma2-9B, and Llama3.1-8B, achieving 99.9% sparse reconstruction across layers on average, and more than 99.8% of atoms satisfy the uniqueness condition, compared to 0.5% for neurons and 68.2% for features, showing that atoms more faithfully capture intrinsic representations of LLMs. Scaling experiments further reveal the link between SAEs size and recovery capacity. Overall, this work systematically introduces and validates Atoms Theory of LLMs, providing a theoretical framework for understanding internal representations and a foundation for mechanistic interpretability. Code available at https://github.com/ChenhuiHu/towards_atoms.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

Current LLM coding agents are predominantly trained on composite benchmarks (e.g., bug fixing), which often leads to task-specific overfitting and limited generalization. To address this, we propose a novel scaling paradigm that shifts the focus from task-level optimization to atomic skill mastery. We first formalize five fundamental atomic skills, code localization, code editing, unit-test generation, issue reproduction, and code review, that serve as the basis vectors for complex software engineering tasks. Compared with composite coding tasks, these atomic skills are more generalizable and composable. Then, we scale coding agents by performing joint RL over atomic skills. In this manner, atomic skills are consistently improved without negative interference or trade-offs between them. Notably, we observe that improvements in these atomic skills generalize well to other unseen composite coding tasks, such as bug-fixing, code refactoring, machine learning engineering, and code security. The observation motivates a new scaling paradigm for coding agents by training with atomic skills. Extensive experiments demonstrate the effectiveness of our proposed paradigm. Notably, our joint RL improves average performance by 18.7% on 5 atomic skills and 5 composite tasks.

In this paper, we address the challenging task of multimodal mathematical reasoning by incorporating the ability of ``slow thinking" into multimodal large language models (MLLMs). Contrary to existing methods that rely on direct or fast thinking, our key idea is to construct long chains of thought (CoT) consisting of atomic actions in a step-by-step manner, guiding MLLMs to perform complex reasoning. To this end, we design a novel AtomThink framework composed of three key modules: (i) a CoT annotation engine that automatically generates high-quality CoT annotations to address the lack of high-quality visual mathematical data; (ii) an atomic step fine-tuning strategy that jointly optimizes an MLLM and a policy reward model (PRM) for step-wise reasoning; and (iii) four different search strategies that can be applied with the PRM to complete reasoning. Additionally, we propose AtomMATH, a large-scale multimodal dataset of long CoTs, and an atomic capability evaluation metric for mathematical tasks. Extensive experimental results show that the proposed AtomThink significantly improves the performance of baseline MLLMs, achieving approximately 50\% relative accuracy gains on MathVista and 120\% on MathVerse. To support the advancement of multimodal slow-thinking models, we will make our code and dataset publicly available on https://github.com/Quinn777/AtomThink.

The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a CTL formula, for a given (possibly infinite-state) program. We propose a method based on encoding the problem as a set of Horn constraints. The method takes a program, modeled as a transition system, and a property given by a CTL formula as input. It first generates a set of forall-exists quantified Horn constraints and well-foundedness constraints by exploiting the syntactic structure of the CTL formula. Then, the generated set of constraints are solved by applying an off-the-shelf Horn constraints solving engine. The program is said to satisfy the property if and only if the generated set of constraints has a solution. We demonstrate the practical promises of the method by applying it on a set of challenging examples. Although our method is based on a generic Horn constraint solving engine, it is able to outperform state-of-art methods specialised for CTL verification.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Signal Temporal Logic (STL) is a powerful formal language for specifying real-time specifications of Cyber-Physical Systems (CPS). Transforming specifications written in natural language into STL formulas automatically has attracted increasing attention. Existing rule-based methods depend heavily on rigid pattern matching and domain-specific knowledge, limiting their generalizability and scalability. Recently, Supervised Fine-Tuning (SFT) of large language models (LLMs) has been successfully applied to transform natural language into STL. However, the lack of fine-grained supervision on atomic proposition correctness, semantic fidelity, and formula readability often leads SFT-based methods to produce formulas misaligned with the intended meaning. To address these issues, we propose RESTL, a reinforcement learning (RL)-based framework for the transformation from natural language to STL. RESTL introduces multiple independently trained reward models that provide fine-grained, multi-faceted feedback from four perspectives, i.e., atomic proposition consistency, semantic alignment, formula succinctness, and symbol matching. These reward models are trained with a curriculum learning strategy to improve their feedback accuracy, and their outputs are aggregated into a unified signal that guides the optimization of the STL generator via Proximal Policy Optimization (PPO). Experimental results demonstrate that RESTL significantly outperforms state-of-the-art methods in both automatic metrics and human evaluations.

This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its standard call-by-name stack machine in two directions. One, "locations", introduces multiple stacks, which enable effect operators to be encoded into the abstraction and application constructs. The second, "sequencing", introduces the imperative notions of "skip" and "sequence", similar to kappa-calculus and concatenative programming languages. The key observation of the RMC is that the first-order fragment of the FMC exhibits a latent duality which, given a simple decomposition of the relevant constructors, can be concretely expressed as an involution on syntax. Semantically, this gives rise to a sound and complete calculus for string diagrams of Frobenius monoids. We consider unification as the corresponding symmetric generalization of beta-reduction. By further including standard operators of Kleene algebra, the RMC embeds a range of computational models: the kappa-calculus, logic programming, automata, Interaction Nets, and Petri Nets, among others. These embeddings preserve operational semantics, which for the RMC is again given by a generalization of the standard stack machine for the lambda-calculus. The equational theory of the RMC (which supports reasoning about its operational semantics) is conservative over both the first-order lambda-calculus and Kleene algebra, and can be oriented to give a confluent reduction relation.

We present egglog, a fixpoint reasoning system that unifies Datalog and equality saturation (EqSat). Like Datalog, it supports efficient incremental execution, cooperating analyses, and lattice-based reasoning. Like EqSat, it supports term rewriting, efficient congruence closure, and extraction of optimized terms. We identify two recent applications--a unification-based pointer analysis in Datalog and an EqSat-based floating-point term rewriter--that have been hampered by features missing from Datalog but found in EqSat or vice-versa. We evaluate egglog by reimplementing those projects in egglog. The resulting systems in egglog are faster, simpler, and fix bugs found in the original systems.

Commonsense reasoning often involves evaluating multiple plausible interpretations rather than selecting a single atomic answer, yet most benchmarks rely on single-label evaluation, obscuring whether statements are jointly plausible, mutually exclusive, or jointly implausible. We introduce LOGICAL-COMMONSENSEQA, a benchmark that re-frames commonsense reasoning as logical composition over pairs of atomic statements using plausibility-level operators (AND, OR, NEITHER/NOR). Evaluating instruction-tuned, reasoning-specialized, and fine-tuned models under zero-shot, few-shot, and chain-of-thought prompting, we find that while models perform reasonably on conjunctive and moderately on disjunctive reasoning, performance degrades sharply on negation-based questions. LOGICAL-COMMONSENSEQA exposes fundamental reasoning limitations and provides a controlled framework for advancing compositional commonsense reasoning.

Scientific texts often convey authority due to their technical language and complex data. However, this complexity can sometimes lead to the spread of misinformation. Non-experts are particularly susceptible to misleading claims based on scientific tables due to their high information density and perceived credibility. Existing table claim verification models, including state-of-the-art large language models (LLMs), often struggle with precise fine-grained reasoning, resulting in errors and a lack of precision in verifying scientific claims. Inspired by Cognitive Load Theory, we propose that enhancing a model's ability to interpret table-based claims involves reducing cognitive load by developing modular, reusable reasoning components (i.e., atomic skills). We introduce a skill-chaining schema that dynamically composes these skills to facilitate more accurate and generalizable reasoning with a reduced cognitive load. To evaluate this, we create SciAtomicBench, a cross-domain benchmark with fine-grained reasoning annotations. With only 350 fine-tuning examples, our model trained by atomic reasoning outperforms GPT-4o's chain-of-thought method, achieving state-of-the-art results with far less training data.

We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates candidate implications, applies normalization and type filters, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. Generated proofs export to navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe prospective integration with probabilistic models (e.g., Large Language Models (LLMs)) for autoformalization and conjecture seeding. The Python and MPL code to reproduce the Peano experiments, along with the full HTML proof graphs, are available in the project's GitHub repository at https://github.com/Generative-Logic/GL/tree/35a111ea9ba53afe051703d6050be0c3923e9724 and are permanently archived at https://doi.org/10.5281/zenodo.16408441. We invite community feedback and collaboration.

Language environments such as web browsers, code terminals, and interactive simulations emit raw text rather than states, and provide none of the runtime structure that MDP analysis requires. No explicit state space, no observation-to-state mapping, no certified transitions, and no termination criterion. We introduce the State-Centric Decision Process (SDP), a runtime framework that constructs these missing inputs by having the agent build them, predicate by predicate, as it acts. At each step the agent commits to a natural-language predicate describing how the world should look, takes an action to make it true, and checks the observation against it. Predicates that pass become certified states, and the resulting trajectory carries the four objects language environments do not provide, namely a task-induced state space, an observation-to-state mapping, certified transitions, and a termination criterion. We evaluate SDP on five benchmarks spanning planning, scientific exploration, web reasoning, and multi-hop question answering. SDP achieves the best training-free results on all five, with the advantage widening as the horizon grows. The certified trajectories additionally support analyses unavailable to reactive agents, including per-predicate credit assignment, failure localization, partial-progress measurement, and modular operator replacement.

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Throughout, we show how the analysis extends to AD methods for computing higher order derivatives using a Taylor approximation.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

The sequential process of conceptualization and instantiation is essential to generalizable commonsense reasoning as it allows the application of existing knowledge to unfamiliar scenarios. However, existing works tend to undervalue the step of instantiation and heavily rely on pre-built concept taxonomies and human annotations to collect both types of knowledge, resulting in a lack of instantiated knowledge to complete reasoning, high cost, and limited scalability. To tackle these challenges, we introduce CANDLE, a distillation framework that iteratively performs contextualized conceptualization and instantiation over commonsense knowledge bases by instructing large language models to generate both types of knowledge with critic filtering. By applying CANDLE to ATOMIC, we construct a comprehensive knowledge base comprising six million conceptualizations and instantiated commonsense knowledge triples. Both types of knowledge are firmly rooted in the original ATOMIC dataset, and intrinsic evaluations demonstrate their exceptional quality and diversity. Empirical results indicate that distilling CANDLE on student models provides benefits across four downstream tasks. Our code, data, and models are publicly available at https://github.com/HKUST-KnowComp/CANDLE.

Recently, neural techniques have been used to generate source code automatically. While promising for declarative languages, these approaches achieve much poorer performance on datasets for imperative languages. Since a declarative language is typically embedded in an imperative language (i.e., the turducken-style programming) in real-world software development, the promising results on declarative languages can hardly lead to significant reduction of manual software development efforts. In this paper, we define a new code generation task: given a natural language comment, this task aims to generate a program in a base imperative language with an embedded declarative language. To our knowledge, this is the first turducken-style code generation task. For this task, we present Lyra: a dataset in Python with embedded SQL. This dataset contains 2,000 carefully annotated database manipulation programs from real-world projects. Each program is paired with both a Chinese comment and an English comment. In our experiment, we adopted Transformer, BERT-style, and GPT-style models as baselines. In the best setting, the generation performance of GPT-style models is better than others, where the AST exact matching accuracy is 24% and 25.5% when using Chinese and English comments, respectively. Therefore, we believe that Lyra provides a new challenge for code generation. Yet, overcoming this challenge may significantly boost the applicability of code generation techniques for real-world software development.

Evaluation is the baton for the development of large language models. Current evaluations typically employ a single-item assessment paradigm for each atomic test objective, which struggles to discern whether a model genuinely possesses the required capabilities or merely memorizes/guesses the answers to specific questions. To this end, we propose a novel evaluation framework referred to as StructEval. Starting from an atomic test objective, StructEval deepens and broadens the evaluation by conducting a structured assessment across multiple cognitive levels and critical concepts, and therefore offers a comprehensive, robust and consistent evaluation for LLMs. Experiments on three widely-used benchmarks demonstrate that StructEval serves as a reliable tool for resisting the risk of data contamination and reducing the interference of potential biases, thereby providing more reliable and consistent conclusions regarding model capabilities. Our framework also sheds light on the design of future principled and trustworthy LLM evaluation protocols.

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.

Large Language Models (LLMs) have exhibited significant potential in performing diverse tasks, including the ability to call functions or use external tools to enhance their performance. While current research on function calling by LLMs primarily focuses on single-turn interactions, this paper addresses the overlooked necessity for LLMs to engage in multi-turn function calling--critical for handling compositional, real-world queries that require planning with functions but not only use functions. To facilitate this, we introduce an approach, BUTTON, which generates synthetic compositional instruction tuning data via bottom-up instruction construction and top-down trajectory generation. In the bottom-up phase, we generate simple atomic tasks based on real-world scenarios and build compositional tasks using heuristic strategies based on atomic tasks. Corresponding functions are then developed for these compositional tasks. The top-down phase features a multi-agent environment where interactions among simulated humans, assistants, and tools are utilized to gather multi-turn function calling trajectories. This approach ensures task compositionality and allows for effective function and trajectory generation by examining atomic tasks within compositional tasks. We produce a dataset BUTTONInstruct comprising 8k data points and demonstrate its effectiveness through extensive experiments across various LLMs.

Large language models (LLMs) exhibit remarkable problem-solving abilities, but struggle with complex tasks due to static internal knowledge. Retrieval-Augmented Generation (RAG) enhances access to external information, yet remains limited in multi-hop reasoning and strategic search due to rigid workflows. Recent advancements in agentic deep research empower LLMs to autonomously reason, search, and synthesize information. However, current approaches relying on outcome-based reinforcement learning (RL) face critical issues such as conflicting gradients and reward sparsity, limiting performance gains and training efficiency. To address these, we first propose Atomic Thought, a novel LLM thinking paradigm that decomposes reasoning into fine-grained functional units. These units are supervised by Reasoning Reward Models (RRMs), which provide Atomic Thought Rewards (ATR) for fine-grained guidance. Building on this, we propose Atom-Searcher, a novel RL framework for agentic deep research that integrates Atomic Thought and ATR. Atom-Searcher uses a curriculum-inspired reward schedule, prioritizing process-level ATR early and transitioning to outcome rewards, accelerating convergence on effective reasoning paths. Experiments on seven benchmarks show consistent improvements over the state-of-the-art. Key advantages include: (1) Atom-Searcher scales computation at test-time. (2) Atomic Thought provides supervision anchors for RRMs, bridging deep research tasks and RRMs. (3) Atom-Searcher exhibits more interpretable, human-like reasoning patterns.

In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal') relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first- order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them.

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our representation satisfies all structural, geometric, efficiency, and generalizability constraints. Afterward, we provide a general algorithm to encode any atomistic system. Finally, we report performance comparable to state-of-the-art methods on numerous tasks. We open-source all code and datasets. The code and data are available at https://github.com/rahulkhorana/PolyatomicComplexes.

JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON Schema documents comprises practically relevant problems, including schema satisfiability, inclusion, and equivalence. These three problems can be reduced to witness generation: given a schema, generate an element of the schema, if it exists, and report failure otherwise. Schema satisfiability, inclusion, and equivalence have been shown to be decidable, by reduction to reachability in alternating tree automata. However, no witness generation algorithm has yet been formally described. We contribute a first, direct algorithm for JSON Schema witness generation. We study its effectiveness and efficiency, in experiments over several schema collections, including thousands of real-world schemas. Our focus is on the completeness of the language, where we only exclude the uniqueItems operator, and on the ability of the algorithm to run in a reasonable time on a large set of real-world examples, despite the exponential complexity of the underlying problem.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

This article establishes a complete approximate axiomatization for the real-closed field R expanded with all differentially-defined functions, including special functions such as sin(x), cos(x), e^x, dots. Every true sentence is provable up to some numerical approximation, and the truth of such approximations converge under mild conditions. Such an axiomatization is a fragment of the axiomatization for differential dynamic logic, and is therefore a finite extension of the axiomatization of real-closed fields. Furthermore, the numerical approximations approximate formulas containing special function symbols by FOL_{R} formulas, improving upon earlier decidability results only concerning closed sentences.

With the goal of benchmarking generative systems beyond expert software development ability, we introduce Commit0, a benchmark that challenges AI agents to write libraries from scratch. Agents are provided with a specification document outlining the library's API as well as a suite of interactive unit tests, with the goal of producing an implementation of this API accordingly. The implementation is validated through running these unit tests. As a benchmark, Commit0 is designed to move beyond static one-shot code generation towards agents that must process long-form natural language specifications, adapt to multi-stage feedback, and generate code with complex dependencies. Commit0 also offers an interactive environment where models receive static analysis and execution feedback on the code they generate. Our experiments demonstrate that while current agents can pass some unit tests, none can yet fully reproduce full libraries. Results also show that interactive feedback is quite useful for models to generate code that passes more unit tests, validating the benchmarks that facilitate its use.

Memory is a fundamental component of AI systems, underpinning large language models (LLMs) based agents. While prior surveys have focused on memory applications with LLMs, they often overlook the atomic operations that underlie memory dynamics. In this survey, we first categorize memory representations into parametric, contextual structured, and contextual unstructured and then introduce six fundamental memory operations: Consolidation, Updating, Indexing, Forgetting, Retrieval, and Compression. We systematically map these operations to the most relevant research topics across long-term, long-context, parametric modification, and multi-source memory. By reframing memory systems through the lens of atomic operations and representation types, this survey provides a structured and dynamic perspective on research, benchmark datasets, and tools related to memory in AI, clarifying the functional interplay in LLMs based agents while outlining promising directions for future researchThe paper list, datasets, methods and tools are available at \href{https://github.com/Elvin-Yiming-Du/Survey_Memory_in_AI{https://github.com/Elvin-Yiming-Du/Survey\_Memory\_in\_AI}.}.

As large language models (LLMs) excel at code reasoning, a natural question arises: can an LLM execute programs (i.e., act as an interpreter) purely based on a programming language's formal semantics? If so, it will enable rapid prototyping of new programming languages and language features. We study this question using the imperative language IMP (a subset of C), formalized via small-step operational semantics (SOS) and rewriting-based operational semantics (K-semantics). We introduce three evaluation sets-Human-Written, LLM-Translated, and Fuzzer- Generated-whose difficulty is controlled by code-complexity metrics spanning the size, control-flow, and data-flow axes. Given a program and its semantics formalized with SOS/K-semantics, models are evaluated on three tasks ranging from coarse to fine: (1) final-state prediction, (2) semantic rule prediction, and (3) execution trace prediction. To distinguish pretraining memorization from semantic competence, we define two nonstandard semantics obtained through systematic mutations of the standard rules. Across strong code/reasoning LLMs, performance drops under nonstandard semantics despite high performance under the standard one. We further find that (i) there are patterns to different model failures, (ii) most reasoning models perform exceptionally well on coarse grained tasks involving reasoning about highly complex programs often containing nested loop depths beyond five, and surprisingly, (iii) providing formal semantics helps on simple programs but often hurts on more complex ones. Overall, the results show a promise that LLMs could serve as programming language interpreters, but points to the lack of their robust semantics understanding. We release the benchmark and the supporting code at https://github.com/EngineeringSoftware/PLSemanticsBench.

We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's trace encoding which is universally defined for any function type, regardless of being impredicative. Direct and concrete interpretations of simultaneous induction and mutually recursive functions are also provided by extending Dybjer's interpretations on the basis of Aczel's rule sets. Our model can be regarded as a higher-order generalization of the truth-table methods. We provide a relatively simple consistency proof of type theory, which can be used as the basis for a theorem prover.

The mechanism by which RL contributes to reasoning capabilities-whether it incentivizes the synthesis of new skills or merely amplifies existing behaviors-remains a subject of intense debate. In this work, we investigate this question through the lens of Complementary Reasoning, a complex task that requires integrating internal parametric knowledge with external contextual information. Using a controlled synthetic dataset of human biographies, we strictly decouple this ability into two atomic skills: Parametric Reasoning (relying on internal knowledge) and Contextual Reasoning (depending on external information). To rigorously assess capability boundaries, we evaluate generalization across three distinct levels of difficulty: I.I.D., Composition, and Zero-shot settings. We find that while SFT is sufficient for in-distribution performance, it struggles with O.O.D. generalization, particularly in Zero-shot settings where relational combinations are novel. Crucially, we identify the SFT Generalization Paradox: Models supervised solely on the composite task achieve near-perfect in-distribution accuracy but collapse on out-of-distribution generalization, indicating their reliance on rote memorization of path shortcuts. In contrast, we find that RL acts as a reasoning synthesizer rather than a probability amplifier. However, we uncover a strict atomic prerequisite: RL can only synthesize these complex strategies if the base model has first mastered the independent atomic skills (Parametric and Contextual) via SFT. These findings challenge the view of RL as a mere amplifier, suggesting that given sufficient atomic foundations, RL can actively synthesize complex reasoning strategies from learned primitives without explicit supervision on such complex strategies. This indicates that decoupled atomic training followed by RL offers a scalable path to generalization for complex reasoning tasks.

Large language models (LLMs) are leading significant progress in code generation. Beyond one-pass code generation, recent works further integrate unit tests and program verifiers into LLMs to iteratively refine the generated programs. However, these works consider the generated programs as an indivisible entity, which falls short for LLMs in debugging the programs, especially when the programs contain complex logic flows and data operations. In contrast, when human developers debug programs, they typically set breakpoints and selectively examine runtime execution information. The execution flow and the intermediate variables play a crucial role in the debugging process, yet they are underutilized in the existing literature on code generation. In this study, we introduce Large Language Model Debugger (LDB), a novel debugging framework that enables LLMs to refine their generated programs with the runtime execution information. Specifically, LDB segments the programs into basic blocks and tracks the values of intermediate variables after each block throughout the runtime execution. This allows LLMs to concentrate on simpler code units within the overall execution flow, verify their correctness against the task description block by block, and efficiently pinpoint any potential errors. Experiments demonstrate that LDB consistently enhances the baseline performance by up to 9.8% across the HumanEval, MBPP, and TransCoder benchmarks, archiving new state-of-the-art performance in code debugging for various LLM selections.

Current research on the Decompose-Then-Verify paradigm for evaluating the factuality of long-form text typically treats decomposition and verification in isolation, overlooking their interactions and potential misalignment. We find that existing decomposition policies, typically hand-crafted demonstrations, do not align well with downstream verifiers in terms of atomicity -- a novel metric quantifying information density -- leading to suboptimal verification results. We formulate finding the optimal decomposition policy for optimal verification as a bilevel optimization problem. To approximate a solution for this strongly NP-hard problem, we propose dynamic decomposition, a reinforcement learning framework that leverages verifier feedback to learn a policy for dynamically decomposing claims to verifier-preferred atomicity. Experimental results show that dynamic decomposition outperforms existing decomposition policies, improving verification confidence by 0.07 and accuracy by 0.12 (on a 0-1 scale) on average across varying verifiers, datasets, and atomcities of input claims.

Fact-checking long-form text is challenging, and it is therefore common practice to break it down into multiple atomic claims. The typical approach to fact-checking these atomic claims involves retrieving a fixed number of pieces of evidence, followed by a verification step. However, this method is usually not cost-effective, as it underutilizes the verification model's internal knowledge of the claim and fails to replicate the iterative reasoning process in human search strategies. To address these limitations, we propose FIRE, a novel agent-based framework that integrates evidence retrieval and claim verification in an iterative manner. Specifically, FIRE employs a unified mechanism to decide whether to provide a final answer or generate a subsequent search query, based on its confidence in the current judgment. We compare FIRE with other strong fact-checking frameworks and find that it achieves slightly better performance while reducing large language model (LLM) costs by an average of 7.6 times and search costs by 16.5 times. These results indicate that FIRE holds promise for application in large-scale fact-checking operations. Our code is available at https://github.com/mbzuai-nlp/fire.git.

This paper presents a case study on applying two model checkers, SPIN and DIVINE, to verify key properties of a C++ software framework, known as ADAPRO, originally developed at CERN. SPIN was used for verifying properties on the design level. DIVINE was used for verifying simple test applications that interacted with the implementation. Both model checkers were found to have their own respective sets of pros and cons, but the overall experience was positive. Because both model checkers were used in a complementary manner, they provided valuable new insights into the framework, which would arguably have been hard to gain by traditional testing and analysis tools only. Translating the C++ source code into the modeling language of the SPIN model checker helped to find flaws in the original design. With DIVINE, defects were found in parts of the code base that had already been subject to hundreds of hours of unit tests, integration tests, and acceptance tests. Most importantly, model checking was found to be easy to integrate into the workflow of the software project and bring added value, not only as verification, but also validation methodology. Therefore, using model checking for developing library-level code seems realistic and worth the effort.

Large language models (LLMs) have shown impressive ability for open-domain NLP tasks. However, LLMs are sometimes too footloose for natural language understanding (NLU) tasks which always have restricted output and input format. Their performances on NLU tasks are highly related to prompts or demonstrations and are shown to be poor at performing several representative NLU tasks, such as event extraction and entity typing. To this end, we present SeqGPT, a bilingual (i.e., English and Chinese) open-source autoregressive model specially enhanced for open-domain natural language understanding. We express all NLU tasks with two atomic tasks, which define fixed instructions to restrict the input and output format but still ``open'' for arbitrarily varied label sets. The model is first instruction-tuned with extremely fine-grained labeled data synthesized by ChatGPT and then further fine-tuned by 233 different atomic tasks from 152 datasets across various domains. The experimental results show that SeqGPT has decent classification and extraction ability, and is capable of performing language understanding tasks on unseen domains. We also conduct empirical studies on the scaling of data and model size as well as on the transfer across tasks. Our model is accessible at https://github.com/Alibaba-NLP/SeqGPT.

Large language models exhibit a systematic tendency toward early semantic commitment: given ambiguous input, they collapse multiple valid interpretations into a single response before sufficient context is available. This premature collapse discards information that may prove essential as dialogue evolves. We present a formal framework for text-to-state mapping (phi: T -> S) that transforms natural language into a non-collapsing state space where multiple interpretations coexist. The mapping decomposes into three stages: conflict detection, interpretation extraction, and state construction. We instantiate phi with a hybrid extraction pipeline that combines rule-based segmentation for explicit conflict markers (adversative conjunctions, hedging expressions) with LLM-based enumeration of implicit ambiguity (epistemic, lexical, structural). On a test set of 68 ambiguous sentences, the resulting states preserve interpretive multiplicity: using hybrid extraction, we obtain mean state entropy H = 1.087 bits across ambiguity categories, compared to H = 0 for collapse-based baselines that commit to a single interpretation. We additionally instantiate the rule-based conflict detector for Japanese markers (kedo, kamoshirenai, etc.) to illustrate cross-lingual portability of the conflict detection stage. This framework extends Non-Resolution Reasoning (NRR) by providing the missing algorithmic bridge between text and the NRR state space, enabling architectural collapse deferment in LLM inference. Design principles for state-to-state transformations are detailed in the Appendix, with empirical validation on 580 test cases (180 single states, 200 contradictory pairs, 200 temporal pairs), demonstrating 0% collapse for principle-satisfying operators versus up to 17.8% for violating operators.

What kind of programming language would be most appropriate to serve the needs of integrative, multi-paradigm, multi-software-system approaches to AGI? This question is broached via exploring the more particular question of how to create a more scalable and usable version of the "Atomese" programming language that forms a key component of the OpenCog AGI design (an "Atomese 2.0") . It is tentatively proposed that the core of Atomese 2.0 should be a very flexible framework of rewriting rules for rewriting a metagraph (where the rules themselves are represented within the same metagraph, and some of the intermediate data created and used during the rule-interpretation process may be represented in the same metagraph). This framework should support concurrent rewriting of the metagraph according to rules that are labeled with various sorts of uncertainty-quantifications, and that are labeled with various sorts of types associated with various type systems. A gradual typing approach should be used to enable mixture of rules and other metagraph nodes/links associated with various type systems, and untyped metagraph nodes/links not associated with any type system. This must be done in a way that allows reasonable efficiency and scalability, including in concurrent and distributed processing contexts, in the case where a large percentage of of processing time is occupied with evaluating static pattern-matching queries on specific subgraphs of a large metagraph (including a rich variety of queries such as matches against nodes representing variables, and matches against whole subgraphs, etc.).

Recent advances in Large Language Models (LLMs) have enabled the development of increasingly complex agentic and multi-agent systems capable of planning, tool use and task decomposition. However, empirical evidence shows that many of these systems suffer from fundamental reliability issues, including hallucinated actions, unexecutable plans and brittle coordination. Crucially, these failures do not stem from limitations of the underlying models themselves, but from the absence of explicit architectural structure linking goals, capabilities and execution. This paper presents a declarative, model-independent architectural layer for grounded agentic workflows that addresses this gap. The proposed layer, referred to as DALIA (Declarative Agentic Layer for Intelligent Agents), formalises executable capabilities, exposes tasks through a declarative discovery protocol, maintains a federated directory of agents and their execution resources, and constructs deterministic task graphs grounded exclusively in declared operations. By enforcing a clear separation between discovery, planning and execution, the architecture constrains agent behaviour to a verifiable operational space, reducing reliance on speculative reasoning and free-form coordination. We present the architecture and design principles of the proposed layer and illustrate its operation through a representative task-oriented scenario, demonstrating how declarative grounding enables reproducible and verifiable agentic workflows across heterogeneous environments.

Large language model (LLM)-based coding agents achieve impressive results on controlled benchmarks yet routinely produce pull requests that real maintainers reject. The root cause is not functional incorrectness but a lack of organicity: generated code ignores project-specific conventions, duplicates functionality already provided by internal APIs, and violates implicit architectural constraints accumulated over years of development. Simply exposing an agent to the latest repository snapshot is not enough: the snapshot reveals the final state of the codebase, but not the repository-specific change patterns by which that state was reached. We introduce Learning to Commit, a framework that closes this gap through Online Repository Memory. Given a repository with a strict chronological split, the agent performs supervised contrastive reflection on earlier commits: it blindly attempts to resolve each historical issue, compares its prediction against the oracle diff, and distils the gap into a continuously growing set of skills-reusable patterns capturing coding style, internal API usage, and architectural invariants. When a new PR description arrives, the agent conditions its generation on these accumulated skills, producing changes grounded in the project's own evolution rather than generic pretraining priors. Evaluation is conducted on genuinely future, merged pull requests that could not have been seen during the skill-building phase, and spans multiple dimensions including functional correctness, code-style consistency, internal API reuse rate, and modified-region plausibility. Experiments on an expert-maintained repository with rich commit history show that Online Repository Memory effectively improves organicity scores on held-out future tasks.

We present Turn, a compiled, actor-based programming language -- statically typed for schema inference, dynamically typed at the value level -- for agentic software: programs that reason and act autonomously by delegating inference to large language models (LLMs). Existing approaches augment general-purpose languages with frameworks, encoding critical invariants (bounded context, typed inference output, credential isolation, durable state) as application-level conventions rather than language guarantees. Turn introduces five language-level constructs that address this gap. Cognitive Type Safety makes LLM inference a typed primitive: the compiler generates a JSON Schema from a struct definition and the VM validates model output before binding. The confidence operator enables deterministic control flow gated on model certainty. Turn's actor-based process model, derived from Erlang, gives each agent an isolated context window, persistent memory, and mailbox. A capability-based identity system returns opaque, unforgeable handles from the VM host, ensuring raw credentials never enter agent memory. Finally, compile-time schema absorption (use schema::<protocol>) synthesizes typed API bindings from external specifications at compile time; the openapi adapter is shipped with graphql, fhir, and mcp in active development. We describe the language design, type rules, schema semantics, and a Rust-based bytecode VM, and evaluate Turn against representative agentic workloads. Turn is open source at https://github.com/ekizito96/Turn.

Memory safety violations in low-level code, written in languages like C, continues to remain one of the major sources of software vulnerabilities. One method of removing such violations by construction is to port C code to a safe C dialect. Such dialects rely on programmer-supplied annotations to guarantee safety with minimal runtime overhead. This porting, however, is a manual process that imposes significant burden on the programmer and, hence, there has been limited adoption of this technique. The task of porting not only requires inferring annotations, but may also need refactoring/rewriting of the code to make it amenable to such annotations. In this paper, we use Large Language Models (LLMs) towards addressing both these concerns. We show how to harness LLM capabilities to do complex code reasoning as well as rewriting of large codebases. We also present a novel framework for whole-program transformations that leverages lightweight static analysis to break the transformation into smaller steps that can be carried out effectively by an LLM. We implement our ideas in a tool called MSA that targets the CheckedC dialect. We evaluate MSA on several micro-benchmarks, as well as real-world code ranging up to 20K lines of code. We showcase superior performance compared to a vanilla LLM baseline, as well as demonstrate improvement over a state-of-the-art symbolic (non-LLM) technique.

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

Recent years have brought about a renewed interest in commonsense representation and reasoning in the field of natural language understanding. The development of new commonsense knowledge graphs (CSKG) has been central to these advances as their diverse facts can be used and referenced by machine learning models for tackling new and challenging tasks. At the same time, there remain questions about the quality and coverage of these resources due to the massive scale required to comprehensively encompass general commonsense knowledge. In this work, we posit that manually constructed CSKGs will never achieve the coverage necessary to be applicable in all situations encountered by NLP agents. Therefore, we propose a new evaluation framework for testing the utility of KGs based on how effectively implicit knowledge representations can be learned from them. With this new goal, we propose ATOMIC 2020, a new CSKG of general-purpose commonsense knowledge containing knowledge that is not readily available in pretrained language models. We evaluate its properties in comparison with other leading CSKGs, performing the first large-scale pairwise study of commonsense knowledge resources. Next, we show that ATOMIC 2020 is better suited for training knowledge models that can generate accurate, representative knowledge for new, unseen entities and events. Finally, through human evaluation, we show that the few-shot performance of GPT-3 (175B parameters), while impressive, remains ~12 absolute points lower than a BART-based knowledge model trained on ATOMIC 2020 despite using over 430x fewer parameters.

We propose a formal reconstruction of quantum mechanics grounded not in external mathematical abstractions, but in the structured dynamics of subjective experience. The Qualia Abstraction Language (QAL) models physical systems as evolving streams of introspective units, structured sequences of modality, shape, and functional effect, rather than as state vectors in Hilbert space. This approach reimagines core quantum concepts: superposition becomes a form of structured ambiguity; collapse is reframed as an introspective contraction; and entanglement is modeled as semantic resonance across streams of qualia. Drawing on insights from nominalist philosophy and oversight theoretic limits in AI, we argue that the observer paradox in quantum mechanics reflects not an ontological lacuna, but a linguistic one: the absence of a formal vocabulary for modeling first person structure. QAL introduces such a vocabulary, providing a morphodynamic framework that embeds the observer within the system and replaces abstract projection with endogenous transformation. We analyze the alignment of QAL with endophysical approaches, contrast it with standard interpretations of quantum theory, and explore its implications for a post Platonist, introspectively grounded physics.

Grounded multi-video question answering over real-world news events requires systems to surface query-relevant evidence across heterogeneous video archives while attributing every claim to its supporting source. We introduce CRAFT (Critic-Refined Adaptive Key-Frame Targeting), a query-conditioned pipeline that combines dynamic keyframe selection, per-video ASR with multilingual fallback, and a hybrid critic loop to iteratively verify and repair claims before consolidation. The pipeline integrates UNLI temporal entailment, DeBERTa-v3 cross-claim screening, and a Llama-3.2-3B adjudicator, with a final citation-merging stage that emits each fact once with all supporting source identifiers. On MAGMaR 2026, CRAFT achieves the best overall average (0.739), reference recall (0.810), and citation F1 (0.635). We further evaluate on a MAGMaR-style conversion of WikiVideo with 52 non-overlapping event queries, where CRAFT also performs strongly (0.823 Avg), showing that its claim-centric evidence aggregation generalizes beyond MAGMaR. Ablations show that atomic claims, ASR, and the critic loop drive the main gains over the vanilla query-conditioned baseline. Code and implementation details are publicly available at https://github.com/bhosalems/CRAFT.

This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open data, and benchmarks that are complete and error-free will accelerate progress in this field. We identify practices that create barriers to contributing to this field and suggest ways to remove them. We also discuss some of the practices that might produce misleading evaluative information. We aim to create discussions that bring together people from various groups contributing to automated theorem proving, autoformalization, and informal reasoning.

Data refinement involves executing multi-step recipes over evolving text states, where both composition and execution order of processing operators determine the outcome. While existing benchmarks either isolate text editing or entangle it with code and tool execution, it remains unclear whether LLMs can directly and faithfully execute these compositional, order-sensitive data refinement recipes. To fill this gap, we introduce CDR-Bench, a comprehensive benchmark featuring 3,462 high-quality tasks spanning four real-world data refinement domains and 29 distinct operators. Our benchmark evaluates models across atomic, order-agnostic, and order-sensitive settings, leveraging deterministic reference outputs to enable exact evaluation. Experiments on 10+ state-of-the-art LLMs reveal consistent failure patterns: performance degrades sharply in compositional settings, and order-sensitive recipe success collapses. These findings underline that current LLMs lack the procedural faithfulness required for reliable compositional data refinement.

Context: Exhaustive fuzzing of modern JavaScript engines is infeasible due to the vast number of program states and execution paths. Coverage-guided fuzzers waste effort on low-risk inputs, often ignoring vulnerability-triggering ones that do not increase coverage. Existing heuristics proposed to mitigate this require expert effort, are brittle, and hard to adapt. Objective: We propose a data-centric, LLM-boosted alternative that learns from historical vulnerabilities to automatically identify minimal static (code) and dynamic (runtime) features for detecting high-risk inputs. Method: Guided by historical V8 bugs, iterative prompting generated 115 static and 49 dynamic features, with the latter requiring only five trace flags, minimizing instrumentation cost. After feature selection, 41 features remained to train an XGBoost model to predict high-risk inputs during fuzzing. Results: Combining static and dynamic features yields over 85% precision and under 1% false alarms. Only 25% of these features are needed for comparable performance, showing that most of the search space is irrelevant. Conclusion: This work introduces feature-guided fuzzing, an automated data-driven approach that replaces coverage with data-directed inference, guiding fuzzers toward high-risk states for faster, targeted, and reproducible vulnerability discovery. To support open science, all scripts and data are available at https://github.com/KKGanguly/DataCentricFuzzJS .

Building deployment-ready LLM agents requires complex orchestration of tools, data sources, and control flow logic, yet existing systems tightly couple agent logic to specific programming languages and deployment models. We present a declarative system that separates agent workflow specification from implementation, enabling the same pipeline definition to execute across multiple backend languages (Java, Python, Go) and deployment environments (cloud-native, on-premises). Our key insight is that most agent workflows consist of common patterns -- data serialization, filtering, RAG retrieval, API orchestration -- that can be expressed through a unified DSL rather than imperative code. This approach transforms agent development from application programming to configuration, where adding new tools or fine-tuning agent behaviors requires only pipeline specification changes, not code deployment. Our system natively supports A/B testing of agent strategies, allowing multiple pipeline variants to run on the same backend infrastructure with automatic metric collection and comparison. We evaluate our approach on real-world e-commerce workflows at PayPal, processing millions of daily interactions. Our results demonstrate 60% reduction in development time, and 3x improvement in deployment velocity compared to imperative implementations. The language's declarative approach enables non-engineers to modify agent behaviors safely, while maintaining sub-100ms orchestration overhead. We show that complex workflows involving product search, personalization, and cart management can be expressed in under 50 lines of DSL compared to 500+ lines of imperative code.

Formal specification is essential for rigorous program verification, yet writing correct specifications remains costly and difficult to automate. Although large language models (LLMs) and agents have shown promising progress, their true capabilities and failure modes remain unclear. We present the first systematic and contamination-aware study of LLM- and agent-based formal specification generation for C programs. We introduce LiveFMBench, a continuously evolving benchmark of 630 ACSL (ANSI/ISO C Specification Language)-annotated C programs, including 360 newly collected cases designed to mitigate data leakage. Using this benchmark, we evaluate direct prompting with different sampling sizes, reasoning-enabled (thinking mode) inference, the agentic pipeline, and perform a fine-grained failure analysis. Experimental results reveal that naive evaluation substantially overestimates performance because models under direct prompting may exhibit unfaithful behaviors, such as deceiving automated provers or ignoring code-context constraints; after excluding such cases, the true specification generation accuracy drops by approximately 20\%. We further find that both increased sampling and thinking mode significantly improve success rates, with smaller models benefiting more from thinking mode. Agentic pipelines are particularly effective under low sampling budgets and on harder datasets. Failure analysis further shows that incorrect loop invariants are the dominant error type, while agentic pipelines notably reduce assertion errors. These results expose fundamental limitations in current LLM-based approaches and suggest they remain far from replacing human-authored formal specifications. We release LiveFMBench at https://huggingface.co/datasets/fm-universe/Live-FM-Bench and all evaluation artifacts to support future research.

Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to work around the undecidability of verification questions. We compare half-duplex communication, existential B-boundedness, and k-synchronisability. These restrictions do not prevent the communication channels from growing arbitrarily large but still restrict the power of the model. Each restriction gives rise to a set of languages so, for every pair of restrictions, we check whether one subsumes the other or if they are incomparable. We investigate their relationship in two different contexts: first, the one of communicating state machines, and, second, the one of communication protocol specifications using high-level message sequence charts. Surprisingly, these two contexts yield different conclusions. In addition, we integrate multiparty session types, another approach to specify communication protocols, into our classification. We show that multiparty session type languages are half-duplex, existentially 1-bounded, and 1-synchronisable. To~show this result, we provide the first formal embedding of multiparty session types into high-level message sequence charts.

Statically analyzing dynamically-typed code is a challenging endeavor, as even seemingly trivial tasks such as determining the targets of procedure calls are non-trivial without knowing the types of objects at compile time. Addressing this challenge, gradual typing is increasingly added to dynamically-typed languages, a prominent example being TypeScript that introduces static typing to JavaScript. Gradual typing improves the developer's ability to verify program behavior, contributing to robust, secure and debuggable programs. In practice, however, users only sparsely annotate types directly. At the same time, conventional type inference faces performance-related challenges as program size grows. Statistical techniques based on machine learning offer faster inference, but although recent approaches demonstrate overall improved accuracy, they still perform significantly worse on user-defined types than on the most common built-in types. Limiting their real-world usefulness even more, they rarely integrate with user-facing applications. We propose CodeTIDAL5, a Transformer-based model trained to reliably predict type annotations. For effective result retrieval and re-integration, we extract usage slices from a program's code property graph. Comparing our approach against recent neural type inference systems, our model outperforms the current state-of-the-art by 7.85% on the ManyTypes4TypeScript benchmark, achieving 71.27% accuracy overall. Furthermore, we present JoernTI, an integration of our approach into Joern, an open source static analysis tool, and demonstrate that the analysis benefits from the additional type information. As our model allows for fast inference times even on commodity CPUs, making our system available through Joern leads to high accessibility and facilitates security research.

We introduce Orb-v3, the next generation of the Orb family of universal interatomic potentials. Models in this family expand the performance-speed-memory Pareto frontier, offering near SoTA performance across a range of evaluations with a >10x reduction in latency and > 8x reduction in memory. Our experiments systematically traverse this frontier, charting the trade-off induced by roto-equivariance, conservatism and graph sparsity. Contrary to recent literature, we find that non-equivariant, non-conservative architectures can accurately model physical properties, including those which require higher-order derivatives of the potential energy surface. This model release is guided by the principle that the most valuable foundation models for atomic simulation will excel on all fronts: accuracy, latency and system size scalability. The reward for doing so is a new era of computational chemistry driven by high-throughput and mesoscale all-atom simulations.

Dense retrieval has become a prominent method to obtain relevant context or world knowledge in open-domain NLP tasks. When we use a learned dense retriever on a retrieval corpus at inference time, an often-overlooked design choice is the retrieval unit in which the corpus is indexed, e.g. document, passage, or sentence. We discover that the retrieval unit choice significantly impacts the performance of both retrieval and downstream tasks. Distinct from the typical approach of using passages or sentences, we introduce a novel retrieval unit, proposition, for dense retrieval. Propositions are defined as atomic expressions within text, each encapsulating a distinct factoid and presented in a concise, self-contained natural language format. We conduct an empirical comparison of different retrieval granularity. Our results reveal that proposition-based retrieval significantly outperforms traditional passage or sentence-based methods in dense retrieval. Moreover, retrieval by proposition also enhances the performance of downstream QA tasks, since the retrieved texts are more condensed with question-relevant information, reducing the need for lengthy input tokens and minimizing the inclusion of extraneous, irrelevant information.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

Using large language models (LLMs) to generate source code from natural language prompts is a popular and promising idea with a wide range of applications. One of its limitations is that the generated code can be faulty at times, often in a subtle way, despite being presented to the user as correct. In this paper, we explore ways in which formal methods can assist with increasing the quality of code generated by an LLM. Instead of emitting code in a target language directly, we propose that the user guides the LLM to first generate an opaque intermediate representation, in the verification-aware language Dafny, that can be automatically validated for correctness against agreed on specifications. The correct Dafny program is then compiled to the target language and returned to the user. All user-system interactions throughout the procedure occur via natural language; Dafny code is never exposed. We describe our current prototype and report on its performance on the HumanEval Python code generation benchmarks.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

Large Language Models (LLMs) have recently shown remarkable progress in code generation, yet their ability to construct complete software repositories from scratch remains poorly understood. A fundamental bottleneck is the lack of verifiable and scalable evaluation: existing benchmarks either focus on patch-based editing or rely on human or LLM-based judgments, which introduce bias and limit reproducibility. In this work, we present RepoZero, the first benchmark that enables fully automated, execution-based verification of repository-level generation from scratch. Our key idea is to reformulate generation as repository reproduction: given only API specifications, an agent must re-implement an entire repository such that its behavior matches the original implementation. This design allows for strict black-box validation via output equivalence, while naturally supporting large-scale construction by reusing existing open-source repositories. To further mitigate data leakage and shortcut solutions, we introduce cross-language constraints and a sandboxed evaluation protocol. Building on this benchmark, we propose an Agentic Code-Test Evolution (ACE) framework that performs iterative test generation and error-driven refinement, enabling effective test-time scaling for repository-level synthesis. Extensive experiments across multiple state-of-the-art LLMs and agent frameworks reveal that even the strongest LLM agents achieve only limited pass rates (30\% - 55\%), exposing a substantial gap between current capabilities and real-world software development requirements. Our results establish RepoZero as a challenging, scalable, and reliable testbed for end-to-end code generation, and highlight self-verification via test generation as a critical direction for advancing LLM-based coding agents.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Engineering efficient implementations of compact and succinct structures is a time-consuming and challenging task, since there is no standard library of easy-to- use, highly optimized, and composable components. One consequence is that measuring the practical impact of new theoretical proposals is a difficult task, since older base- line implementations may not rely on the same basic components, and reimplementing from scratch can be very time-consuming. In this paper we present a framework for experimentation with succinct data structures, providing a large set of configurable components, together with tests, benchmarks, and tools to analyze resource requirements. We demonstrate the functionality of the framework by recomposing succinct solutions for document retrieval.

While accurately detecting and correcting factual contradictions in language model outputs has become increasingly important as their capabilities improve, doing so is highly challenging. We propose a novel method, FACTTRACK, for tracking atomic facts and addressing factual contradictions. Crucially, FACTTRACK also maintains time-aware validity intervals for each fact, allowing for change over time. At a high level, FACTTRACK consists of a four-step pipeline to update a world state data structure for each new event: (1) decompose the event into directional atomic facts; (2) determine the validity interval of each atomic fact using the world state; (3) detect contradictions with existing facts in the world state; and finally (4) add new facts to the world state and update existing atomic facts. When we apply FACTTRACK to contradiction detection on structured story outlines, we find that FACTTRACK using LLaMA2-7B-Chat substantially outperforms a fair baseline using LLaMA2-7B-Chat, and achieves performance comparable to a GPT4 baseline. Moreover, when using GPT4, FACTTRACK significantly outperforms the GPT4 baseline.

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to embed computational effects, evaluation strategies, and control flow operations. The first instalment modelled sequential higher-order computation with global store, input/output, probabilities, and non-determinism, and embedded both the call-by-name and call-by-value lambda-calculus, as well as Moggi's computational metalanguage and Levy's call-by-push-value. The present paper extends the calculus from sequential to branching and looping control flow. This allows the faithful embedding of a minimal but complete imperative language, including conditionals, exception handling, and iteration, as well as constants and algebraic data types. The calculus is defined through a simple operational semantics, extending the (simplified) Krivine machine for the lambda-calculus with multiple operand stacks to model effects and a continuation stack to model sequential, branching, and looping computation. It features a confluent reduction relation and a system of simple types that guarantees termination of the machine and strong normalization of reduction (in the absence of iteration). These properties carry over to the embedded imperative language, providing a unified functional-imperative model of computation that supports simple types, a direct and intuitive operational semantics, and a confluent reduction semantics.

Autoformalization addresses the scarcity of data for Automated Theorem Proving (ATP) by translating mathematical problems from natural language into formal statements. Efforts in recent work shift from directly prompting large language models to training an end-to-end formalizer model from scratch, achieving remarkable advancements. However, existing formalizer still struggles to consistently generate valid statements that meet syntactic validity and semantic consistency. To address this issue, we propose the Autoformalizer with Tool Feedback (ATF), a novel approach that incorporates syntactic and consistency information as tools into the formalization process. By integrating Lean 4 compilers for syntax corrections and employing a multi-LLMs-as-judge approach for consistency validation, the model is able to adaptively refine generated statements according to the tool feedback, enhancing both syntactic validity and semantic consistency. The training of ATF involves a cold-start phase on synthetic tool-calling data, an expert iteration phase to improve formalization capabilities, and Direct Preference Optimization to alleviate ineffective revisions. Experimental results show that ATF markedly outperforms a range of baseline formalizer models, with its superior performance further validated by human evaluations. Subsequent analysis reveals that ATF demonstrates excellent inference scaling properties. Moreover, we open-source Numina-ATF, a dataset containing 750K synthetic formal statements to facilitate advancements in autoformalization and ATP research.

We present JAttack, a framework that enables template-based testing for compilers. Using JAttack, a developer writes a template program that describes a set of programs to be generated and given as test inputs to a compiler. Such a framework enables developers to incorporate their domain knowledge on testing compilers, giving a basic program structure that allows for exploring complex programs that can trigger sophisticated compiler optimizations. A developer writes a template program in the host language (Java) that contains holes to be filled by JAttack. Each hole, written using a domain-specific language, constructs a node within an extended abstract syntax tree (eAST). An eAST node defines the search space for the hole, i.e., a set of expressions and values. JAttack generates programs by executing templates and filling each hole by randomly choosing expressions and values (available within the search space defined by the hole). Additionally, we introduce several optimizations to reduce JAttack's generation cost. While JAttack could be used to test various compiler features, we demonstrate its capabilities in helping test just-in-time (JIT) Java compilers, whose optimizations occur at runtime after a sufficient number of executions. Using JAttack, we have found six critical bugs that were confirmed by Oracle developers. Four of them were previously unknown, including two unknown CVEs (Common Vulnerabilities and Exposures). JAttack shows the power of combining developers' domain knowledge (via templates) with random testing to detect bugs in JIT compilers.

Prompt engineering for LLMs remains complex, with existing frameworks either hiding complexity behind restrictive APIs or providing inflexible canned patterns that resist customization -- making sophisticated agentic programming challenging. We present the Prompt Declaration Language (PDL), a novel approach to prompt representation that tackles this fundamental complexity by bringing prompts to the forefront, enabling manual and automatic prompt tuning while capturing the composition of LLM calls together with rule-based code and external tools. By abstracting away the plumbing for such compositions, PDL aims at improving programmer productivity while providing a declarative representation that is amenable to optimization. This paper demonstrates PDL's utility through a real-world case study of a compliance agent. Tuning the prompting pattern of this agent yielded up to 4x performance improvement compared to using a canned agent and prompt pattern.

We present Universal Conditional Logic (UCL), a mathematical framework for prompt optimization that transforms prompt engineering from heuristic practice into systematic optimization. Through systematic evaluation (N=305, 11 models, 4 iterations), we demonstrate significant token reduction (29.8%, t(10)=6.36, p < 0.001, Cohen's d = 2.01) with corresponding cost savings. UCL's structural overhead function O_s(A) explains version-specific performance differences through the Over-Specification Paradox: beyond threshold S* = 0.509, additional specification degrades performance quadratically. Core mechanisms -- indicator functions (I_i in {0,1}), structural overhead (O_s = gamma * sum(ln C_k)), early binding -- are validated. Notably, optimal UCL configuration varies by model architecture -- certain models (e.g., Llama 4 Scout) require version-specific adaptations (V4.1). This work establishes UCL as a calibratable framework for efficient LLM interaction, with model-family-specific optimization as a key research direction.

Large language models generate plausible code but cannot verify correctness. Existing multi-agent systems simulate execution or leave verification optional. We introduce execution-grounded verification as a first-class principle: every code change must survive sandboxed execution before propagation. We instantiate this principle in AGENTFORGE, a multi-agent framework where Planner, Coder, Tester, Debugger, and Critic agents coordinate through shared memory and a mandatory Docker sandbox. We formalize software engineering with LLMs as an iterative decision process over repository states, where execution feedback provides a stronger supervision signal than next-token likelihood. AGENTFORGE achieves 40.0\% resolution on SWE-BENCH Lite, outperforming single-agent baselines by 26--28 points. Ablations confirm that execution feedback and role decomposition each independently drive performance. The framework is open-source at https://github.com/raja21068/AutoCodeAI.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

Database systems incorporate an ever-growing number of functions in their kernels (a.k.a., database native functions) for scenarios like new application support and business migration. This growth causes an urgent demand for automatic database native function synthesis. While recent advances in LLM-based code generation (e.g., Claude Code) show promise, they are too generic for database-specific development. They often hallucinate or overlook critical context because database function synthesis is inherently complex and error-prone, where synthesizing a single function may involve registering multiple function units, linking internal references, and implementing logic correctly. To this end, we propose DBCooker, an LLM-based system for automatically synthesizing database native functions. It consists of three components. First, the function characterization module aggregates multi-source declarations, identifies function units that require specialized coding, and traces cross-unit dependencies. Second, we design operations to address the main synthesis challenges: (1) a pseudo-code-based coding plan generator that constructs structured implementation skeletons by identifying key elements such as reusable referenced functions; (2) a hybrid fill-in-the-blank model guided by probabilistic priors and component awareness to integrate core logic with reusable routines; and (3) three-level progressive validation, including syntax checking, standards compliance, and LLM-guided semantic verification. Finally, an adaptive orchestration strategy unifies these operations with existing tools and dynamically sequences them via the orchestration history of similar functions. Results show that DBCooker outperforms other methods on SQLite, PostgreSQL, and DuckDB (34.55% higher accuracy on average), and can synthesize new functions absent in the latest SQLite (v3.50).

Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to the critic phase-the evaluation of whether generated formalizations truly capture the semantic intent of the original problem. In this paper, we introduce CriticLean, a novel critic-guided reinforcement learning framework that elevates the role of the critic from a passive validator to an active learning component. Specifically, first, we propose the CriticLeanGPT, trained via supervised fine-tuning and reinforcement learning, to rigorously assess the semantic fidelity of Lean 4 formalizations. Then, we introduce CriticLeanBench, a benchmark designed to measure models' ability to distinguish semantically correct from incorrect formalizations, and demonstrate that our trained CriticLeanGPT models can significantly outperform strong open- and closed-source baselines. Building on the CriticLean framework, we construct FineLeanCorpus, a dataset comprising over 285K problems that exhibits rich domain diversity, broad difficulty coverage, and high correctness based on human evaluation. Overall, our findings highlight that optimizing the critic phase is essential for producing reliable formalizations, and we hope our CriticLean will provide valuable insights for future advances in formal mathematical reasoning.

Quantified formulas with Uninterpreted Functions (UFs) over non-linear real arithmetic pose fundamental challenges for Satisfiability Modulo Theories (SMT) solving. Traditional quantifier instantiation methods struggle because they lack semantic understanding of UF constraints, forcing them to search through unbounded solution spaces with limited guidance. We present AquaForte, a framework that leverages Large Language Models to provide semantic guidance for UF instantiation by generating instantiated candidates for function definitions that satisfy the constraints, thereby significantly reducing the search space and complexity for solvers. Our approach preprocesses formulas through constraint separation, uses structured prompts to extract mathematical reasoning from LLMs, and integrates the results with traditional SMT algorithms through adaptive instantiation. AquaForte maintains soundness through systematic validation: LLM-guided instantiations yielding SAT solve the original problem, while UNSAT results generate exclusion clauses for iterative refinement. Completeness is preserved by fallback to traditional solvers augmented with learned constraints. Experimental evaluation on SMT-COMP benchmarks demonstrates that AquaForte solves numerous instances where state-of-the-art solvers like Z3 and CVC5 timeout, with particular effectiveness on satisfiable formulas. Our work shows that LLMs can provide valuable mathematical intuition for symbolic reasoning, establishing a new paradigm for SMT constraint solving.

We perform a thorough analysis of the formal and informal statements in the miniF2F benchmark from the perspective of an AI system that is tasked to participate in a math Olympiad consisting of the problems in miniF2F. In such setting, the model has to read and comprehend the problems in natural language, formalize them in Lean language, then proceed with proving the problems, and it will get credit for each problem if the formal proof corresponds to the original informal statement presented to the model. Our evaluation results reveal that the best accuracy of such pipeline can be about 36% using the SoTA models in the literature, considerably lower than the individual SoTA accuracies, 97% and 69% reported in the autoformalization and theorem proving literature. Analyzing the failure modes, we trace back a considerable portion of this drop to discrepancies between the formal and informal statements for more than half of the problems in miniF2F. We proceed with correcting all the errors, discrepancies and simplifications in formal and informal statements, and present the miniF2F-v2 with fully verified formal and informal statements and proofs. Evaluating the full theorem proving pipeline on miniF2F-v2 leads to the best accuracy of 70%, a significant improvement from the 40% on the original miniF2F, yet indicating considerable misalignment between the autoformalization models and theorem provers. Our deep analysis suggests that a higher quality benchmark can help the community better evaluate progress in the field of formal reasoning and also better diagnose the failure and success modes of autoformalization and theorem proving models. Our dataset is available at https://github.com/roozbeh-yz/miniF2F_v2.

Mining specifications from execution traces presents an automated way of capturing characteristic system behaviors. However, existing approaches are largely restricted to Boolean abstractions of events, limiting their ability to express data-aware properties. In this paper, we extend mining procedures to operate over richer datatypes. We first establish candidate functions in our domain that cover the set of traces by leveraging Syntax Guided Synthesis (SyGuS) techniques. To capture these function applications temporally, we formalize the semantics of TSL_f, a finite-prefix interpretation of Temporal Stream Logic (TSL) that extends LTL_f with support for first-order predicates and functional updates. This allows us to unify a corresponding procedure for learning the data transformations and temporal specifications of a system. We demonstrate our approach synthesizing reactive programs from mined specifications on the OpenAI-Gymnasium ToyText environments, finding that our method is more robust and orders of magnitude more sample-efficient than passive learning baselines on generalized problem instances.

One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.

We introduce MorphNLI, a modular step-by-step approach to natural language inference (NLI). When classifying the premise-hypothesis pairs into {entailment, contradiction, neutral}, we use a language model to generate the necessary edits to incrementally transform (i.e., morph) the premise into the hypothesis. Then, using an off-the-shelf NLI model we track how the entailment progresses with these atomic changes, aggregating these intermediate labels into a final output. We demonstrate the advantages of our proposed method particularly in realistic cross-domain settings, where our method always outperforms strong baselines with improvements up to 12.6% (relative). Further, our proposed approach is explainable as the atomic edits can be used to understand the overall NLI label.

Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this work, we address this scalability bottleneck by exploiting an informative structure in formal verification: the observation that compilers map a vast space of diverse proof attempts to a compact set of structured failure modes. We introduce a learning-to-refine framework that leverages this compression to perform efficient learning and proof exploration. We perform tree search that corrects errors locally conditioned on explicit verifier feedback, thereby circumventing the costs associated with accumulating a long history of proof attempts. Extensive evaluations show that our method consistently amplifies the reasoning capabilities of base provers across varying scales. Notably, our approach achieves state-of-the-art performance on PutnamBench among publicly reported sim8B and sim32B parameter models under comparable test-time budgets, offering a scalable paradigm for next-generation verifier-guided reasoning.

Verifying the reliability of complex, multi-step reasoning in Large Language Models (LLMs) remains a fundamental challenge, as existing methods often lack both faithfulness and precision. To address this issue, we propose the Graph of Verification (GoV) framework. GoV offers three key contributions: First, it explicitly models the underlying deductive process as a directed acyclic graph (DAG), whether this structure is implicit or explicitly constructed. Second, it enforces a topological order over the DAG to guide stepwise verification. Third, GoV introduces the notion of customizable node blocks, which flexibly define the verification granularity, from atomic propositions to full paragraphs, while ensuring that all requisite premises derived from the graph are provided as contextual input for each verification unit. We evaluate GoV on the Number Triangle Summation task and the ProcessBench benchmark with varying levels of reasoning complexity. Experimental results show that GoV substantially improves verification accuracy, faithfulness, and error localization when compared to conventional end-to-end verification approaches. Our code and data are available at https://github.com/Frevor/Graph-of-Verification.

Modern AI systems rely on vector embeddings stored and searched using floating-point arithmetic. While effective for approximate similarity search, this design introduces fundamental non-determinism: identical models, inputs, and code can produce different memory states and retrieval results across hardware architectures (e.g., x86 vs. ARM). This prevents replayability and safe deployment, leading to silent data divergence that prevents post-hoc verification and compromises audit trails in regulated sectors. We present Valori, a deterministic AI memory substrate that replaces floating-point memory operations with fixed-point arithmetic (Q16.16) and models memory as a replayable state machine. Valori guarantees bit-identical memory states, snapshots, and search results across platforms. We demonstrate that non-determinism arises before indexing or retrieval and show how Valori enforces determinism at the memory boundary. Our results suggest that deterministic memory is a necessary primitive for trustworthy AI systems. The reference implementation is open-source and available at https://github.com/varshith-Git/Valori-Kernel (archived at https://zenodo.org/records/18022660).

Vibe coding produces correct, executable code at speed, but leaves no record of the structural commitments, dependencies, or evidence behind it. Reviewers cannot determine what invariants were assumed, what changed, or why a regression occurred. This is not a generation failure but a control failure: the dominant artifact of AI-assisted development (code plus chat history) performs dimension collapse, flattening complex system topology into low-dimensional text and making systems opaque and fragile under change. We propose Agentic Consensus: a paradigm in which the consensus layer C, an operable world model represented as a typed property graph, replaces code as the primary artifact of engineering. Executable artifacts are derived from C and kept in correspondence via synchronization operators Phi (realize) and Psi (rehydrate). Evidence links directly to structural claims in C, making every commitment auditable and under-specification explicit as measurable consensus entropy rather than a silent guess. Evaluation must move beyond code correctness toward alignment fidelity, consensus entropy, and intervention distance. We propose benchmark task families designed to measure whether consensus-based workflows reduce human intervention compared to chat-driven baselines.

We introduce the FCHL19 representation for atomic environments in molecules or condensed-phase systems. Machine learning models based on FCHL19 are able to yield predictions of atomic forces and energies of query compounds with chemical accuracy on the scale of milliseconds. FCHL19 is a revision of our previous work [Faber et al. 2018] where the representation is discretized and the individual features are rigorously optimized using Monte Carlo optimization. Combined with a Gaussian kernel function that incorporates elemental screening, chemical accuracy is reached for energy learning on the QM7b and QM9 datasets after training for minutes and hours, respectively. The model also shows good performance for non-bonded interactions in the condensed phase for a set of water clusters with an MAE binding energy error of less than 0.1 kcal/mol/molecule after training on 3,200 samples. For force learning on the MD17 dataset, our optimized model similarly displays state-of-the-art accuracy with a regressor based on Gaussian process regression. When the revised FCHL19 representation is combined with the operator quantum machine learning regressor, forces and energies can be predicted in only a few milliseconds per atom. The model presented herein is fast and lightweight enough for use in general chemistry problems as well as molecular dynamics simulations.

We introduce Object Graph Programming (OGO), which enables reading and modifying an object graph (i.e., the entire state of the object heap) via declarative queries. OGO models the objects and their relations in the heap as an object graph thereby treating the heap as a graph database: each node in the graph is an object (e.g., an instance of a class or an instance of a metadata class) and each edge is a relation between objects (e.g., a field of one object references another object). We leverage Cypher, the most popular query language for graph databases, as OGO's query language. Unlike LINQ, which uses collections (e.g., List) as a source of data, OGO views the entire object graph as a single "collection". OGO is ideal for querying collections (just like LINQ), introspecting the runtime system state (e.g., finding all instances of a given class or accessing fields via reflection), and writing assertions that have access to the entire program state. We prototyped OGO for Java in two ways: (a) by translating an object graph into a Neo4j database on which we run Cypher queries, and (b) by implementing our own in-memory graph query engine that directly queries the object heap. We used OGO to rewrite hundreds of statements in large open-source projects into OGO queries. We report our experience and performance of our prototypes.

Turning ideas into full software projects from scratch has become a popular use case for language models. Agents are being deployed to seed, maintain, and grow codebases over extended periods with minimal human oversight. Such settings require models to make high-level software architecture decisions. However, existing benchmarks measure focused, limited tasks such as fixing a single bug or developing a single, specified feature. We therefore introduce ProgramBench to measure the ability of software engineering agents to develop software holisitically. In ProgramBench, given only a program and its documentation, agents must architect and implement a codebase that matches the reference executable's behavior. End-to-end behavioral tests are generated via agent-driven fuzzing, enabling evaluation without prescribing implementation structure. Our 200 tasks range from compact CLI tools to widely used software such as FFmpeg, SQLite, and the PHP interpreter. We evaluate 9 LMs and find that none fully resolve any task, with the best model passing 95\% of tests on only 3\% of tasks. Models favor monolithic, single-file implementations that diverge sharply from human-written code.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

We present and test the largest benchmark for vericoding, LLM-generation of formally verified code from formal specifications - in contrast to vibe coding, which generates potentially buggy code from a natural language description. Our benchmark contains 12,504 formal specifications, with 3,029 in Dafny, 2,334 in Verus/Rust and 7,141 in Lean. Of these, 6,174 are new unseen problems. We find vericoding success rates of 27% in Lean, 44% in Verus/Rust and 82% in Dafny using off-the-shelf LLMs. Adding natural-language descriptions does not significantly improve performance. We also find that LLM progress has improved progress on pure Dafny verification from 68% to 96% over the past year. The benchmark and vericoding results are shared at https://github.com/Beneficial-AI-Foundation/vericoding-benchmark

We extend JAX with the capability to automatically differentiate higher-order functions (functionals and operators). By representing functions as a generalization of arrays, we seamlessly use JAX's existing primitive system to implement higher-order functions. We present a set of primitive operators that serve as foundational building blocks for constructing several key types of functionals. For every introduced primitive operator, we derive and implement both linearization and transposition rules, aligning with JAX's internal protocols for forward and reverse mode automatic differentiation. This enhancement allows for functional differentiation in the same syntax traditionally use for functions. The resulting functional gradients are themselves functions ready to be invoked in python. We showcase this tool's efficacy and simplicity through applications where functional derivatives are indispensable. The source code of this work is released at https://github.com/sail-sg/autofd .

Intermediate Representations (IRs) play a critical role in compiler design and program analysis, yet their comprehension by Large Language Models (LLMs) remains underexplored. In this paper, we present an explorative empirical study evaluating the capabilities of six state-of-the-art LLMs: GPT-4, GPT-3, DeepSeek, Gemma 2, Llama 3, and Code Llama, in understanding IRs. Specifically, we assess model performance across four core tasks: control flow graph reconstruction, decompilation, code summarization, and execution reasoning. While LLMs exhibit competence in parsing IR syntax and identifying high-level structures, they consistently struggle with instruction-level reasoning, especially in control flow reasoning, loop handling, and dynamic execution. Common failure modes include misinterpreting branching instructions, omitting critical operations, and relying on heuristic reasoning rather than precise instruction-level logic. Our findings highlight the need for IR-specific enhancements in LLM design. We recommend fine-tuning on structured IR datasets and integrating control-flow-sensitive architectures to improve model effectiveness. All experimental data and source code are publicly available at

We present Springdrift, a persistent runtime for long-lived LLM agents. The system integrates an auditable execution substrate (append-only memory, supervised processes, git-backed recovery), a case-based reasoning memory layer with hybrid retrieval (evaluated against a dense cosine baseline), a deterministic normative calculus for safety gating with auditable axiom trails, and continuous ambient self-perception via a structured self-state representation (the sensorium) injected each cycle without tool calls. These properties support behaviours difficult to achieve in session-bounded systems: cross-session task continuity, cross-channel context maintenance, end-to-end forensic reconstruction of decisions, and self-diagnostic behaviour. We report on a single-instance deployment over 23 days (19 operating days), during which the agent diagnosed its own infrastructure bugs, classified failure modes, identified an architectural vulnerability, and maintained context across email and web channels -- without explicit instruction. We introduce the term Artificial Retainer for this category: a non-human system with persistent memory, defined authority, domain-specific autonomy, and forensic accountability in an ongoing relationship with a specific principal -- distinguished from software assistants and autonomous agents, drawing on professional retainer relationships and the bounded autonomy of trained working animals. This is a technical report on a systems design and deployment case study, not a benchmark-driven evaluation. Evidence is from a single instance with a single operator, presented as illustration of what these architectural properties can support in practice. Implemented in approximately Gleam on Erlang/OTP. Code, artefacts, and redacted operational logs will be available at https://github.com/seamus-brady/springdrift upon publication.