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Coding and computation remain major bottlenecks in Markov chain Monte Carlo (MCMC) workflows, especially as modern sampling algorithms have become increasingly complex and existing probabilistic programming systems remain limited in model support, extensibility, and composability. We introduce \textbf{AI4BayesCode}, an extensible LLM-driven system that translates natural-language Bayesian model descriptions into runnable, validated MCMC samplers. To improve reliability, AI4BayesCode adopts a modular design that decomposes models into modular sampling blocks and maps each block to a built-in sampling component, reducing the need to implement complex sampling algorithms from scratch. Reliability is further improved through pre-generation validation of model specifications and post-generation validation of generated sampler code. AI4BayesCode also introduces a novel recursively stateful coding paradigm for MCMC, allowing modular sampling components, potentially developed by different contributors, to be composed coherently within larger MCMC procedures. We develop a benchmark suite to evaluate AI4BayesCode for sampler-generation. Experiments show that AI4BayesCode can implement a wide range of Bayesian models from natural-language descriptions alone. As an open-ended system, its capability can continue to expand with improvements in the underlying AI agent and the addition of new built-in blocks.

Traffic regulations are written for human interpretation and therefore rely on shared background knowledge and flexible phrasing, which inherently introduce ambiguity, context dependence, and semantic underspecification. These linguistic characteristics conflict with the precision required by computational reasoning engines such as Prolog, which demand explicit logical structure. This study evaluates two baseline translation approaches, Natural Language to Prolog ($NL\rightarrow Prolog$) and Logical English to Prolog ($LE\rightarrow Prolog$), and introduces a new reasoning-guided translation framework called Structured Four-Stage Legal Translation ($S4L\rightarrow Prolog$). The proposed S4L framework performs semantic role extraction, scene completion, logical mapping, and Prolog rule generation within a single guided prompt, enabling direct translation of raw traffic rules into executable logic without human intervention. A benchmark consisting of twenty real-world traffic rules was used to evaluate each approach in terms of syntactic validity, semantic correctness, and logical completeness. $S4L\rightarrow Prolog$ achieves the highest accuracy, correctly formalizing 75 percent of the rules, while $NL\rightarrow Prolog$ reaches 60 percent and $LE\rightarrow Prolog$ reaches 55 percent. Qualitative analysis further shows that S4L captures implicit causal relations, deontic modality, and exception structure more reliably than the baselines. These results demonstrate that structured reasoning prompts can substantially improve the reliability of natural-language-to-logic translation for legal and safety-critical applications.

Language models are typically trained to predict the next token in a sequence. Here, we explore an alternative predictive principle from reinforcement learning: Successor Representations (SRs), which model the expected discounted distribution of future states rather than the immediate next state. We transfer this framework to natural language and train neural networks to predict future word distributions across multiple temporal horizons, thereby learning representations of long-range transition structure. We train a deep residual neural network on WikiText-103 (103 million tokens; 20,000-word vocabulary) and optimize successor representations as probability distributions using KL divergence. Without explicit linguistic supervision, structured language representations emerge spontaneously. After training, the learned space develops a clear geometric organization with respect to part-of-speech (POS) categories: nouns, verbs, and adjectives become separable and recoverable through unsupervised clustering. This organization depends systematically on predictive horizon, with short horizons producing the strongest syntactic structure and longer horizons increasingly integrating broader contextual and semantic information. At finer resolutions, additional interpretable lexical substructure emerges, revealing coherent subclasses within major word categories. These findings suggest that syntactic categories need not be explicitly encoded but may arise as a consequence of predictive sequence learning. To our knowledge, this work provides the first systematic application of successor representations to natural language and establishes a conceptual bridge between reinforcement learning, linguistics, and cognitive neuroscience.

We systematically compare word order preferences in decoder-only language models across 192 artificial languages and typologically diverse natural languages. On artificial languages, models exhibit a left-branching preference that aligns with neither natural language universals nor human word order learning biases. On natural languages, monolingual models show no clear base word order bias at small scales, but as data grows, a preference for right-branching subject-verb-object (SVO) languages emerges while SOV falls behind despite being the most frequent order cross-linguistically. This SVO advantage extends to multilingual models and correlates with language resource level and data quality rather than word order. Thus, the same architecture exhibits opposite preferences on artificial and natural languages, establishing that word order biases observed in practice are data-driven. Since highly-resourced languages are overwhelmingly SVO, these biases risk gradually reducing word order diversity, particularly in languages that productively use multiple word orders, with the widespread adoption of LLMs.

Program evolution can measure whether a mutation helped, but it rarely controls how far the mutation moves in behavior space. Syntactic edit size is an unreliable proxy: a small code change can alter nearly every action, while a larger rewrite can preserve the same execution trace. We introduce an Evolutionary Language Model that searches over natural-language policy descriptions and compiles typed programs for execution. A fully fine-tuned Qwen3-8B model learns three task-conditioned operations: conditional semantic mutation, natural language to domain-specific language (GPTL) compilation, and GPTL to natural language translation. The model is fine-tuned with conditional input on the mutation strength (low, medium, high) using Direct Preference Optimization (oDPO). Across 252 fixed-budget evolutionary searches, oDPO improves both behavioral calibration and finite-budget search efficiency. Natural-language attains the highest observed held-out fitness. Our analysis shows that the condition input (mutation strength) systematically changes semantic edit composition and that language mutations preserve more parent fitness at matched small-to-moderate behavioral displacement. These results show that language can serve as a steerable, execution-grounded search representation over executable program space.

Jupyter Notebooks have become widely adopted in data science, as they allow the sharing of reproducible computational analysis. They are, however, accessible only to people who understand computer code. To reach the broader audience of scientists interested in data analysis and computation, but unfamiliar with code, we introduce Plainbook, notebooks centered on natural language rather than code. Plainbook is based on two principles: promote the natural language descriptions, and verify the values. In plainbook, the natural language descriptions are preserved, rather than the resulting code; the code is generated automatically from the cell descriptions. As natural language is read top to bottom, Plainbook adopts a linear execution semantics, in which cells are guaranteed to be executed in the order in which they appear; there is no "hidden state" or out-of-order execution as in Jupyter. To allow users who may not understand code to verify the correctness of the computation, we have built into Plainbook verification mechanisms centered on values and value inspection. These include mechanisms that focus on individual cells, akin to unit tests, as well as global mechanisms. Both the linear execution semantics, and the verification mechanisms, are underpinned by a snapshot kernel that caches execution states and makes execution and verification efficient.

Maintaining consistency between natural language documentation of business rules and their evolving internal implementations is a significant challenge in large-scale systems. We present SIRNA, a tool and framework for checking such consistency using SMT solvers. Using the case study of cost calculations in tax domains, we demonstrate a three-part system that combines large language models (LLMs) with formal verification methods. SIRNA translates natural language documentation into candidate SMT formulas using LLMs, followed by checks to validate the translations. Then, corresponding business rules are converted into equivalent SMT representations and validated against the natural language formalizations. Our method is generalizable to domains where business logic exists in both natural language documentation and programmatic implementation. Compared to baseline evaluations, SIRNA significantly reduces the number of false positives and false negatives while offering explainability for its findings.

Natural language requirements (NLRs) are essential for bridging communication gaps among diverse stakeholders in software development. However, the inherent ambiguity in NLRs can pose significant challenges. In particular, some requirements may be misinterpreted due to varying contextual knowledge and domain-specific expectations of the stakeholders, a phenomenon known as pragmatic ambiguity. This paper presents an approach for detecting and resolving pragmatic ambiguities in NLRs. The approach leverages retrieval-augmented generation techniques with novice, intermediate, and expert domain knowledge bases to simulate stakeholders with varying domain expertise and detect discrepancies in requirement interpretation. Candidate disambiguated requirements are generated using the expert domain knowledge base, with final validation by a requirements analyst required to ensure alignment with the intended functionality. We evaluate the approach on two requirements specification documents from the PUblic REquirements dataset, using four large language models: GPT-4o-mini, Mistral-7B, Llama-3.1-8B, and Qwen2.5-7B. Detection performance is assessed using macro-averaged accuracy, precision, recall, F1, and F2 scores. The resolution quality of the candidate disambiguated requirements is measured through human evaluation of relevance, clarity, and consistency. In this initial evaluation, results show that the proposed approach can detect pragmatic ambiguities and produce candidate disambiguated requirements that are relevant, clear, and consistent with the intended system functionality. Among the evaluated models, GPT-4o-mini achieved the highest macro-averaged recall (0.75) and F2 score (0.75) for pragmatic ambiguity detection. In the resolution task, GPT-4o-mini received the highest relevance scores from human evaluators, while Mistral-7B achieved the highest scores for clarity and consistency.

Natural Language Processing (NLP) has traditionally been published in its core disciplinary venues like ACL. However, advances in Large Language Models (LLMs) has led to a blurring of the disciplinary lines between NLP and general Machine Learning (ML), with authors regularly publishing in venues from both fields. Here, we ask whether the disciplinary center of gravity is shifting. Using NLP research published from 2010 to 2026 and studies of both established and new authors, we find that a migration is taking place. First, comparing the pre- and post-LLM eras, established authors lost 19.2pp of share at flagship *ACL main-conference tracks while gaining 14.8pp in the newer Findings tracks, and general ML venues rose 8.6pp, even when adjusting for parallel growth in the fields. Second, among newer authors who debut with at least three first-author NLP-topic papers, the share whose work appears mostly at *ACL venues fell from 84% (2019) to 74% (2024), while the share appearing mostly at general ML venues rose from 5% to 21%. Using causal inference techniques, we estimate that these general ML venues confer a significant citation premium, which influences venue selection. Together, these results point to a significant shift in where NLP research is published.

A natural language interface can be used to make cancer genomics databases easier to use, but even if a question is perfectly fluent, its scientific meaning can be ambiguous. We propose CLARA, a framework that represents a question as a typed scientific query specification, considers a few possible interpretations, executes them, and asks for clarification when the estimates diverge. CLARA was assessed on mutation-prevalence contrasts among eight TCGA PanCancer Atlas cohorts and a 30-gene panel. This benchmark consisted of 330 unique executable contrasts varying in mutation scope, assay denominator, and sample context; 115 contrasts were result-sensitive and 215 were result-stable, per the preregistered definition of relative divergence greater than 0.10 or absolute divergence greater than 5 percentage points. An independently implemented pandas execution engine perfectly replicated all 660 results from the SQLite engine. In a separate 120-question LLM-generated, manually vetted language stress test, CLARA recognized all 60 result-sensitive contrasts and needlessly clarified 13 of 60 stable contrasts (accuracy 89.2%, sensitivity/recall 100%, specificity 78.3%). Standalone machine learning had superior overall accuracy (97.5%) but missed one critical contrast. This demonstrates that downstream execution can distinguish consequential from inconsequential ambiguity and reveal an explicit trade-off between safety and burden.

In the age of large language models, Natural Language to SQL (NL2SQL) translation remains an open problem with many useful applications. We explore interactions between several NL2SQL pipeline extensions to inspire development of more lightweight models. Specifically, we integrate the NatSQL intermediate representation, include a preprocessing step and a fine-tuning step based on synthetic data, and develop a novel reranker model to improve SQL selection in the final beam. We perform an ablation study supplemented by a Shapley analysis of these different components integrated with two backbone architectures, SmBoP and RASAT. We find that simply combining all of them does not lead to best results, but that their impact depends on their interactions with the baseline system, as well as each other.

Natural Language Processing (NLP) models predicting mental health outcomes rarely specify what they measure: contextual knowledge, emotional content, or syntactic structure. NLP Psychometrics treats psychological prediction from text as a psychometric problem, linking scores to interpretable linguistic evidence and testing beyond the training text format. Nine LLMs, conditioned on controlled personas (cognitive digital shadows), completed psychometric questionnaires with textual explanations per item. We extracted emotional profiles and syntactic-semantic structure via textual forma mentis networks, combined with personality and sociodemographic variables in ablated random forest (RF) regressors, using SHAP to identify which features drove performance and in which direction. Full RF models explained up to 70.8% of variance in life satisfaction (SWLS), 55.7% in depression (PHQ-9), and, for DASS-21, 68.5% depression, 76.0% anxiety, 72.4% stress. Sociodemographics alone explained no meaningful variance in depression, anxiety, or stress, but did so for life satisfaction, where emotion features and income were the strongest predictors; neuroticism and network topology instead dominated depression and anxiety, reversing direction between them. Without retraining, RF models separated diaries from low- and high-score personas ($r$ up to 0.91) and, using only network/emotion features, classified clinical from control participants in real transcripts with up to 68% accuracy. These results show the promise and limits of synthetic data: LLM personas can expose model biases, recover patterns consistent with clinical rumination, and support psychometric prediction from human text without a matched questionnaire, but cannot substitute for human validation. NLP Psychometrics makes these distinctions explicit, measurable, and testable through interpretable AI and network/emotional features.

Natural language to SQL (NL2SQL) conversion is an important problem for researchers and enterprises due to the ubiquitous importance of relational databases in broad-ranging practical problems. Despite the rapid advancements in the capabilities of LLMs, NL2SQL has not reached parity in accuracy with human expert SQL writers, hence needing additional improvements in NL2SQL algorithms. This study presents a new multi-agent method for NL2SQL that achieves 78.1% semantic accuracy on the BIg Bench for LaRge-scale Database (BIRD) benchmark. Our method leverages a semantically enriched representation of user-provided schema, adds user-provided business rules, and produces accurate SQL queries. The main contributions of this study are (a) We designed an optimized new orchestrator in a multi-agent solution that uses LLMs to plan, orchestrate, reflect, and self-correct to generate accurate SQL queries, (b) We developed an advanced schema enrichment method that creates context-aware metadata to improve accuracy, and (c) We demonstrated the accuracy and generalizability of the method across different domains and datasets by evaluating it on the BIRD-SQL benchmark.

Natural language interfaces to databases have traditionally suffered from three structural limitations: exclusive targeting of relational SQL, unconditional dependence on large language model (LLM) inference at query time, and absence of any runtime signal when generated queries are semantically incorrect. This paper presents text2ql, an open-source Python framework that addresses all three limitations through a language-agnostic Intermediate Representation (QueryIR) and a pluggable renderer architecture. A single seven-stage detection pipeline serves both SQL and GraphQL targets; a zero-LLM deterministic mode delivers 100% execution accuracy at a median latency of 3.2 ms with no API cost; and every generated query carries a runtime confidence score in [0.15, 0.97] computed from an additive signal model. Evaluated on 50-query random samples from the Spider and BIRD benchmarks (indicative results; full-set evaluation is planned), the LLM-backed mode achieves 62-70% exact match and 84-91% execution accuracy; the deterministic mode achieves 100% execution accuracy with zero parse errors across all 100 test cases. An ablation study isolates schema-aware prompting as the dominant accuracy lever, contributing +18.4 percentage points of exact-match gain over the schema-free baseline on both benchmarks. text2ql is publicly available at https://pypi.org/project/text2ql/ under the Apache 2.0 license.

Egocentric Natural Language Query (NLQ) grounding asks a model to localize, in a long first-person video, the temporal interval that answers a free-form text query. Existing methods fuse video appearance with the query but ignore hand motion, despite the fact that roughly 41% of Ego4D NLQ queries are answered at a moment of hand--object manipulation or their immediate outcomes.We propose a hand-trajectory encoder for converting a sequence of hand skeletons into highly-semantic hand kinematic features, which are then aligned and combined with pretrained video--text features through a cross-attention fusion strategy with adaptive gating. On the Ego4D NLQ v2 validation split, the clearest gains appear for Hand-Object Interaction queries (+2.54 R1@IoU=0.3) and Quantity/State queries (+4.32 R1@IoU=0.3), indicating that hand trajectory provides grounding cues beyond appearance alone.

Natural-language software requirements are often ambiguous, inconsistent, and underspecified; in safety-critical domains, these defects propagate into formal models that verify the wrong specification and into implementations that ship unsafe behavior. We show that large language models, equipped with an SMT solver, can audit such requirements: translating them into formal logic, detecting ambiguity through stochastic variation in the generated formalization, and exposing inconsistency, vacuousness, and safety violations through solver queries on the resulting specification. We present VERIMED, a neurosymbolic pipeline that operationalizes this idea for medical-device software requirements, and report two findings. First, stochastic variation across independent formalizations is a signal of ambiguity: requirements that admit multiple plausible interpretations produce SMT-inequivalent formalizations, and bidirectional SMT equivalence checking turns this disagreement into a solver-checkable test. Second, the usefulness of symbolic feedback depends on its granularity: in counterexample-guided repair on a hemodialysis question-answering benchmark, concrete SMT counterexamples raise verified accuracy from 55.4% to 98.5%. Over an extensive experimental evaluation on open-source hemodialysis safety requirements, we show that the LLM-based approach in VERIMED successfully reduces ambiguity-sensitive requirements and enables rigorous auditing of software requirements through SMT-based queries.

Robots deployed in human-centric environments routinely receive natural-language descriptions of spatial information ("I left my backpack on the table") that reference parts of the world beyond their perceptual field of view. Traditional metric-semantic mapping ignores this signal, while off-the-shelf multimodal models remain limited in 3D spatial reasoning and are not directly amenable to fusion with other sensor modalities. To convert language observations into a calibrated spatial distribution, we train a Language Sensor Model (LSM) that maps each utterance and its scene-graph context to a multimodal distribution, with mixture weights encoding referential ambiguity (e.g., "which table") and component covariances encoding spatial uncertainty (e.g., where "on the table" the target lies). We then introduce VL-Map (Vision-Language Metric-Semantic Mapping), a probabilistic framework that treats these language predictions as stochastic observations and fuses them with onboard perception within a unified belief map. On the VLA-3D benchmark as well as on a real-world mobile robot, LSM is the only language predictor whose covariance estimates remain within the calibrated regime; fused into VL-Map, it leads to more accurate predictions of the target object location (~70% more probability mass on the true target compared to the strongest foundation-model baseline).

Vision-language tracking guided by natural language specifications leverages high-level semantic cues of target objects to substantially boost tracking accuracy and robustness. Existing studies have verified that adaptively optimizing textual descriptions throughout the tracking process can effectively mitigate the semantic-visual mismatch induced by dynamic variations in target appearance, position, and other inherent attributes. Nevertheless, mainstream methods that directly generate textual information via sequence models or large language models inevitably suffer from inherent defects, including erroneous target updating, excessive background distraction, and pervasive hallucination artifacts. To address the aforementioned limitations, this paper proposes a novel language dependency parsing mechanism to precisely distill core tracking principal components, encompassing target objects, semantic concepts, and background contextual information. On this basis, we perform component-aware adaptive textual description updates by exploiting the powerful cross-modal understanding capability of the pre-trained vision-language model Qwen-VL. By integrating the proposed elaborately designed modules into the baseline framework, our method achieves consistent and superior tracking performance on multiple large-scale vision-language tracking benchmarks, including TNL2K, LaSOT, TNLLT, and OTB-LANG. The source code and pre-trained models will be released at https://github.com/Event-AHU/Open_VLTrack.

We introduce SmartEval, a benchmark for systematically evaluating the quality of Solidity smart contracts generated by large language models (LLMs) from natural language specifications. SmartEval provides a corpus of 9,000 generated contracts paired with expert-written ground-truth implementations drawn from the FSMSCG dataset, a five-dimensional evaluation rubric covering functional completeness, variable fidelity, state-machine correctness, business-logic fidelity, and code quality, and a reproducible generation-and-evaluation pipeline. To validate the benchmark's reliability, we conduct three independent empirical studies: a five-condition ablation study (N=300 per condition) isolating the contribution of each pipeline component, a human expert evaluation by three Columbia University PhD researchers confirming automated scores align with expert judgment to within 0.34 points, and external security analysis via the Slither static analyzer confirming 79.4% agreement between the LLM auditor and a non-LLM rule-based tool. Systematic analysis of 9,000 generated contracts reveals characteristic failure modes (logic omissions at 35.3%, state transition errors at 23.4%, and complexity-driven degradation) and quantifies a +8.29 composite-score advantage of generated contracts over ground-truth implementations, attributable to LLMs' literal specification-following behavior. SmartEval establishes a reproducible, validated foundation for empirical research on LLM smart contract synthesis quality, with all data, evaluation code, and generated contracts publicly released.

Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable empirical success, yet they face persistent structural limitations in compositional semantics, type sensitivity, and interpretability. I argue in this paper that geometric algebra (GA) -- specifically, Clifford algebras -- provides a mathematically superior foundation for semantic representation, and that a Functional Geometric Algebra (FGA) framework extends GA toward a typed, compositional semantics capable of supporting inference, transformation, and interpretability while retaining full compatibility with distributional learning and modern neural architectures. I develop the formal foundations, identify three core capabilities that GA provides and linear algebra does not, present a detailed worked example illustrating operator-level semantic contrasts, and show how GA-based operations already implicit in current transformer architectures can be made explicit and extended. The central claim is not merely increased dimensionality but increased structural organization: GA expands an $n$-dimensional embedding space into a $2^n$ multivector algebra where base semantic concepts and their higher-order interactions are represented within a single, principled algebraic framework.

Knowledge graphs (KGs) can be enhanced through rule mining; however, the resulting logical rules are often difficult for humans to interpret due to their inherent complexity and the idiosyncratic labeling conventions of individual KGs. This work presents Rule2Text, a comprehensive framework that leverages large language models (LLMs) to generate natural language explanations for mined logical rules, thereby improving KG accessibility and usability. We conduct extensive experiments using multiple datasets, including Freebase variants (FB-CVT-REV, FB+CVT-REV, and FB15k-237) as well as the ogbl-biokg dataset, with rules mined using AMIE 3.5.1. We systematically evaluate several LLMs across a comprehensive range of prompting strategies, including zero-shot, few-shot, variable type incorporation, and Chain-of-Thought reasoning. To systematically assess models' performance, we conduct a human evaluation of generated explanations on correctness and clarity. To address evaluation scalability, we develop and validate an LLM-as-a-judge framework that demonstrates strong agreement with human evaluators. Leveraging the best-performing model (Gemini 2.0 Flash), LLM judge, and human-in-the-loop feedback, we construct high-quality ground truth datasets, which we use to fine-tune the open-source Zephyr model. Our results demonstrate significant improvements in explanation quality after fine-tuning, with particularly strong gains in the domain-specific dataset. Additionally, we integrate a type inference module to support KGs lacking explicit type information. All code and data are publicly available at https://github.com/idirlab/KGRule2NL.

Recent advances in large language models (LLMs) have made natural language interfaces (NLIs) widely accessible for data exploration, yet analysts who have a broad analytical objective still face the challenge of decomposing it into effective step-by-step queries, especially over unfamiliar, multi-table relational databases. Rather than generating high-level analytical agendas, we investigate how to augment an NLI with semantic- and context-aware next-step query recommendations that act as analytical scaffolding for relational database exploration. Our approach goes beyond interestingness-only methods by jointly integrating semantic relevance, data interestingness, and context coherence to guide exploration toward coherent, topic-focused analyses and potentially insightful subsets. We evaluate QRec-NLI with NL2SQL benchmarking, LLM-enhanced description validation, agentic comparisons against interestingness-only and LLM-based prompting baselines, and a 12-participant user study. In the agentic comparison, QRec-NLI yields more topically relevant and locally coherent query sequences than both baselines. In the user study against the interestingness-only baseline, it receives stronger ratings for insight-generation support and decision support.

Effectively translating between natural language (NL) and formal logics like Linear Temporal Logic (LTL) requires expertise that limits formal verification's reach in safety-critical development. Template-based approaches sacrifice expressiveness for reliability; neural methods achieve fluency but provide no correctness guarantees. We present NeuroNL2LTL, a neurosymbolic architecture unifying learned translation with formal verification. NeuroNL2LTL routes translation through an intermediate representation whose mapping to LTL is structure-preserving by construction. Generated specifications undergo satisfiability and non-triviality checking; a minimal-edit repair mechanism corrects near-miss outputs before they reach downstream tools. The central innovation is verifier-in-the-loop training: verification outcomes serve as reward signals for reinforcement learning, producing neural components that optimize directly for formal correctness. On 200,000+ requirements spanning aerospace, robotics, autonomous vehicles, and ten additional domains, NeuroNL2LTL achieves 28% semantic equivalence with reference specifications while ensuring 86% of outputs are verified satisfiable. The system also generates contextually grounded explanations from LTL, enabling domain experts to validate specifications without specialized training. This work demonstrates that formal verification can function as both training objective and runtime filter for neural specification systems, allowing us to build neural-based tools whose reliability derives from logical guarantees rather than statistical confidence.

Lean is increasingly used to judge natural-language mathematical answers, but its signal is partial: many answers never formalize, and a failed proof may reflect an ill-typed statement or a missing library fact, not a wrong answer. On MATH-500 we show this signal is (i) sharply coverage-dependent, that is the proof-winning answer is correct 96% of the time at high proved coverage but 20% at low, and (ii) sparse and often unfaithful: a 7B autoformalizer proves a class for only 28% of problems, and a manual audit finds only approximately 43% of those proofs faithful. We propose COVCAL, a selector over Lean-trace diagnostics that certifies a finite-sample selective-risk bound on accepted answers or abstains, under two regimes (a conservative Bonferroni bound and a tighter dev-then-cal rule). Feasibility depends on autoformalization coverage: with the 7B formalizer the signal is too sparse and Bonferroni abstains on all 20 bootstrap partitions, whereas a prover-specialized formalizer reaches 79% coverage and flips it to feasible on 17 of 20, accepting approximately 48% of problems at 0.98 accepted accuracy. Since self-consistency alone is already 91% accurate, our contribution is a precise account of when, and with which formalizer, a partial formal signal can be trusted under risk control.

LLMs can generate hardware descriptions from natural language specifications, but the resulting Verilog often contains width mismatches, combinational loops, and incomplete case logic that pass syntax checks yet fail in synthesis or silicon. We present CktFormalizer, a framework that redirects LLM-driven hardware generation through a dependently-typed HDL embedded in Lean 4. Lean serves three roles: (i) type checker:dependent types encode bit-width constraints, case coverage, and acyclicity, turning hardware defects into compile-time errors that guide iterative repair; (ii) correctness firewall:compiled designs are structurally free of defects that cause silent backend failures (the baseline loses 20% of correct designs during synthesis and routing; CktFormalizer preserves all of them); (iii) proof assistant:the agent constructs machine-checked equivalence proofs over arbitrary input sequences and parameterized widths, beyond the reach of bounded SMT-based checking. On VerilogEval (156 problems), RTLLM (50 problems), and ResBench (56 problems), CktFormalizer achieves simulation pass rates competitive with direct Verilog generation while delivering substantially higher backend realizability: 95--100% of compiled designs complete the full synthesis, place-and-route, DRC, and LVS flow. A closed-loop PPA optimization stage yields up to 35% area reduction and 30% power reduction through validated architecture exploration, with automated theorem proof ensuring that each optimized variant remains functionally equivalent to its formal specification.

Large language model (LLM) agents are increasingly entrusted with natural-language workflow instructions (e.g., retail-payment policies) that specify not only what outcome to achieve, but also which steps, branches, and tool interactions are permitted. When these instructions are supplied as prompt context, however, the model retains control over both procedure selection and step execution. As interactions accumulate, an agent can skip required steps, take unsupported branches, or execute a valid step with unsupported arguments or effects--a failure mode we call workflow misalignment. In this work, we propose COVENANT, a compiler-and-interpreter architecture for workflow-aligned agent execution. Our key insight is to treat workflow instructions as source programs rather than prompts. COVENANT converts the instructions into a workflow abstract syntax tree (WAST) and lowers it to a workflow control-flow graph (WCFG). At runtime, a controller interprets the WCFG one node at a time, checks each proposal against requirements extracted from the instructions before committing controller state or advancing the graph, and returns diagnostic feedback for repair. To evaluate COVENANT, we use 120 cases from three existing benchmarks, spanning seven workflow scenarios. Compared with state-of-the-art LLM agents, COVENANT improves benchmark success from 50.00% to 83.33% and reduces the workflow-misalignment failure rate from 42.50% to 15.83% (62.75% relative). These results show that COVENANT substantially mitigates workflow misalignment, moving LLM-agent alignment beyond isolated prompt following toward reliable execution of complex and multi-step workflows.

Large language models increasingly write TLA$^{+}$ formal specifications from natural-language descriptions, but progress is hard to measure: existing resources grade by resemblance to a reference or by whether the output parses, neither of which shows correctness. We present TLA$^{+}$-Bench, a dataset and benchmark that grades by execution. Every gold specification ships a configuration the TLA$^{+}$ model checker runs over the full reachable state space, deciding exactly whether the specification holds the properties that configuration names. The dataset holds 403 model-checked gold and 897 parse-only silver specifications from 13 public repositories, subsumes prior TLA$^{+}$ generation data, and carries four model-written descriptions in two styles from two providers, with difficulty and category labels. Our main finding is about measurement itself: an exact oracle gives not one correctness number but a range. Varying only the grading choices earlier benchmarks leave unstated, on one fixed set of model outputs, the correct rate moves sixfold, from 10.0% to 1.7%; adding the interface-supply choice, where the model is told the configuration's names, widens the range to elevenfold, from 18.7% to 1.7%. We call this range the correctness envelope and measure each of its bounds. The findings inside it are stable. Every model writes valid TLA$^{+}$ far more often than correct TLA$^{+}$: the strongest is correct 16% of the time by default and 26% when given the interface names, open models at most 1%, and correctness falls sharply with difficulty.

We introduce GeoBuildBench, a benchmark designed to evaluate whether large language models and multimodal agents can ground informal natural-language plane geometry problems into executable geometric constructions. Unlike existing geometry benchmarks that focus on answer correctness or static diagram interpretation, GeoBuildBench treats geometry diagram as an interactive construction task: given a textual problem, an agent must generate a domain-specific language (DSL) program to produce a diagram satisfying explicitly specified geometric objects and verifiable constraints. The benchmark features 489 Chinese textbook-style problems, curated through automated filtering and human validation to ensure text-complete, constructible problem specifications. We evaluate several state-of-the-art multimodal models in a bounded iterative setting and show that, despite reasonable success rates, models frequently exhibit structural hallucinations, missing objects, and failures to satisfy geometric constraints, with limited ability to exploit visual and constraint-based feedback for self-correction. These results highlight geometry construction as a rigorous testbed for grounded, executable reasoning beyond textual or visual plausibility. Our benchmark and code are publicly available.

This paper addresses the problem of translating natural-language routing rules written by business administrators into executable workflow graphs for enterprise contact centers. Each target is a directed acyclic graph (DAG) of conditional actions with parallel branches, hit-first fallback chains, and per-branch Boolean predicates, encoded in the JSON dialect of a commercial routing platform. We show that neuro-symbolic decomposition enables lower-cost, non-reasoning large language models to generate complex workflow DAGs at production-relevant quality without expensive extended-reasoning models. Our central diagnostic is an emission-density bottleneck: on a 635-rule benchmark of manufactured synthetic data, models select the correct graph nodes with high accuracy but increasingly misconfigure attributes and Boolean grouping as the number of interdependent nodes emitted in one pass grows. We therefore move combinatorial graph construction from the model into a deterministic compiler driven by a compact intermediate representation, with a learned registry-selection front end that focuses generation on relevant vocabulary. Across four models, the full system reaches approximately 89% LLM-judge validity, approximately 90% exact-match condition accuracy, and 99-100% valid JSON while using roughly half the per-rule prompt tokens of a monolithic prompt. On GPT-5.3-chat, the method improves judge validity by 24 percentage points and achieves statistical equivalence to a reasoning model's out-of-the-box quality, although an approximately 8-point frontier gap remains. We also present a deployment path and transferable lessons for structured-generation applications.

Recent frontier large language models (LLMs) have shown strong performance in identifying security vulnerabilities in large, mature open-source systems. As LLM-generated code becomes increasingly common, a natural goal is to prevent such models from producing vulnerable implementations in the first place. Formal verification offers a principled route to this objective, but existing verification pipelines typically require specifications written in rigid formal languages. Prior work has explored using LLMs to synthesize such specifications, with limited success. In this paper, we investigate a different approach: using LLMs both to generate specifications and to verify implementations compositionally when the specifications are expressed in natural language. Our preliminary results suggest that this approach is promising.