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We present MechGeo, a Mathlib native agentic framework that jointly addresses faithful autoformalization and certified proof construction for Euclidean geometry. In this framework, GeoFormalizer represents informal problems in GeoIR, deterministically translates them into Lean 4, and iteratively repairs candidate statements using structural diagnostics and semantic evaluation. GeoProver constructs geometric proof plans, derives intermediate lemmas, and selectively algebraizes suitable subgoals through a library verified in Lean. Singular or SymPy may generate algebraic certificates, but all resulting proofs and counterexamples are checked by Lean's kernel. Experiments across seven LLM backbones show substantial improvements in autoformalization, particularly for models with weaker direct translation performance. On 43 historical IMO geometry problems, GeoFormalizer generates formal statements that GeoProver proves in 29 cases; for the remaining 14, it constructs counterexamples verified in Lean and proves all repaired statements after expert correction. Together with IMO 2026 Problem 2, this yields, to the best of our knowledge, the largest reported collection of automated, kernel-checked Lean proofs for IMO geometry problems. On the 14 geometry statements in LEAP's Lean-IMO-Bench, MechGeo proves 12 for the first time, formally refutes the remaining two, and proves both repaired statements. These results establish counterexample guided diagnosis, geometric reasoning, and certified symbolic computation as a practical foundation for trustworthy formal geometry.

Post-training large language models (LLMs) via reinforcement learning (RL) has significantly advanced code generation capabilities. To bypass the heavy memory footprint of critic networks, current state-of-the-art frameworks leverage critic-free paradigms like Group Relative Policy Optimization (GRPO) tied to rule-based verification sandboxes. However, applying these frameworks to low-level systems programming, such as CUDA kernel generation-presents severe challenges: binary pass/fail rewards introduce severe signal sparsity, while multi-turn environmental feedback loops suffer from prohibitive compilation latencies and reward dilution across trajectories. In this work, we introduce LEAP (Lean Environment-Feedback via Adaptive Pruning), a scalable and computationally efficient multi-turn RL framework optimized for low-level hardware accelerator alignment. LEAP features Difficulty-Conditioned Pruning (DCP), a dynamic gating mechanism that adaptively cuts off simple and overly catastrophic tasks from multi-turn expansion, focusing resource-heavy compilation and hardware exploration exclusively on high-value, complex tasks. To fully operationalize these paths without manual hyperparameter engineering, we propose a Rank-Based Reward formulation. By deriving scale-free relative advantages from pairwise tournament outcomes within the GRPO rollout group, our method inherently penalizes token inefficiency on simple prompts while maximizing learning gradients on challenging distributions. Empirical evaluations show that LEAP achieves superior first-turn proficiency and robust multi-turn debugging resilience while converging faster than unpruned multi-turn baselines, establishing a practical paradigm for low-level code RL.

Alternating-time temporal logic and its extensions provide several ways of combining strategic and quantitative reasoning. We study a particular combination: whether a coalition has a single strategy that enforces a temporal objective while guaranteeing given long-run mean-payoff thresholds. We introduce ATL*_mp, an extension of ATL* over weighted concurrent game structures in which each strategic modality carries a conjunctive mean-payoff constraint. The temporal and quantitative requirements must hold against every behaviour of the remaining agents, and the existence of such a strategy cannot in general be reduced to the two requirements considered separately. For one-dimensional constraints, model checking is 2EXPTIME-complete under both perfect-recall and finite-memory semantics, matching ATL*. For the pure quantitative fragment and fragments restricted to ATL or GR(1) temporal objectives, model checking has lower complexity. With multi-dimensional conjunctive constraints, model checking under finite-memory semantics remains 2EXPTIME-complete. We show that memoryless, finite-memory, and perfect-recall abilities form a strict hierarchy, while finite-memory strategies still achieve every threshold strictly below the perfect-recall supremum. We give tight linear upper and lower bounds on the required memory as a function of the denominator of the threshold, even when the game and temporal monitor are fixed. We give several examples of properties expressible in the logic, including temporal synthesis with performance guarantees and aggregate and multi-criteria objectives. We also relate the logic to cooperative rational verification, showing that it can express beneficial deviations from fixed payoff baselines, but not directly reproduce the standard ATL* encoding of the core for dichotomous preferences.

Many high-level security requirements are about the allowed flow of information in programs and are difficult to make precise because they involve selective downgrading. Notions from epistemic logic have emerged as a good approach to policy semantics but a robust general framework remains elusive. A paper appearing in CSF 2018, entitled ``Assuming You Know: Epistemic Semantics of Relational Annotations for Expressive Flow Policies'', attempted to provide a unifying framework---but the formalization was sketchy and a correction was announced during the conference presentation. With aid from an agentic AI coding assistant, a corrected formalization has been machine checked in the Rocq proof assistant. The simplicity and generality of the framework may help compare different policy specification styles and enforce them by leveraging existing techniques.

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.

AI coding agents increasingly author pull requests (PRs), often under developers' own accounts, obscuring who actually produced a change. Reliable attribution is important for repository governance, empirical studies of AI-assisted software development, and measuring the impact of AI coding agents. Existing work focuses on closed-set identification of known agents, leaving the practical limits of open-world AI coding agent attribution largely unexplored. In this paper, we present AgenTag, a multimodal framework for open-world AI coding agent attribution, evaluated on AIDev, comprising 33,580 PRs from five AI coding agents and 6,618 human-authored PRs. We represent each PR using textual, behavioral, and code-based modalities, and compare conventional classification with supervised contrastive learning for open-set recognition and few-shot enrollment of previously unseen agents. AgenTag identifies authoring agents with a weighted F1 of 0.96 (macro F1 of 0.84), distinguishes AI- from human-authored PRs with a balanced F1 of 0.89, and detects previously unseen agents with an AUC of 0.84. We further show that PR descriptions and commit messages provide nearly all of the attribution signal, whereas code diffs contribute little across multiple representations, indicating that coding agents are distinguished primarily by how they communicate changes rather than by the code they generate. Moreover, these behavioral fingerprints persist after removing explicit self-disclosed markers, demonstrating that attribution relies largely on latent stylistic characteristics. These findings show that reliable attribution of AI coding agents is feasible and clarify the practical trade-offs between attribution accuracy and the information required to achieve it.

Testing mobile applications often relies on tools, such as Exerciser Monkey for Android systems, that simulate user input. Exerciser Monkey, for example, generates random events (e.g., touches, gestures, navigational keys) that give developers a sense of what their application will do when deployed on real mobile phones with real users interacting with it. These tools, however, have no knowledge of the underlying applications' structures and only interact with them randomly or in a predefined manner (e.g., if developers designed scenarios, a labour-intensive task) -- making them slow and poor at finding bugs. In this paper, we propose a novel control flow structure able to represent the code of Android applications, including all the interactive elements. We show that our structure can increase the effectiveness (higher coverage) and efficiency (removing duplicate/redundant tests) of the Exerciser Monkey by giving it knowledge of the test environment. We compare the interface coverage achieved by the Exerciser Monkey with our new Monkey++ using a depth first search of our control flow structure and show that while the random nature of Exerciser Monkey creates slow test suites of poor coverage, the test suite created by a depth first search is one order of magnitude faster and achieves full coverage of the user interaction elements. We believe this research will lead to a more effective and efficient Exerciser Monkey, as well as better targeted search based techniques for automated Android testing.

Code refactoring aims to enhance the internal structure of source code without affecting its functional behavior. The recent advancements of Large Language Models (LLMs) have demonstrated potential for automating software engineering tasks, such as code refactoring. However, the refactorings produced by LLMs often introduce subtle errors, leading to functional behavior changes and failed unit tests, which limit their practical adoption. To address the limitations of LLM-generated refactorings, we analyze the root causes of their failures and develop the RefactorAssist agent to improve the functional correctness of LLM-generated refactorings. To this end, we use 10 open-source Java projects with their native test suites and manually evaluate why LLM-generated refactorings fail unit tests. We then design an agentic approach that leverages unit-test logs, error explanations, project context retrieval, and code diffs to guide the iterative refactoring. Our findings show that the main reasons for failure are context misunderstanding/hallucination (24.3%), incorrect or inconsistent renaming (15.3%), adding new functionality or variables (13.7%), code incompleteness (11.3%), syntax and structural errors (9.7%), edge cases not handled (9%), improper type handling (8.7%), and variables outside scope (8%). To make our approach cost-effective, RefactorAssist first applies a static repair step for missing imports, unbalanced brackets, and compilation errors without LLMs. For remaining failures, RefactorAssist incorporates error logs and code diffs, achieving up to a 70.8% repair rate on the remaining failures and a 94.2% cumulative pass rate under the best-performing configuration. These results indicate that static checks and test-guided, context-aware agentic repair can increase the reliability of LLM-generated refactorings, bringing them closer to practical integration within developer workflows.

Retrieval-augmented generation (RAG) imposes a prefill cost proportional to retrieved context length, and -- with Transformer backbones -- a KV-cache that grows with each generated token. State-Space Models (SSMs) avoid the second cost by construction; we eliminate the first, collapsing prefill from $O(L_{context})$ to $O(1)$ per query. We introduce PRECOG (Pre-Computed Context Injection), a retrieval mechanism that exploits a property unique to SSMs: the fixed-size, position-agnostic recurrent hidden state is a complete summary of everything the model has read. PRECOG pre-encodes document corpora offline as SSM hidden states and injects the best-matching state directly at query time, bypassing in-context re-ingestion entirely. The same state-injection mechanism enables SMC (Structured Memory Consolidation): a hierarchical persistent memory with cognitive-domain clustering, an adjustable fidelity-vs-storage dial, and $O(1)$ session initialization, which consolidates short-term episodic states into long-term semantic memory and fuses both with retrieved corpus states at query time. We demonstrate the system on TENNs-LLM, a 1.2B-parameter gated-SSM language model with a 192 KB hidden state. PRECOG matches in-context RAG answer quality, reducing prefill latency from $\sim$27 s to $<$6 ms on edge hardware -- a $\sim$4500$\times$ speedup that crosses the threshold from unusable to interactive. The mechanism is architecturally impossible for Transformer KV-caches, which are position-entangled and grow linearly with context length.

Learning-based memory systems for self-evolving LLM agents face two tightly coupled challenges. First, trajectory-indexed utilities grow with the interaction history, thereby dispersing limited feedback over an ever-expanding state space. Second, because trajectory-level rewards are jointly assigned to co-retrieved memories, irrelevant experiences may receive misleading utility updates and consequently enter the memory-reward trap. To address these challenges, we introduce Reduced-Order Memory Reinforcement Learning (RoMeRL), which represents the growing trajectory-indexed utility space using a fixed-dimensional per-task memory state factorized by outcome polarity and memory dynamics. RoMeRL incorporates new experiences through a fixed set of semantic coordinates whose contents are updated or replaced over time, thereby concentrating feedback over a bounded utility support. Theoretically, we show that this reduced-order parameterization increases the average feedback received by each utility coordinate and characterize the steady-state occupancy of erroneous coordinates under a generic coordinate-transition model. Empirically, across ALFWorld and LifelongAgentBench, RoMeRL improves task performance, reduces the Cold-Q ratio by 80.0%, increases feedback density by approximately 6.0 times, reduces the maintained memory size by 84.4%, and cuts LLM calls by 21.1%. These results show that reduced-order utility states support efficient self-evolving agent memory while limiting persistent reward contamination. Code is available at: https://github.com/YOUNG-fnxm/RoMeRL

Long-term personalized dialogue agents must track user preferences as their personas evolve. Existing memory systems organize past events well, but store personas as flat profiles detached from the events that justify them. This loose coupling leads to the memory-persona validity gap and the persona-aware retrieval gap. We propose PGMem, a heterogeneous persona-memory graph that connects event and persona nodes through typed provenance and evidence edges, keeping each persona signal traceable to the events that support or revise it. At retrieval time, PGMem expands from query-relevant seeds and ranks signals by evidential validity. Across three benchmarks with small language model backbones, PGMem consistently outperforms summary-based, persona-aware, graph-structured, and agentic memory baselines, and improves performance as the context grows. The source code of PGMem is available at https://github.com/wonjunchoi23/pgmem/

Persistent memory allows (self-evolving) LLM agents to adapt across tasks by consolidating heterogeneous interaction histories into reusable facts, preferences, observations, and rules. Yet consolidation also imposes an implicit authorization boundary: it determines whether stored information may later be consumed as a user fact, an attested observation, or a standing instruction. We identify authority collapse, in which consolidation preserves a claim while erasing the source constraints governing its authorized use, causing the stored memory to imply greater authority than its source permits. We introduce AuthMem-Bench, a controlled paired benchmark that holds the focal claim and downstream task fixed while varying only source authority. It evaluates write-time collapse, downstream authorization errors, and automatic authority preservation. Across seven consolidators based on widely used agent-memory systems and seven LLM backbones, we observe authority collapse in 48 of 49 evaluated configurations. In a controlled action-grounded evaluation, collapsed memories without authority metadata yield a mean unauthorized-action rate of 50.3%. In an end-to-end evaluation, automatically predicted and persisted authority labels reduce the observed unauthorized-action rate from 16.9% to 0.0%, while benign task success remains essentially unchanged. These findings show that memory-driven adaptation must preserve not only what was learned, but also the authority under which it may be reused.

Memory-augmented agents can know that a user's stored state is outdated and still plan around the old value. The STALE benchmark calls this the implicit policy adaptation (IPA) gap. We identify one structural contributor: draft-anchored verification checks what a response says, and in an open-ended response the stale dependency is usually unsaid. StateAuditor therefore audits in the opposite direction, from stored state to draft. An LLM proposes candidate old-to-new transitions from timestamped evidence; deterministic code pins each quotation to a single entry, checks that the new evidence really is newer, and lets only these verified transitions trigger repair. What is verified is provenance and chronology - not semantic supersession. On STALE's full protocol (400 scenarios, 50-session histories, one independent response per query), strict single-query VTA scores .736 against .686 for our locked predecessor under the same judge: a +5.0-point paired gain (95% CI [+2.9, +7.2]) coming almost entirely from IPA and premise resistance (PR). The benchmark's own judge, from a third model family, reproduces the gain (.738 vs. .680). On an independent cross-family preference-evolution benchmark (HorizonBench), the full draft-audit-repair pipeline over a gold-derived structured store raises current-preference accuracy (user-clustered p<.01), though a matched control shows most of this external gain is the draft-side audit itself; a harder authored lifecycle set gives no gain, bounding the claim while false invalidation stays controlled. On STALE, by contrast, a matched control (same evidence, adapter, and call budget) scores only .692 (+0.6 over the predecessor, n.s.), attributing the STALE gain to the transition machinery rather than added context or calls. We make no claim about general-purpose agent memory.

Large language model (LLM) agents learn world dynamics from local interaction experience to support subsequent planning and action selection. However, the experience available to a single client is often incomplete, which motivates sharing knowledge across clients. Existing federated methods mainly aggregate model parameters, while agent memory-sharing methods commonly pool trajectories, memories, or rules without checking whether they remain valid for each client. This assumption is problematic because the same abstract action may produce different effects under different policies, environments, or exception conditions. Consequently, a rule supported by most clients may overwrite correct knowledge held by a minority client. To address this problem, we propose FEDWORLD, a scope-aware federated world-model protocol that exchanges structured abstract transition rules. Each client converts private transitions into normalized rules, and the server aligns related rules to identify each rule supporting and contradicting evidence across clients. The resulting evidence determines whether a rule is shared, cluster-specific, private, or unresolved. Each target client retains its local rules and accepts federated updates only for uncovered cases whose inferred scope is compatible; ambiguous rules are withheld. Experiments on $τ$-bench and ALFWorld show that FEDWORLD reduces negative transfer under conflicting dynamics while retaining useful cross-client transfer, leading to fewer state regressions, repeated actions, and excess steps, as well as higher task success.

Interaction between users and LLM agents is increasingly multimodal: conversations interleave text with images, and a later question may target either. Yet most agent memories are designed around text, and even the few that support multimodal conversations still fail on vision-related questions. We trace this failure to an assumption behind the similarity search they rely on: in the index space, a query lies close to the relevant evidence that answers it. In multimodal settings, two gaps break it. By the modality gap, a query lies closer to memory content of its own modality than to evidence in another, even in a trained joint embedding space. By the similarity-relevance gap, the content most similar to a query is often not the evidence that answers it, most acutely when a query carries both text and image and its evidence resembles neither part alone. We present V-Mem, a multimodal agentic memory system that routes retrieval by the modality of the query and that of the target evidence, both recognized from the query alone. To cross the modality gap, V-Mem organizes the conversation into rounds and returns the target-modality content from the same round as the match, without comparing across modalities. To close the similarity-relevance gap, it searches with an LLM-generated anchor that sits closer to the relevant evidence than the query does: a hypothetical caption for a text-only query seeking an image, and an enriched search anchor, the query text plus relevant keywords extracted from the query image, when the evidence is reachable only by combining the two. On Mem-Gallery, V-Mem reaches an LLM-judge score of 0.82 versus 0.56 for the second best, with the largest margin on questions carrying an image (0.87, no baseline above 0.47); on LoCoMo it scores 0.69 versus 0.58.

The continued development of LLMs toward persistent and adaptive intelligence increasingly requires long-term memory mechanisms that preserve and reuse information across interactions. Existing memory systems either compress and structure histories for efficient access or perform deep research over broader trajectories. The former lowers online cost but may omit temporal, causal, or cross-step dependencies, while the latter improves evidence coverage at substantial latency and inference cost. This raises a key question: can a memory system achieve strong answer quality while maintaining low online latency? We introduce Router-Mem, an evidence-conditioned progressive execution framework for long-horizon agent memory. Router-Mem first applies a shared low-cost retrieval prefix to obtain evidence. A lightweight sufficiency router then predicts whether the context supports early termination, which enable a single-token decision at inference time. It is trained with evidence-level supervision and rationale-conditioned representation distillation. When evidence is insufficient, Router-Mem reuses retrieval hits to expand memory blocks and perform deeper analysis and aggregation. Experiments on AMA-Bench and BEAM show that Router-Mem achieves 55.17\% and 38.77\% score while reducing average inference time by 27.3\% and 25.5\% compared with full memory execution.

Long-term memory is essential for LVLM agents to maintain consistency and integrate information across extended multimodal interactions. Existing agent memory systems, however, often reduce visual experiences into textual summaries or rely on static retrieve-then-reason pipelines, which are inefficient at query time and brittle when questions require image-text binding, temporal updates, or visual details. We propose Prospective Multimodal Memory Compilation, a framework that shifts part of the memory reasoning process from query time to memory consolidation time. Given accumulated multimodal interactions, a Questioner predicts future question candidates, a Planner compiles question-conditioned multimodal memory programs, and a Doubter verifies whether the planned evidence path can support the predicted answer. The verified question-program pairs form a structured question bank for efficient query-time routing and evidence retrieval. Experiments on multimodal long-term memory benchmarks show that our method improves answer quality and visual evidence recall while reducing query-time token and latency costs. Extensive ablations analyze the effects of self-feedback, dynamic planning, raw-image access, and question bank coverage.

Service robots operating for months in the same homes, offices, and facilities should become more reliable with experience instead of searching familiar space from scratch for every request. Yet ObjectNav is predominantly formulated as one-shot exploration, leaving a central deployment challenge unresolved: recognizing an object does not identify a reachable place to stop, and one confident map error can terminate the task. We introduce SSTG-Nav, a reusable metric-semantic memory that turns a one-time survey into actionable object goals, consolidates evidence across viewpoints, and retains spatially distinct recovery standoffs. On 1,000 HM3D-v2 episodes across 36 scenes, our goal-independent topology achieves a 99.4% geometric success ceiling. Holding semantic responses fixed, metric grounding raises SR/SPL from 0.835/0.560 to 0.920/0.603, and source-aware fusion reaches 0.926/0.586. Fusion-aware Top-3 recovery raises Success@1/2/3 to 0.928/0.965/0.975 and reaches 0.601 SPL@3. Model, field-of-view, density, and corruption controls identify where these gains originate, and a ROS2/Nav2 realization demonstrates the complete reusable query-to-execution pipeline. Together, the results establish pre-exploration as a powerful practical regime for dependable, repeated semantic navigation.