Understanding why independently trained neural networks from different modalities converge toward shared representations, and where this convergence leads, remains an open question in representation learning. All existing evidence relies on symmetric similarity measures, which can detect convergence but are structurally blind to its direction. We introduce directional convergence analysis using cycle-kNN, an asymmetric alignment measure, applied across dozens of independently trained unimodal models spanning point clouds, vision, and language. We uncover a consistent directional asymmetry: non-language modalities move toward the neighborhood structure of language significantly more than the reverse, and this pattern holds across all model families and scales--yet is entirely invisible to symmetric measures. Mechanistic analysis traces the directionality to feature density asymmetry, whereby language representations occupy the most compact regions of representational space. The Information Bottleneck framework provides a principled interpretation: optimization under compression drives representations toward discrete, compositional structures characteristic of language. We formalize this as the Wittgensteinian Representation Hypothesis: the semantic structure of language is the asymptotic attractor of multimodal representation convergence.

Smart-contract exploits have caused billions of USD in cumulative losses, yet audits remain expensive and slow. Automated tools have emerged to close this gap, but each class has a characteristic failure mode. Static analyzers report findings that frequently fail manual triage at high rates, while large language models (LLMs) hallucinate findings that contradict the source code. Thus, we propose Chaintrix, an end-to-end auditing framework whose central architectural commitment is that every LLM-generated claim must be discharged against a deterministic structural contract representation. We introduce a Cross-Contract Interaction Model (CCIM) that parses Solidity into a structured map of function-level reads, writes, modifiers and resolved cross-contract calls. CCIM serves as the substrate against which all 12 of Chaintrix's deterministic signal engines and the parallel LLM audit pipelines operate. A staged false-positive-reduction pipeline, terminating in a Structural Verdict Engine (SVE) that applies deterministic structural checks against parsed code, filters the merged finding set, with selected high-confidence findings further validated through symbolic execution and fuzz testing. We evaluate Chaintrix on EVMbench, the smart-contract security benchmark by OpenAI, Paradigm, OtterSec. Chaintrix detects 86 of 120 high-severity vulnerabilities (71.7% recall), with 25 audits scoring 100% recall, placing Chaintrix 26 percentage points above the strongest frontier-model baseline.

Large Language Models (LLMs) provide flexible natural language processing capabilities, while knowledge graphs (KGs) offer explicit and structured knowledge. Integrating these two in a complementary manner enables the development of reliable and verifiable AI systems. In particular, knowledge graph question answering (KGQA) has attracted attention as a means to reduce LLM hallucinations and to leverage knowledge beyond the training data. However, existing KGQA benchmark datasets are biased toward encyclopedic knowledge, limited to a single modality, and lack fine-grained spatiotemporal data, which limits their applicability to real-world scenarios targeted by Embodied AI. We introduce HOME-KGQA, a novel KGQA benchmark dataset built on a multimodal KG of daily household activities. HOME-KGQA consists of complex, multi-hop natural language questions paired with graph database query languages. Compared to existing benchmarks, it includes more challenging questions that involve multi-level spatiotemporal reasoning, multimodal grounding, and aggregate functions. Experimental results show that the LLM-based KGQA methods fail to achieve performance comparable to that on existing datasets when evaluated on HOME-KGQA. This highlights significant challenges that should be addressed for the real-world deployment of KGQA systems. Our dataset is available at https://github.com/aistairc/home-kgqa

Discrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete variables is to binarize them into Boolean variables to allow the use of Boolean computational machinery such as SAT solvers. This technique can face both computational and semantical challenges though. In this work, we develop a native SAT solver for discrete logic, which is a direct extension of Boolean logic in which variables can take arbitrary values. Our proposed solver has a similar design to Boolean SAT solvers, with ingredients such as unit resolution and clause learning but ones that operate natively on discrete variables. We illustrate the merits of the developed SAT solver by comparing it empirically to CSP solvers applied to discrete CNFs, to Boolean SAT solver applied to binarized CNFs, and to some hybrid solvers.

The Chain-of-Thought (CoT) paradigm, while enhancing the interpretability of Large Language Models (LLMs), is constrained by the inefficiencies and expressive limits of natural language. Latent Chain-of-Thought (latent CoT) reasoning, which operates in a continuous latent space, offers a promising alternative but faces challenges from structural complexities in existing multi-step or multi-model paradigms, such as error propagation and coordination overhead. In this paper, we introduce One-Model One-Step, a novel compression framework for Latent Reasoning with Rule-Based Priors(RuPLaR) to address this challenge. Our method trains an LLM to autonomously generate latent reasoning tokens in a single training stage, guided by rule-based prior probability distributions, thereby eliminating cascaded processes and inter-model dependencies. To ensure reasoning quality, we design a joint training objective that enforces answer consistency via cross-entropy, aligns soft tokens with rule-based priors via KL divergence (the Soft Thinking constraint), and adds a problem-thought semantic alignment constraint in the representation space. Extensive experiments show that our compression framework not only improves accuracy by 11.1% over existing latent CoT methods but also achieves this with minimal token usage, underscoring its effectiveness and extensibility. Code: https://github.com/xiaocen-luo/RuPLaR.

We identify a Selection Plateau phenomenon in one-shot neural network pruning: all rank-monotone weight scorers converge to identical accuracy at fixed sparsity, independent of functional form. We propose the Sparsity-Information-Complexity Spectrum (SICS) hypothesis: a sparsity-dependent minimum feature complexity kappa(S) governs plateau escape, with kappa=0 sufficient at low sparsity (S<0.65), kappa=1 dominant at critical sparsity (S~0.7), and kappa=2 necessary at extreme sparsity (S>0.75). On ViT-Small/CIFAR-10, testing nine feature classes across four sparsities, smooth non-monotone features provide +6.6% escape at S=0.7, while only raw features with high-frequency wiggle escape at S=0.8 (+2.6%). A fake non-monotone scorer underperforms the gradient baseline, indicating the requirement is magnitude-independent non-monotonicity. A handcrafted Gaussian bump achieves only +0.006 escape vs. chaos-derived +0.046, indicating rank-alignment is necessary but insufficient. SICS provides a unifying explanation for the performance clustering of diverse pruning methods and suggests that future selection algorithms should adapt feature complexity to target sparsity.

Most path planners assume fully known, static environments, assumptions that fail when robots navigate in dynamic and partially observable environments. SMART-3D addresses these issues by real-time replanning, where it morphs the underlying RRT* tree whenever new obstacles or structures are discovered in the environment. Instead of rebuilding the tree entirely from scratch, SMART-3D prunes invalid nodes and edges and subsequently repairs the disjoint subtrees at hot-nodes to find a new path, thus providing high computational efficiency for real-time adaptability. We extend SMART-3D to perception-enabled collaborative multi-agent navigation (PECMAN) in unknown environments. PECMAN is built upon distributed tree morphing and shared perception strategies, where each agent reacts to environmental changes and morphs its respective tree to replan its path, while simultaneously broadcasting newly discovered structures to other agents, thus enabling them to proactively replan even in areas that have not yet been explored by them. This approach reduces redundant reactions and unnecessary replannings of the agents due to improved situational awareness. The performance of PECMAN was evaluated by 28,000 multi-agent simulations on seven 2D scenarios with different case studies. The results show that PECMAN achieves up to 52% reduction in the team-completion time, while maintaining near 100% success rates. Finally, PECMAN was tested by real experiments on two autonomous robots in a building environment.

Decision making in large-scale complaint handling systems increasingly relies on heterogeneous evidence, including complaint narratives, screenshots, order metadata, historical interactions, and platform policies. Existing complaint understanding systems mainly perform shallow classification or template matching over isolated modalities, while underutilizing explicit scene structure, rule knowledge, and cross-evidence dependencies. To address this limitation, we present SKG-VLA for multimodal complaint decision making. The core idea is to model each case as a structured complaint scene and represent its decision-relevant semantics with a \emph{Scene Knowledge Graph} (SKG), which organizes complaint entities, evidence items, policy clauses, temporal events, transactional states, and action-relevant relations into a unified graph. Based on SKG, we build a data synthesis pipeline that generates complaint scene descriptions, rule-consistent graph generalizations, question-answer supervision, and decision recommendations. We further construct a large-scale complaint scene dataset with both text-only and multimodal in-domain benchmarks. Finally, we adopt a three-stage training strategy -- domain-adaptive pre-training, task-oriented instruction fine-tuning, and end-to-end multimodal alignment -- to inject structured scene priors into a multimodal decision model. Experiments show that SKG-VLA consistently improves policy-grounded reasoning, complaint decision accuracy, long-tail generalization, and robustness under incomplete evidence.

Human color categories are not uniformly distributed in perceptual space, yet most computational color models still assume fixed and evenly structured representations. In this paper, we present a focused analytical extension of the COLIBRI fuzzy color model by investigating perceptual asymmetry between hue categories. Using previously collected large-scale human color categorization data, we introduce quantitative measures of category extent and boundary uncertainty, namely Wideness and Boundary Width, derived from fuzzy membership functions at the α = 0.5 level. The analysis reveals a strong imbalance between the two categories: yellow occupies a compact and sharply constrained region of the hue space, whereas green spans a substantially broader interval and exhibits a more extended transition structure. The results show that perceptual color categories are not only fuzzy, but also highly non-uniform in their geometric organization. This asymmetry suggests that some categories behave as narrow, highly specific perceptual labels, while others function as broad, tolerant regions of human color naming. These findings provide a new perspective on linguistic color categorization and extend the interpretability of the COLIBRI framework for perceptually grounded color modeling.

We propose FAR-SIGN (Fully Asynchronous Robust optimization via SIGNed directional projections) for adversary-resilient learning in parameter-server--worker systems. FAR-SIGN achieves robustness through sign-based updates along carefully designed directions and mitigates the resulting bias via a two-timescale mechanism. It admits both first-order and zeroth-order implementations and enables fully asynchronous execution without requiring a private reference dataset at the server. We establish almost-sure convergence of FAR-SIGN to the set of stationary points for smooth, nonconvex objectives. Moreover, we prove the near-optimal rate of $O(n^{-1/4+ε})$ in the first-order setting and the standard $O(n^{-1/6+ε})$ in the zeroth-order setting, where $n$ is the iteration count and $ε>0$ can be chosen arbitrarily small. Experiments on MNIST show that FAR-SIGN outperforms robust aggregation-based methods in both accuracy and wall-clock time.

Sparse goal-conditioned reinforcement learning can produce policies whose failures are hidden by aggregate success rates. We analyze trained goal-conditioned value policies through the deterministic functional graphs induced by greedy evaluation: for each goal, every state maps to a single successor, decomposing behavior into attractors and basins. This reveals a local-to-global structure in learned policies. We define local goal support (LGS), a one-step statistic measuring the fraction of valid neighboring states whose greedy successor is the goal. In deterministic sparse GridWorlds, zero LGS exactly precludes goal entry from non-goal starts. Empirically, weak LGS is a strong diagnostic of goal-level failure across update rules, curricula, larger grids, and bottleneck geometries: the fixed rule LGS <= 0.5 identifies low-success goals with precision 0.921, recall 0.929, and F1 0.925 in the main 8x8 TD setting, with similar performance across variants. However, local support is not sufficient for global success: some supported goals still fail because distant states are captured by competing attractors or fragmented basin structure. We therefore introduce a compact post-hoc taxonomy of policy-induced graphs -- goal-dominant, competitor-dominated, partial/contested, and fragmented -- to characterize residual failure modes beyond local support. These results show that sparse GCRL failures can be understood as structured policy-induced dynamics, and that local one-step policy structure provides a cheap post-training diagnostic for goal-level failure.

Modern Large Language Model (LLM) training is fundamentally bottlenecked by pathologically flat saddle points in extreme high-dimensional landscapes. Motivated by this challenge, we analyze the saddle-point escape dynamics of the emerging Muon optimizer, demonstrating its resilience against the $\mathcal{O}(D)$ dimensional curse that severely traps element-wise adaptive optimizers like AdamW. By extending generalized matrix perturbation theory, we develop a theoretical framework to capture Muon's non-equilibrium optimization trajectories. This theoretical machinery mathematically proves that Muon elegantly bypasses the dimensional curse via a non-linear spectral shaping mechanism. By leveraging resolvent functional calculus and macroscopic Cauchy contour integration, we avoid isotropic noise assumptions and Tracy-Widom edge singularities. We establish that structural incoherence securely shields the trajectory from orthogonal drift, enabling a dimension-free saddle-point escape, and triggering a deterministic $\mathcal{O}(1)$ discrete ballistic ejection under sufficient spectral gap. Consequently, we provide an algebraically dimension-free escape bound for Muon, formalizing the underlying mechanics of its non-convex optimization dynamics.

Agentic memory enables LLMs to persist information beyond a single context window and reuse it in later decisions, but it also introduces a new vulnerability: spurious correlations, where retrieved memory carries miscorrelated evidence and propagates erroneous reasoning into downstream decisions. Despite the widespread use of agentic memory, this risk remains largely underexplored. We address it from two aspects. First, we benchmark several canonical types of spurious patterns identified through causal structure and record them across trajectory-level memory. Diagnosing agentic memory systems on this benchmark reveals that memory improves reasoning on clean inputs but amplifies reliance on spurious patterns when they are present. Second, we propose CAMEL, a plug-and-play calibration method that operates across diverse memory architectures at both write and retrieval time. CAMEL consistently reduces reliance on spurious patterns across all three types while preserving or improving performance on clean inputs and staying robust under adaptive attacks targeting the calibration. Overall, CAMEL offers a principled and lightweight solution toward more reliable agentic memory deployment.

Pre-trained text-to-image (T2I) diffusion models have shown strong potential for real-world image super-resolution (Real-ISR), owing to their noise-started generation process that enables realistic texture synthesis and captures the one-to-many nature of super-resolution. However, diffusion-based Real-ISR methods still face a fundamental efficiency-quality trade-off. Multi-step methods generate high-quality results by iteratively denoising random Gaussian noise under LR conditioning, but suffer from slow sampling. Recent one-step methods greatly improve efficiency, yet they typically replace noise-started generation with direct LR-to-HR restoration, which weakens stochasticity and limits realistic detail synthesis. To address this issue, we propose SMFSR, a noise-started one-step Real-ISR framework via LR-conditioned SplitMeanFlow and GAN refinement. SMFSR preserves the random-noise starting point of diffusion models and learns a direct noise-to-HR mapping conditioned on the LR image. To this end, Interval Splitting Consistency distills the multi-step generative trajectory into a single average-velocity prediction, enabling efficient one-step generation. To compensate for the reduced opportunity for progressive refinement, we further introduce a GAN refinement stage, where a DINOv3-based discriminator enhances realistic texture synthesis and variational score distillation aligns the generated outputs with the natural image distribution under a frozen diffusion teacher. Extensive experiments demonstrate that SMFSR achieves state-of-the-art perceptual quality among one-step diffusion-based Real-ISR methods while retaining fast single-step inference.

With the proliferation of AI-generated images, digital watermarking has become an essential safeguard for protecting intellectual property and mitigating malicious exploitation. Recent works on semantic watermarking have enabled efficient copyright protection for diffusion models. However, the dependence of semantic watermarking on diffusion inversion for watermark detection creates a critical vulnerability. Imprint removal and forgery attacks exploit this weakness to produce deceptive results. Our analysis reveals that these attacks succeed by displacing watermarked latents into the unwatermarked region, while guiding unwatermarked latents into the watermarked region. Based on that, we propose Progressive Guided Inversion and Denoising (PGID), the first plug-and-play, training-free noise extraction framework designed to defend against both attack strategies. PGID effectively defends by projecting perturbed latents back to the region where they originally belong. The projection is achieved by eliminating intermediate latent deflections and mitigating adversarial perturbations through progressive inversion-denoising cycles. Comprehensive evaluations across multiple schemes demonstrate that PGID successfully restores detection reliability by recovering removed watermarks and identifying forged instances.

GUI agents are beginning to operate the web, mobile, and desktop as interactive worlds, where successful control depends on carrying forward visual, procedural, and task-level evidence beyond the fleeting present screen. Yet most agents still treat memory as an external, human-readable artifact: histories are summarized, categorized, retrieved, and reinserted as text or structured records before being encoded again by the policy. This creates a mismatch between the representational form in which experience is stored and the latent embedding sequence over which modern GUI policies actually act. We introduce Mem-W, a series of latent-memory-native GUI agents that treat memory as part of the agent's continuous context rather than as an auxiliary symbolic scaffold. Mem-W weaves both historical trajectories (as experiential memory) and in-session segments (as working memory) into compact memory tokens through a shared trajectory-to-latent compressor. These tokens are woven with the current GUI observation and local context into one continuous embedding sequence, allowing the agent to read successes, failures, and unfinished progress through the same machine-native interface. Mem-W is trained with self-distillation and outcome-aware supervision to preserve decision-relevant state while filtering memory toward evidence that truly supports task success. Across four web and mobile navigation benchmarks, Mem-W consistently improves diverse backbones and memory-enhanced baselines, with gains of up to $+30.0$, suggesting that latent-context-native memory can serve as a scalable foundation for long-horizon GUI agency.

Recent advances in LLM agents enable systems that autonomously refine workflows, accumulate reusable skills, self-train their underlying models, and maintain persistent memory. However, we show that such self-evolution is often non-monotonic: adapting to new task distributions can progressively degrade previously acquired capabilities across all major evolution channels. We identify this phenomenon as \emph{capability erosion under self-evolution} and show that it consistently emerges across workflow, skill, model, and memory evolution. To mitigate this issue, we propose \emph{Capability-Preserving Evolution} (CPE), a general stabilization principle that constrains destructive capability drift during continual adaptation. Across all four evolution dimensions, CPE consistently improves retained capability stability while preserving adaptation performance. For example, in workflow evolution, CPE improves retained simple-task performance from 41.8\% to 52.8\% under GPT-5.1 optimization while simultaneously achieving stronger complex-task adaptation. Our findings suggest that stable long-horizon self-evolving agents require not only acquiring new capabilities, but also explicitly preserving previously learned ones during continual adaptation.

Language models can be persuaded to abandon factual knowledge. This vulnerability is central to AI safety, but its internal mechanism remains poorly understood. We uncover a compact causal mechanism for persuasion-induced factual errors. A small set of mid-layer attention heads almost entirely determines the model's answer. These heads write answer options into a low-dimensional polyhedron, with options occupying distinct vertices. Persuasion does not blur belief or merely reduce confidence; it causes a discrete latent jump from the correct-answer vertex to the persuasion-target vertex. We show that decision heads are not reasoning over evidence. Instead, they copy whichever option token their attention selects. Persuasion works by redirecting attention. We isolate a rank-one evidence-routing feature that controls the route. Directly modifying this feature steers the model's choice, and removing it blocks persuasion. We then trace the feature back to a band of shallower attention heads that build it from persuasive keywords in the input. Every step is validated by intervention. This mechanism appears across open-source LLMs and realistic poisoning scenarios such as Generative Engine Optimization, revealing persuasion as a narrow, monitorable circuit.

Neural Radiance Fields (NeRF) achieve high-quality novel-view synthesis, but their long training times and reliance on dense input views limit accessibility. We present a comparative study of three accelerated NeRF variants - DS-NeRF, TensoRF, and HashNeRF and explore extensions targeted at the low-compute, low-data regime. First, we add a depth-supervision loss derived from COLMAP keypoints to TensoRF (TensoRF-DS) and evaluate it on the LLFF dataset under reduced view counts. Second, we ablate the feature-decoding MLP of TensoRF and study the effect of input downsampling on PSNR and runtime on the synthetic Lego scene. Third, we propose four architectural variants of the HashNeRF color and density networks, including residual and convolutional designs, and report PSNR/training-time tradeoffs under matched iteration budgets. Under iso-time evaluation, none of our extensions conclusively outperform the published baselines, but the experiments characterize which extensions transfer to constrained settings and surface design questions for future work.

Unlike most static material properties widely studied in the machine learning literature, ionic transport properties are inherently dynamic, making their fast and accurate prediction from static atomic structures challenging. The current standard approach, molecular dynamics (MD) simulations, suffers from prohibitively high computational cost. Recent autoregressive learning-based MD acceleration methods requiring sequential inference remain slow and prone to error accumulation; in contrast, existing non-autoregressive material property prediction models are less accurate because they fail to exploit dynamics. Moreover, existing methods typically benefit from datasets either with or without atomic trajectories, but not both. To overcome these limitations, we propose a non-autoregressive learning framework based on auxiliary modality learning, which treats atomic trajectories as an auxiliary modality during training but does not require them at inference. This enables the predictor to learn dynamics without sequential inference while benefiting from both types of datasets. As a result, our framework achieves over 200 times speedup compared to autoregressive models on the dataset with atomic trajectories while substantially reducing prediction error relative to non-autoregressive benchmarks across both types of datasets. Our code is available at https://github.com/jykim-git/MD.

ESG-aware portfolio optimization is increasingly important for sustainable capital allocation, yet most learning-based methods still operationalize ESG by appending static scores to the policy observation or reward. This creates a mismatch for sequential control: ESG scores are noisy, provider-dependent, low-frequency, and temporally misaligned with sequential portfolio decisions, while financial evidence suggests that ESG is better treated as a portfolio preference, risk-exposure, or hedge dimension than as a robust alpha factor. We propose to impose ESG constraints without modifying the financial policy's observation or reward, using a Multimodal Action-Conditioned Constraint Field (MACF) that learns mechanism-specific ESG costs from point-in-time multimodal evidence and contemplated portfolio transitions. We then introduce MACF-X, a family of optimizer-specific adapters that converts MACF costs and uncertainties into native constrained-optimization interfaces through a shared slack- and uncertainty-aware pressure layer. Across multiple constraint-integration interfaces, MACF-X reduces tail ESG budget pressure while maintaining competitive financial performance. Ablations show that this improvement depends on dynamic evidence inputs and three-head decomposition, while static ESG-score proxies are nearly indistinguishable from score-shuffled noise baselines.

Graph Neural Networks (GNNs) excel at relational reasoning but face two persistent challenges: the lack of interpretable attribution for heterogeneous node types, and the computational overhead of message passing over large, noisy graphs. We propose the Hierarchical Attention-based Heterogeneous GNN (HA-HeteroGNN), a framework that addresses both issues through a unied explainability-to-pruning pipeline. A two-tier attention mechanism separates sensor-level and context-level computation across 16 node types and 18 edge types, producing per-node relevance scores via an attention-based GNN Explainer without requiring gradient backpropagation. These relevance scores then serve as a principled pruning criterion: removing nodes identied as consistently uninformative yields a 27% reduction in graph edges while simultaneously improving classication accuracy by 2.46.1% across all model variants, challenging the conventional assumption that pruning necessarily trades accuracy for eciency. Experiments on a 50,000-record synthetic dataset spanning 11 report categories demonstrate 97.5% cross-strategy explanation stability and domain consistent sensor attribution, with training-time reductions of up to 43.9% and real-time inference latency of approximately 5860 ms per sample.

Diffusion language models (DLMs) offer a structural alternative to autoregressive generation: denoising can update tokens in arbitrary orders or in parallel rather than along a fixed left-to-right chain. In practice, fast DLM decoding remains strongly order-sensitive and often drifts toward autoregressive-like trajectories. We trace this tension to compatibility. At each reverse-time step, a DLM provides local denoising conditionals over the unresolved tokens. Arbitrary-order denoising becomes well defined when these local conditionals compose into order-invariant pseudo-joints. We formalize this view by defining order-induced pseudo-joints and a local denoising circulation: the log-ratio between the two pseudo-joints obtained by swapping a pair of unresolved positions. This circulation is zero under compatible conditionals, and global order gaps decompose into sums of local circulations along adjacent swaps. We further separate incompatibility-driven path dependence from conditional-dependence error in parallel updates and from order-specific estimation error. The resulting framework provides inference-only diagnostics for testing when DLM decoding is genuinely order-free.

We study posterior sampling for inverse problems in discrete state spaces using discrete diffusion models as generative priors. While continuous diffusion models have become widely used for inverse problems, their discrete counterparts remain comparatively underexplored. Existing discrete posterior samplers often rely on continuous relaxations of discrete variables, Gibbs-style updates, or mechanisms specialized to particular corruption processes, which can limit scalability or generality. We propose $Δ$LPS, a Discrete Langevin-Inspired Posterior Sampler that uses gradient information to identify promising discrete moves without leaving the discrete state space. The resulting approach enables efficient parallel updates across all token dimensions and is agnostic to the training paradigm of the discrete diffusion prior, including masked and uniform-state diffusion. We evaluate our method on image restoration tasks across MNIST, CIFAR, and FFHQ, as well as spatial mapping, covering linear, nonlinear, and blind inverse problems. Across these settings, we improve over recent discrete diffusion posterior samplers and are competitive with strong continuous diffusion-based inverse solvers. Our results suggest that fully discrete, gradient-informed posterior samplers offer a scalable and general path toward solving inverse problems over discrete representations.

The Capacitated Vehicle Routing Problem (CVRP) underpins modern last-mile logistics. Current Neural Combinatorial Optimization (NCO) methods construct CVRP solutions autoregressively, inheriting sequential decoding bottlenecks, sensitivity to spatial symmetries, and brittle out-of-distribution behavior. We revisit the classical Cluster-First-Route-Second (CFRS) paradigm -- long known to be asymptotically optimal but largely overlooked by NCO -- and argue that it is structurally aligned with the core strengths of deep learning: similarity and assignment over global context, rather than the construction of long sequential tours. We introduce Neural CFRS, the first purely non-autoregressive one-shot neural CFRS framework for the CVRP. It enforces global fleet-capacity constraints end-to-end via a differentiable entropic Optimal Transport layer, producing a continuous transport plan to sparsify an exact capacitated assignment solver. We provide formal theoretical guarantees that our architecture intrinsically abstracts away $E(2)$ spatial, inter-route permutation, and intra-route traversal symmetries. By equipping the framework with a pre-trained spatial vocabulary, we unlock extreme parameter efficiency and zero-shot scaling. Designed primarily for real-world spatial distributions under a constant capacity setting, Neural CFRS scales robustly to out-of-distribution $N=1000$ instances with a < 4% gap -- retaining an approximate 5% gap at this scale even as an ultra-lightweight, single-layer architecture. Furthermore, when deployed out-of-the-box on standard benchmarks, we achieve a highly competitive 2.73% optimality gap on size-100 problems.

Recent generative models can produce images that appear highly realistic, raising challenges in distinguishing real and AI-generated images. Yet existing detectors based on pre-trained feature extractors tend to over-rely on global semantics, limiting sensitivity to the critical micro-defects. In this work, we propose Micro-Defects expose Macro-Fakes (MDMF), a local distribution-aware detection framework that amplifies micro-scale statistical irregularities into macro-level distributional discrepancies. To avoid localized forensic cues being diluted by plain aggregation, we introduce a learnable Patch Forensic Signature that projects semantic patch embeddings into a compact forensic latent space. We then use Maximum Mean Discrepancy (MMD) to quantify distributional discrepancies between generated and real images. Our theory-grounded analysis shows that patch-wise modeling yields provably larger discrepancies when localized forensic signals are present in generated images, enabling more reliable separation from real images. Extensive experiments demonstrate that MDMF consistently outperforms baseline detectors across multiple benchmarks, validating its general effectiveness. Project page: https://zbox1005.github.io/MDMF-project/

Text-to-SQL translates natural language questions into executable SQL queries, enabling intuitive database access for non-experts. While large language models achieve strong performance on Text-to-SQL with prompting, they still struggle with complex queries that involve deeply nested logic or multiple clauses. A widely used approach employs SQL skeletons--intermediate representations of query logic--to streamline generation, but existing methods are limited by their reliance on a single structural hypothesis and lack of progressive reasoning. To overcome these limitations, we propose LEAF-SQL, a novel framework that reframes skeleton prediction as a coarse-to-fine tree search process. LEAF-SQL enables systematic exploration of diverse structural hypotheses with adaptive refinement. Several key techniques are employed in LEAF-SQL: (1) a three-level skeleton hierarchy to guide the search, (2) a Skeleton Formulation Agent to generate diverse candidates, and (3) a Skeleton Evaluation Agent to efficiently prune the search space. This integrated design yields skeleton candidates that are both structurally diverse and granularity-adaptive, providing a stronger foundation for the SQL generation. Extensive experiments show that LEAF-SQL consistently improves the performance of various LLM backbones. On the official hidden test set of the challenging BIRD benchmark, our method achieves 71.6 execution accuracy, which outperforms leading search-based and skeleton-based methods, affirming its effectiveness for complex queries.

We propose Representational Effective Theory (RET), a framework for describing large language model computation in terms of learned macrostates rather than microscopic details. RET learns these macrostates from hidden-state trajectories using a BYOL/JEPA-style self-supervised objective, coarse-graining activations into macrovariables that preserve higher-level structure relevant for prediction and interpretation. We evaluate whether these macrovariables are practically relevant for interpretability: RET yields temporally consistent states that reveal "mental-state" trajectories of reasoning, capture high-level semantic structure, support early prediction of behavioral outcomes such as sycophancy, and provide causal handles for steering generations toward interpretable computational phases. Together, these results suggest that LLM computation admits useful effective descriptions via RET: high-level, dynamically meaningful variables that support interpretation, prediction, and intervention.

Large language models now achieve high final-answer accuracy on mathematical reasoning benchmarks, but accuracy alone does not capture reasoning flexibility. We introduce a strategy-level evaluation framework instantiated on 80 AMC 10/12 and AIME problems with 217 AoPS-derived reference strategy families. Model outputs are annotated for strategy identity, validity, and correctness using dual-AI coding with human adjudication. Across four frontier models, we find a pronounced decoupling between answer accuracy and strategy diversity. Under a single-solution prompt, all models achieve high accuracy (95%-100%), but under a multiple-strategy prompt they recover substantially fewer strategies than the human reference set. Gemini, DeepSeek, GPT, and Claude generate 184, 152, 151, and 110 distinct valid strategies, respectively, with the largest gaps in Geometry and Number Theory. The models collectively produce 50 benchmark-novel valid strategies, indicating both incomplete coverage of human strategies and some capacity for alternative reasoning. A repeated-run robustness check on 20 problems shows diminishing gains in discovered strategies, with the strongest model recovering only 39 of 55 AoPS-reference strategies (71%) after three runs. These findings position strategy diversity as a complementary dimension for evaluating mathematical reasoning beyond answer correctness.

Discrete flow models (DFMs) are a class of flexible generative models for generating discrete data, and diffusion large language models (dLLMs) can be viewed as a special case with a specific choice of mixture path and a masked source distribution. While several recent works have explored reinforcement learning into dLLMs, its application to more general discrete flow models remains underexplored. In this work, we present discrete Flow-GRPO (dFlowGRPO), a unified reinforcement learning framework for discrete flow models that supports a broad family of probability paths and non-masked source distributions. We derive the full trajectory probability for DFMs and formulate denoising as a Markov decision process, enabling dFlowGRPO to incorporate information from both the associated conditional transition rates and the posterior model during reinforcement learning. We apply dFlowGRPO to FUDOKI, a recent multimodal discrete flow model, and evaluate it on both image generation and multimodal understanding tasks. Empirical results show that dFlowGRPO outperforms existing GRPO-type methods for dLLMs on text-to-image generation tasks and achieves performance competitive with continuous flow-based models trained using FlowGRPO, while also demonstrating strong capabilities on understanding tasks.