arXiv:2507.06445v2 Announce Type: replace
Abstract: Interpretability research often predicts model responses to targeted mechanistic interventions. But can we predict responses to unseen input data? We propose and demonstrate this alternate objective by using model internals to predict their out-of-distribution (OOD) behavior. We train hundreds of Transformers on simple synthetic tasks, where perfect in-distribution accuracy is compatible with multiple OOD generalization rules. We successfully use attention patterns -- observed only on in-distribution data -- to predict which rule each model follows on OOD data. Our experiments decouple the mechanistic faithfulness of our interpretation from its predictive value; ablations reveal such internal patterns can suppress rather than support the rule they predict, showing observational analysis can forecast behavior even when causal analysis fails to support a simple cause-effect link. Our findings are a proof-of-concept for a new interpretability objective: understanding model internals to predict behavior and assess reliability under distribution shift.
Science Journals
arXiv:2507.07247v2 Announce Type: replace
Abstract: As large language models (LLMs) and visual language models (VLMs) grow in scale and application, attention mechanisms have become a central computational bottleneck due to their high memory and time complexity. While many efficient attention variants have been proposed, there remains a lack of rigorous evaluation on their actual energy usage and hardware resource demands during training. In this work, we benchmark eight attention mechanisms in training GPT-2 architecture, measuring key metrics including training time, GPU memory usage, FLOPS, CPU usage, and power consumption. Our results reveal that attention mechanisms with optimized kernel implementations, including Flash Attention, Locality-Sensitive Hashing (LSH) Attention, and Multi-Head Latent Attention (MLA), achieve the best energy efficiency. We further show that lower GPU power alone does not guarantee reduced energy use, as training time plays an equally important role. Our study highlights the importance of energy-aware benchmarking in attention design and provides a practical insight for selecting resource-efficient mechanisms. All our codes are available at GitHub.
arXiv:2507.11234v3 Announce Type: replace
Abstract: The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) $\langle u_n \rangle_{n=0}^\infty$ over the integers has a zero term, that is, whether there exists $n$ such that $u_n = 0$. Decidability of the problem is open in general, with the most notable positive result being a decision procedure for LRS of order at most 4.
In this paper we consider a bounded version of the Skolem Problem, in which the input consists of an LRS $\langle u_n \rangle_{n=0}^\infty$ and a bound $N \in \mathbb N$ (with all integers written in binary), and the task is to determine whether there exists $n\in\{0,\ldots,N\}$ such that $u_n=0$. We give a randomised algorithm for this problem that, for all $d\in \mathbb N$, runs in polynomial time on the class of LRS of order at most $d$. As a corollary we show that the (unrestricted) Skolem Problem for LRS of order at most 4 lies in $\mathsf{coRP}$, improving the best previous upper bound of $\mathsf{NP}^{\mathsf{RP}}$.
The running time of our algorithm is exponential in the order of the LRS -- a dependence that appears necessary in view of the $\mathsf{NP}$-hardness of the Bounded Skolem Problem. However, even for LRS of a fixed order, the problem involves detecting zeros within an exponentially large range. For this, our algorithm relies on results from $p$-adic analysis to isolate polynomially many candidate zeros and then test in randomised polynomial time whether each candidate is an actual zero by reduction to arithmetic-circuit identity testing.
arXiv:2507.13576v4 Announce Type: replace
Abstract: This paper proposes a characterization of when one axiomatic theory, as a proof system for tautologies, $p$-simulates another, by showing: (i)~if c.e. theory $\mathcal{S}$ efficiently interprets $\mathcal{S}{+}\phi$, then $\mathcal{S}$ $p$-simulates $\mathcal{S}{+}\phi$ (Je\v{r}\'abek in Pudl\'ak17 proved simulation), since the interpretation maps an $\mathcal{S}{+}\phi$-proof whose lines are all theorems into an $\mathcal{S}$-proof; (ii)~$\mathcal{S}$ proves ``$\mathcal{S}$ efficiently interprets $\mathcal{S}{+}\phi$'' iff $\mathcal{S}$ proves ``$\mathcal{S}$ $p$-simulates $\mathcal{S}{+}\phi$'' (if so, $\mathcal{S}$ already proves the $\Pi_1$ theorems of $\mathcal{S}{+}\phi$). To explore whether this framework conceivably resolves other open questions, the paper formulates conjectures stronger than ``no optimal proof system exists'' that imply Feige's Hypothesis, the existence of one-way functions, and circuit lower bounds.
arXiv:2507.17091v3 Announce Type: replace
Abstract: Viscous drag arises from the fluid at a surface having zero relative velocity, a phenomenon known as the no-slip condition. Superhydrophobic surfaces, when submerged in water, trap a layer of air in their surface texture, partially replacing the liquid-solid interface with a liquid-gas interface. This air layer, called the plastron, results in partial slip at the surface, thereby reducing the viscous drag. In turbulent flows, large fluctuations in pressure and velocity can deplete or completely remove the plastron from the surface. This makes evaluating the effects of superhydrophobic surface treatments on flow dynamics particularly challenging. This study examines the impact of a sustained plastron on the dynamics in the shear layer of a sphere, achieved by supplying air at low pressure through pores in the sphere's surface. Instantaneous planar velocities in the wakes of spheres, both with and without superhydrophobic surface treatment, are measured within a plane passing through the spheres' centre. Dynamic mode decomposition (DMD) is applied to the velocity fluctuations in the shear layer to evaluate how superhydrophobic surface treatment affects the instabilities there. It is shown that the addition of the pores has a relatively small effect on the instabilities in the shear layer, while they are significantly changed by the addition of superhydrophobic surface treatment when the plastron is sustained.
arXiv:2507.18780v2 Announce Type: replace
Abstract: We consider data-driven reduced-order models of partial differential equations with shift equivariance. Shift-equivariant systems typically admit traveling solutions, and the main idea of our approach is to represent the solution in a traveling reference frame, in which it can be described by a relatively small number of basis functions. Existing methods for operator inference allow one to approximate a reduced-order model directly from data, without knowledge of the full-order dynamics. Our method adds additional terms to ensure that the reduced-order model not only approximates the spatially frozen profile of the solution, but also estimates the traveling speed as a function of that profile. We validate our approach using the Kuramoto-Sivashinsky equation, a one-dimensional partial differential equation that exhibits traveling solutions and spatiotemporal chaos. Results indicate that our method robustly captures traveling solutions, and exhibits improved numerical stability over the standard operator inference approach.
arXiv:2507.20804v3 Announce Type: replace
Abstract: Large Language Models (LLMs) suffer from hallucinations due to their static parametric knowledge. Retrieval-Augmented Generation (RAG) and GraphRAG mitigate this issue by incorporating external knowledge and structured reasoning over knowledge graphs (KGs). However, existing approaches remain largely text-centric, as constructing fine-grained multimodal knowledge graphs (MMKGs) with explicit cross-modal semantics remains challenging. In this paper, we propose MMGraphRAG, a framework for building interpretable MMKGs that unify textual and visual knowledge. Our approach represents visual content as structured scene graphs and integrates them with textual KGs through a novel cross-modal entity linking method, SpecLink, which leverages spectral clustering to jointly model semantic similarity and graph structure. This design preserves explicit entities, relations, and reasoning paths across modalities, enabling structure-aware retrieval and generation. To support evaluation, we introduce the CMEL dataset, a benchmark for fine-grained cross-modal entity alignment. Experimental results on CMEL demonstrate improved entity linking accuracy, while evaluations on DocBench and MMLongBench show that MMGraphRAG achieves superior performance and stronger robustness, particularly in complex multimodal reasoning scenarios.
arXiv:2507.21987v2 Announce Type: replace
Abstract: Graph modification problems aim to find a small set of modifications to a graph so that it satisfies a desired property. The literature is rather rich in NP-completeness results and polynomial time solvable cases for special graph classes. However, no exact algorithm has been proposed for perfect graph modification problems. In this work, we propose the first exact solution methods based on integer programming for three variants: minimum perfect editing, minimum perfect completion, and the perfect sandwich problems. The minimum perfect editing problem inquires about the smallest number of edge additions and deletions needed to make a graph perfect, while the completion problem allows only for edge additions. The perfect sandwich problem is a decision problem that asks whether a perfect graph can be formed by adding edges from a restricted subset. To solve these problems, we formulate an integer programming model based on the Strong Perfect Graph Theorem. To address the resulting exponential number of constraints, we propose a branch-and-cut algorithm that dynamically generates them on demand. At the core of this approach is an efficient separation routine for enumerating odd holes and odd antiholes. We also release this underlying routine as "is_perfect"-a standalone open-source perfect graph recognizer and odd hole enumerator designed for broader community reuse. To enhance the practical efficiency of the branch-and-cut algorithm, we calculate the expected number of odd holes and odd antiholes in random Erdos Renyi graphs. In addition, we propose "IterativeModificationHeuristic", the first heuristic for the editing and completion problems, which provides upper bounds. Finally, we demonstrate the empirical effectiveness of the proposed methods through computational experiments on a wide range of instance types; all benchmark instances are publicly available.
arXiv:2508.01438v3 Announce Type: replace
Abstract: The capacity of bandlimited direct-detection channels is challenging to compute or approach due to the receiver non-linearity. A generalized vector approximate message passing (GVAMP) detector is designed to achieve high rates at a reasonable level of complexity. The rates increase by using multi-level coding and successive interference cancellation. The methods are applied to fiber-optic channels with intersymbol interference caused by spectrally efficient pulse shapes, chromatic dispersion, and receiver sampling at twice the baud rate. Bipolar modulation operates within 0.26 bits per channel use (bpcu) of the real-alphabet coherent capacity for optically amplified links, reducing the best-known theoretical gap of 1 bpcu. Remarkably, bipolar modulation achieves 6 dB and 3 dB of power gain over unipolar modulation with and without optical amplification, respectively. Simulations with polar-coded modulation confirm the gains. The GVAMP complexity, measured in multiplications per information bit (mpib), is proportional to the number of iterations and to the logarithm of the block length, and is substantially lower than that of other equalizers. For example, a system with 64-ary bipolar modulation and a root-raised cosine pulse with a 1% roll-off factor was simulated over 4 km of optically amplified standard single-mode fiber in the C-band. The GVAMP receiver requires 93 mpib to achieve 5 bpcu at 300 gigabaud.
arXiv:2508.04225v4 Announce Type: replace
Abstract: Behavior Regularized Policy Optimization (BRPO) leverages asymmetric divergence regularization to mitigate distribution shift in offline reinforcement learning. This paper is the first to study the open question of symmetric BRPO. Using didactic examples, we show that symmetric regularization can outperform asymmetric regularization in addressing one-sided bias, near-boundary policy updates, and projection geometry consistency. However, symmetric divergences do not fit BRPO naturally: they do not permit a closed-form solution when used as regularizers, and can lead to numerical instability when used as optimization objectives. We first introduce a universal BRPO framework using an infinite series of Pearson-Vajda divergences to represent any $f$-divergence, which includes both symmetric and asymmetric divergences. We use a finite-series approximation to obtain the following results for symmetric BRPO: (1) a closed-form optimal policy expression; (2) a numerically stable optimization surrogate; and (3) a tight upper bound on the approximation quality. On the D4RL benchmark and in didactic examples, we show that the proposed method achieves consistently strong results and is robust to the number of terms in the approximation.
arXiv:2508.05298v3 Announce Type: replace
Abstract: We present GhostShell, a novel approach that leverages Large Language Models (LLMs) for streaming and concurrent behavioral programming in embodied systems. In contrast to predefined behavioral structures and plan-then-execute paradigms, GhostShell enables reasoning-while-acting by incrementally invoking functions during LLM streaming generation. We define function tokens as an XML-based function-call representation that GhostShell parses from the LLM generation stream and maps to callable functions. A multi-channel scheduling algorithm further orchestrates these calls with intra-channel synchronous and inter-channel asynchronous dispatch, coordinating sequential-parallel behavior execution across multiple robotic components. We evaluate GhostShell on our robotic prototype CoCo across 33 real-world tasks with LLMs from nine providers. On 30 grounded Human-Robot Interaction (HRI) tasks, our approach achieves the highest Directed Structured Behavior Correctness (DSBC) score of 0.83 with Claude-Sonnet-4, while on three long-horizon multimodal tasks, GPT-4.1 attains a top human evaluation score of 7.0/10. Compared to native LLM function calling, our function token schema achieves a 15/15 task completion rate versus 6/15, particularly in coordinating concurrent linguistic and physical actions. Supplementary materials, including videos, are available at https://coco-robot.github.io/GhostShell.
arXiv:2508.08368v2 Announce Type: replace
Abstract: Molecules with heavy, radioactive nuclei promise extreme sensitivity to fundamental nuclear and particle physics. However, these nuclei are available in limited quantities, which challenges their use in precision measurements. Here we demonstrate the gas-phase synthesis, cryogenic cooling, and high-resolution laser spectroscopy of radium monohydroxide, monodeuteroxide, and monofluoride molecules ($^{226}$RaOH, $^{226}$RaOD, and $^{226}$RaF) in a tabletop apparatus by combining novel radioactive target production protocols, optically driven chemistry in a cryogenic buffer gas, and low-background spectroscopic detection methods. The molecules are cooled in the lab frame, creating conditions that are the same starting points as many current molecular precision measurement and quantum information experiments. This approach is readily applied to a wide range of species and establishes key capabilities for molecular quantum sensing of exotic nuclei.
arXiv:2508.09125v3 Announce Type: replace
Abstract: Instruction following has catalyzed the recent era of Large Language Models (LLMs) and is the foundational skill underpinning more advanced capabilities such as reasoning and agentic behaviors. As tasks grow more challenging, the logic structures embedded in natural language instructions becomes increasingly intricate. However, how well LLMs perform on such logic-rich instructions remains under-explored. We propose LogicIFGen and LogicIFEval. LogicIFGen is a scalable, automated framework for generating verifiable instructions from code functions, which can naturally express rich logic such as conditions, loops, and function calls. We further curate a collection of complex code functions and use LogicIFGen to construct LogicIFEval, a benchmark comprising 426 verifiable logic-rich instructions. Our experiments demonstrate that current state-of-the-art LLMs still struggle to correctly follow the instructions in LogicIFEval. Most LLMs can only follow fewer than 60% of the instructions, revealing significant deficiencies in the instruction-following ability. Code and Benchmark: https://github.com/mianzhang/LogicIF
arXiv:2508.10201v4 Announce Type: replace
Abstract: Computer-Aided Design (CAD) models, given their compactness and precision, remain the industry standard for designing and fabricating engineering objects. However, language-guided CAD editing is still in its infancy, largely due to missing semantic connection between user commands and underlying shape geometry, a problem exacerbated by the shortage of paired text-and-edit CAD datasets. While recent Multimodal Large Language Models (mLLMs) have attempted to bridge this gap, their reliance on CAD construction history -- often an expensive and hard to obtain input -- severely limits their expressiveness and restricts their usage. We present B-repLer, a novel framework that directly connects natural language with editing CAD models by operating in a learned latent space. Importantly, our approach bypasses the need for construction history, enabling semantic edits on a wide range of geometries, from simple prismatic parts to complex freeform shapes defined by B-Spline surfaces. To facilitate this research, we introduce BrepEDIT-240K, the first large-scale dataset for this task. We demonstrate how this paired dataset can be automatically generated, (user) validated, and scaled by leveraging existing CAD tools, in conjunction with mLLMs, to create the required paired data without relying on any external annotations. Our results demonstrate that B-repLer can accurately perform complex edits on complex CAD shapes, even when the input edit specifications are high-level and ambiguous to interpret, consistently producing valid, high-quality CAD outputs enabling a class of text-guided edits not previously possible.
arXiv:2508.10742v5 Announce Type: replace
Abstract: Recent experiments have demonstrated that the resolution of superlensing slabs can be significantly enhanced with complex frequency illuminations. In this study, we introduce a novel theoretical framework for analyzing superlensing. The framework offers new and transparent insights. It helps clarify what resolution can be expected with complex frequency, or more generally pulse illuminations, but it also highlights inherent limitations and tempers high expectations raised by the recent electromagnetic experiments. [accepted Optica]
arXiv:2508.10848v3 Announce Type: replace
Abstract: Amidst a shortage of qualified mental health professionals, the integration of large language models (LLMs) into psychological applications offers a promising way to alleviate the growing burden of mental health disorders. Recent reasoning-augmented LLMs have achieved remarkable performance in mathematics and programming, while research in the psychological domain has predominantly emphasized emotional support and empathetic dialogue, with limited attention to reasoning mechanisms that are beneficial to generating accurate responses. Therefore, in this paper, we propose \logopsyche\textit{Psyche-R1}, the first Chinese psychological LLM that jointly integrates empathy, psychological expertise, and reasoning, built upon a novel data curation pipeline. Specifically, we design a comprehensive data synthesis pipeline that produces over 75k high-quality psychological questions paired with detailed rationales, generated through an iterative prompt-rationale optimization procedure, along with 73k empathetic dialogues. Subsequently, we employ a hybrid training strategy wherein challenging samples are identified through a multi-LLM cross-selection strategy for group relative policy optimization (GRPO) to improve reasoning ability, while the remaining data are used for supervised fine-tuning (SFT) to enhance empathetic response generation and psychological domain knowledge. Extensive experiment results demonstrate the effectiveness of \textit{Psyche-R1} across several psychological benchmarks, where our 7B \textit{Psyche-R1} achieves comparable results to 671B \texttt{DeepSeek-R1}.
arXiv:2508.12745v2 Announce Type: replace
Abstract: Image set classification (ISC), which can be viewed as a task of comparing similarities between sets consisting of unordered heterogeneous images with variable quantities and qualities, has attracted growing research attention in recent years. How to learn effective feature representations and how to explore the similarities between different image sets are two key yet challenging issues in this field. However, existing traditional ISC methods classify image sets based on raw pixel features, ignoring the importance of feature learning. Existing deep ISC methods can learn deep features, but they fail to adaptively adjust the features when measuring set distances, resulting in limited performance in few-shot ISC. To address the above issues, this paper combines traditional ISC methods with deep models and proposes a novel few-shot ISC approach called Deep Class-specific Collaborative Representation (DCSCR) network to simultaneously learn the frame- and concept-level feature representations of each image set and the distance similarities between different sets. Specifically, DCSCR consists of a fully convolutional deep feature extractor module, a global feature learning module, and a class-specific collaborative representation-based metric learning module. The deep feature extractor and global feature learning modules are used to learn (local and global) frame-level feature representations, while the class-specific collaborative representation-based metric learning module is exploit to adaptively learn the concept-level feature representation of each image set and thus obtain the distance similarities between different sets by developing a new CSCR-based contrastive loss function. Extensive experiments on several well-known few-shot ISC datasets demonstrate the effectiveness of the proposed method compared with some state-of-the-art image set classification algorithms.
arXiv:2508.13187v4 Announce Type: replace
Abstract: Homelessness is a persistent social challenge, impacting millions worldwide. Over 876,000 people experiencing homelessness (PEH) were recorded in the U.S. in 2025. Social bias is a significant barrier to alleviating homelessness, shaping public perception and influencing policymaking. Because online textual media and offline city council discourse both reflect and influence public opinion, they provide valuable signals for identifying and tracking social biases against PEH. We release the first multi-domain PEH bias corpus with a 16-category multi-label taxonomy: a 1,698-item stratified gold-standard set annotated by partner-trained raters, plus 50,447 GPT-4.1-labeled texts, drawn from Reddit, X (formerly Twitter), news, and council meeting transcripts across ten U.S. cities (2015-2025). We benchmark six prompted LLMs on the gold-standard set and complement F1 with prevalence-gap audits. Moderate F1 coexists with large miscalibration: every model over-tags "not in my backyard" (NIMBY) (+11.5 pp) and under-detects factual claims (-30.5 pp). Error analysis on consensus false positives reveals that models treat housing vocabulary and question form as opposition proxies, producing NIMBY false positives on pro-service text. The corpus and audit protocol support municipal PEH stigma monitoring without treating teacher labels as ground truth.
arXiv:2508.13213v4 Announce Type: replace
Abstract: Strategic decision-making requires balancing immediate opportunities against long-term objectives: a tension fundamental to competitive environments. We investigate this trade-off in chess by analyzing the dynamics of human and AI gameplay through a network-based metric that quantifies piece-to-piece interactions. Our analysis reveals that elite AI players sustain substantially higher levels of strategic tension for longer durations than top human grandmasters. We find that cumulative tension scales with algorithmic complexity in AI systems and increases linearly with skill level (Elo rating) in human play. Longer time controls are associated with higher tension in human games, reflecting the additional strategic complexity players can manage with more thinking time. The temporal profiles reveal contrasting approaches: highly competitive AI systems tolerate densely interconnected positions that balance offensive and defensive tactics over extended periods, while human players systematically limit tension and game complexity. These differences have broader implications for understanding how artificial and biological systems navigate complex strategic environments and for the deployment of AI in high-stakes competitive scenarios.
arXiv:2508.15017v2 Announce Type: replace
Abstract: Active Flux (AF) is a numerical method for hyperbolic conservation laws, whose degrees of freedom are averages/moments and (shared) point values at cell interfaces. It has been noted previously in a heuristic fashion that it thus combines ideas from Finite Volume/Discontinuous Galerkin (DG) methods with a continuous approximation common in continuous Finite Element (CG) methods. This work shows that semi-discrete Active Flux methods can be obtained from a variational formulation through a particular choice of (biorthogonal) test functions. These latter being discontinuous, the new formulation emphasizes the intermediate nature of AF between DG and CG. Explicit constructions are given for the case of arbitrarily high-order Active Flux with additional moments in 1-d, and for the classical third-order Active Flux on two-dimensional Cartesian meshes.
arXiv:2508.19913v2 Announce Type: replace
Abstract: A well-known result by Kant [Algorithmica, 1996] implies that $n$-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in $O(n^{2})$ area. In this paper, we present an algorithm to compute such drawings in $O(n^{1.5})$ area. We also consider outerplanar drawings in which the internal faces are required to be strictly-convex polygons. In this setting, we provide a $\Theta(nk^2)$ area bound for $n$-vertex outerplanar graphs whose weak dual is a path and whose maximum face size is $k$ and a $\Theta(nd^2)$ area bound for $n$-vertex outerplanar graphs whose diameter is bounded by $d$.
arXiv:2508.21424v2 Announce Type: replace
Abstract: Deep learning models have achieved state-of-the-art performance in many computer vision tasks. However, in real-world scenarios, novel classes that were unseen during training often emerge, requiring models to acquire new knowledge incrementally. Class-Incremental Learning (CIL) methods enable a model to learn novel classes while retaining knowledge of previous classes. However, these methods make the strong assumption that the incremental dataset is fully labeled, which is unrealistic in practice. In this work, we propose an unsupervised Incremental Learning method using Confidence-based Pseudo-labels (ICPL), which replaces human annotations with pseudo-labels, enabling incremental learning from unlabeled datasets. We integrate these pseudo-labels into various CIL methods with confidence-based selection and evaluate performance degradation on CIFAR100 and ImageNet100. Then, we compare our approach to popular Class Incremental Novel Category Discovery (class-iNCD) methods addressing similar challenges. Additionally, we apply our method to fine-grained datasets to demonstrate its real-world practicality and measure its computational complexity to validate its suitability for resource-constrained environments. ICPL achieves competitive results compared to supervised methods and outperforms state-of-the-art class-iNCD methods by more than 5% in final accuracy.
arXiv:2509.00446v2 Announce Type: replace
Abstract: Recent advances in autonomous digital agents from industry (e.g., Manus AI and Gemini's research mode) highlight their potential for structured tasks through autonomous decision-making and task decomposition, but it remains unclear how well such systems support real-world information-intensive workflows. We study this question in journalism, where newswriting requires iterative planning, contextual reasoning, and active discovery of missing background to produce a coherent article. We introduce NEWSAGENT, a benchmark for evaluating how agents search raw materials, select relevant information, and iteratively revise drafts through core journalistic functions. Given a writing instruction and partial firsthand materials, agents must identify narrative perspectives, issue keyword-based queries, retrieve historical context, and generate complete news articles. Unlike typical summarization or retrieval tasks, essential context is not directly available and must be actively discovered, reflecting real-world reporting constraints. NEWSAGENT consists of 6k human-verified examples derived from real news. We evaluate open- and closed-sourced LLMs with commonly-used agentic frameworks on NEWSAGENT, which shows that agents are capable of retrieving relevant facts but struggling with planning and narrative integration. We believe that NEWSAGENT serves a realistic testbed for iterating and evaluating agent capabilities in terms of web data manipulation to real-world productivity.
arXiv:2509.00930v2 Announce Type: replace
Abstract: Large language models (LLMs) exhibit strong general reasoning, yet the community lacks controllable, scalable, and verifiable tools to analyze and improve these abilities. We present SATQuest, a verifier that generates diverse SAT-based reasoning tasks directly from Conjunctive Normal Form (CNF) instances and checks answers objectively with PySAT. SATQuest factorizes evaluation along three orthogonal dimensions: instance, problem type, and question format, enabling fine-grained, multi-dimensional analysis and reinforcement fine-tuning. Randomized CNF generation mitigates memorization and supports reproducible experiments. Using SATQuest, we benchmark a range of open- and closed-weight LLMs and uncover persistent gaps in logical reasoning, particularly on higher-complexity tasks and in transfer beyond familiar mathematical notation to machine or narrative formats. We further show that reinforcement fine-tuning with SATQuest rewards substantially boosts targeted performance and generalizes to larger instances, while cross-format robustness remains challenging. Collectively, SATQuest provides verifier-backed infrastructure for controlled, scalable, and reproducible empirical research on LLM logical reasoning and its training.
arXiv:2509.01235v2 Announce Type: replace
Abstract: Balancing training accuracy and adversarial robustness has beeen a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal representations of deep neural networks. This framework promotes intra-class compactness and inter-class separation in feature space, leading to manifold smoothness and adversarial robustness against white or black box attacks. The performance can be explained by \blue{data-dependent statistical mechanics of integrating out the network parameters}, \blue{supplemented by a phenomenological model} with Hebbian coupling between elements of the hidden representation. Based on the current geometry-aware learning framework, the deep network can assimilate new information into existing knowledge structures while reducing representation interference.