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01.
bioRxiv (Bioinfo) 2026-06-15

Inferring Cell Fate Trajectories in Time-Resolved Metabolic RNA Labeling data

Single-cell RNA sequencing provides high-resolution snapshots of cellular states but lacks direct information about transcriptional dynamics. Metabolic RNA labeling addresses this limitation by distinguishing newly synthesized RNA, offering insight into the direction of cell state changes, and providing valuable information when attempting to recover the underlying continuous dynamics from static snapshots of cell distributions. However, existing trajectory inference methods do not fully exploit this additional signal. Here, we propose FLOWSATATE, a framework for single-cell trajectory inference that leverages time-resolved RNA labeling within an Optimal Transport setting. We model cell dynamics as a gradient flow in an inferred potential landscape parameterized by a neural network, integrating both total and labeled RNA across time points. The learned potential enables identification of key genes and transcription factors driving cell fate decisions and supports prediction of future cellular states. We benchmark our approach on its ability to generalize unseen data and recover coherent trajectories. We also apply it to study colorectal cancer response to demethylation treatment as well as neuronal differentiation of embryonic stem cells.

03.
arXiv (CS.AI) 2026-06-16

Proximal Policy Optimization for Amortized Discrete Sampling

arXiv:2606.15793v1 Announce Type: cross Abstract: This paper explores policy gradient algorithms for training stochastic policies to sample from structured discrete probability distributions under the Generative Flow Network (GFlowNet) framework. Building on extensive theoretical connections between GFlowNets and entropy-regularized reinforcement learning, we derive equivalents of standard policy gradient algorithms for training GFlowNets, as well as experimentally explore their various methodological aspects, including baseline training and advantage estimation. Most importantly, our work is the first to derive and successfully apply proximal policy optimization to GFlowNets, showing its improved convergence speed and data efficiency compared to standard GFlowNet training objectives on benchmarks ranging from synthetic energies to molecular graph generation.

04.
arXiv (math.PR) 2026-06-16

Sharp freezing time estimates for the subcritical Facilitated Exclusion Process

arXiv:2606.15233v1 Announce Type: new Abstract: We investigate the exact transience time of the Facilitated Exclusion Process (FEP) on the one-dimensional torus with $N$ sites. The FEP exhibits an active/inactive phase transition at critical density $1/2$, such that in the subcritical density regime $(0,1/2)$, it becomes frozen after a finite time period – the transience time or freezing time. We first show that for the FEP starting from a Bernoulli product measure of marginal density $\rho \in (0,1/2)$, the transience time has exactly the scale of $\Theta(\log^3 N)$. Secondly, we prove that in the near-critical case $\rho \simeq 1/2 - N^{-\alpha}$ for $\alpha \in (0,1)$, the transience time is polynomial and has a scale of $N^{1 \wedge (2\alpha)}$. The key idea is to estimate the typical size of locally supercritical intervals of the initial distribution, which has order $\log N$ in the subcritical case and $N^{1 \wedge (2\alpha)}$ in the near-critical case. In the subcritical case this is enough, whereas in the near-critical case we need additional dynamical decorrelation inequalities to apply this static result to estimate the freezing time.

05.
arXiv (CS.CV) 2026-06-16

EdgeZSAD: Practical Zero-Shot Anomaly Detection on Edge Devices

Industrial inspection needs zero-shot anomaly detection (ZSAD) that remains useful under edge deployment constraints. Recent methods often rely on ViT-L foundation backbones (~300M parameters), which exceed the memory and operator budget of typical embedded hardware. We study this regime through EdgeZSAD, a compact reference system built around a TinyViT-21M-512 backbone, an asymmetric global-local readout (EdgeGLR), and a reproducible source-side training recipe (Real-IAD-DR). We train a single checkpoint in a source-trained, target-unseen protocol and evaluate it across six industrial benchmarks. Across three independent runs, the resulting model reaches an average image AUROC of 91.6 on MVTec-AD and 88.2 on VisA, while remaining directly deployable on Jetson Orin Nano Super (TensorRT FP16) and RB5 Gen2 (QNN GPU FP16). Across the six device-rescored benchmarks, image-AUROC drift stays below 0.2 points, indicating that the exported graph preserves host-side ranking behavior in the evaluated deployment setting.

06.
arXiv (CS.AI) 2026-06-11

Runtime Enforcement of Hybrid System Properties

arXiv:2606.12022v1 Announce Type: cross Abstract: Runtime enforcement has emerged as a promising approach for ensuring the safety of autonomous and cyber-physical systems operating in uncertain and dynamic environments. Unlike traditional runtime verification, runtime enforcement actively intervenes during execution to prevent property violations by modifying unsafe system behaviors. Existing enforcement frameworks primarily focus on untimed or discrete-time specifications and are often limited to delaying or suppressing events, making them inadequate for reactive systems exhibiting complex continuous dynamics. In this paper, we propose a runtime enforcement framework where safety requirements are modeled using Hybrid Automata (HA). The framework combines discrete-event editing with continuous-time monitoring to support enforcement actions such as suppression, delay, and insertion of events at arbitrary time instants. Upon observing environmental inputs, the automaton is initialized, and runtime reachability analysis is used to synthesize safe corrective actions. We formally define the enforcement problem for safety hybrid automata, establish enforceability conditions, and present an online enforcement algorithm for reactive systems. A detailed case study on an Adaptive Cruise Control (ACC) system demonstrates the effectiveness of the proposed approach in maintaining safety properties under unsafe controller behaviors. Experimental results show that the framework introduces minimal computational overhead while ensuring continuous compliance with safety requirements in real time.

07.
arXiv (CS.LG) 2026-06-11

TacCoRL: Integrating Tactile Feedback into VLA via Simulation

arXiv:2606.11743v1 Announce Type: cross Abstract: Vision-language-action (VLA) models provide strong visual, language, and action priors for robot manipulation, but visual observations alone often miss the local contact state required for contact-rich tasks. We present TacCoRL, a scalable framework that injects Tactile feedback into VLA policies and improves them through sim-real Co-training and simulation-based reinforcement learning (RL), without requiring large-scale tactile pretraining or extensive real-world contact exploration. The key idea is not only adding touch as an input, but learning how contact readings should modulate action responses in near-failure states that are rare in demonstrations and risky to collect on hardware. We use a real-aligned simulator as a closed-loop training environment for contact interaction. Mixed simulated and real trajectories first warm-start tactile-conditioned actions in the pretrained policy. Reinforcement learning with verifiable task rewards then optimizes the policy using simulated contact rollouts. It reinforces tactile-conditioned actions that lead to task completion, while a supervised objective on real trajectories keeps the refined policy anchored to deployment visual, tactile, and action distributions. The resulting policy transfers directly to the real robot without privileged simulation state or online real-world RL. Across four bimanual contact-rich tasks, the final visuo-tactile policy achieves an average success rate of 72.5%, compared to baseline of 50.0%. Result videos and more details are available at https://tac-corl.github.io/

08.
arXiv (CS.CL) 2026-06-12

Unsafer in Many Turns: Benchmarking and Defending Multi-Turn Safety Risks in Tool-Using Agents

LLM-based agents are becoming increasingly capable, yet their safety lags behind. This creates a gap between what agents can do and should do. This gap widens as agents engage in multi-turn interactions and employ diverse tools, introducing new risks overlooked by existing benchmarks. To systematically scale safety testing into multi-turn, tool-realistic settings, we propose a principled taxonomy that transforms single-turn harmful tasks into multi-turn attack sequences. Using this taxonomy, we construct MT-AgentRisk (Multi-Turn Agent Risk Benchmark), the first benchmark to evaluate multi-turn tool-using agent safety. Our experiments reveal substantial safety degradation: the Attack Success Rate (ASR) increases by 16% on average across open and closed models in multi-turn settings. To close this gap, we propose ToolShield, a training-free, tool-agnostic, self-exploration defense: when encountering a new tool, the agent autonomously generates test cases, executes them to observe downstream effects, and distills safety experiences for deployment. Experiments show that ToolShield effectively reduces ASR by 30% on average in multi-turn interactions. Our code is available at https://github.com/CHATS-lab/ToolShield.

09.
arXiv (CS.LG) 2026-06-19

MortarBench: Evaluating Mortgage Loan Origination Agents

arXiv:2606.19416v1 Announce Type: new Abstract: Loan origination is the process by which a lender creates a new loan, from application and underwriting through approval and funding. This process serves a critical role in evaluating the eligibility and level of risk posed by an applicant. Recently, firms have begun using mortgage loan agents to augment human loan officers, despite a lack of any public benchmark. To fill this gap, we present MortarBench, a loan origination agent benchmark. MortarBench uses a financial data synthesis and mutation pipeline to generate examples with broad edge case coverage that match real-world distributions and questions. We find that state-of-the-art large language models (LLMs) perform poorly, with closed-source models achieving at most 77.1\% exact match accuracy. We also discover systematic biases in LLM perception of foreignness related to non-English names. Noting these weaknesses, we introduce CRIT, a confidence calibration framework. Our method increases accuracy to 80.5\% while improving risk management steering and reducing bias.

10.
arXiv (CS.CL) 2026-06-11

System Report for CCL25-Eval Task 5: New Dataset and LoRA-Fine-Tuned Qwen2.5

作者:

Recently, large language models (LLMs) have achieved promising progress in the fields of classical Chinese translation and the generation of classical poetry. However, domain-specific research on precise translation and affective-semantic understanding of classical poetry remains limited. The main challenge is that most studies treat the poetic appreciation task as a general-domain problem, neglecting the distinctive features of poetic appreciation, while high-quality and domain-specific datasets are extremely limited. To address this limitation, we decompose the task into three subtasks: term interpretation, semantic interpretation, and emotional inference. Based on multiple open-source datasets, we perform data cleansing and alignment to construct the Classical Chinese Poetry Instruction Pair Dataset (CCPoetry-49K), which comprises 49,404 high-quality instruction-response pairs explicitly optimized for this domain. We then propose a domain-specialized LLM, called PoetryQwen, by applying Low-Rank Adaptation (LoRA) to fine-tune the Qwen2.5-14B model. Experimental results on the CCL25-Eval Task 5 benchmark demonstrate that PoetryQwen achieves a score of 0.757, representing a 9.7% improvement over the Qwen2.5-14B-Instruct baseline (0.690). These findings clearly indicate that PoetryQwen significantly enhances performance in precise translation and emotional understanding of classical poetry. We present new dataset and methodological considerations intended to support the domain-specific optimization of LLMs.

11.
arXiv (CS.CV) 2026-06-19

CoMo: Learning Continuous Latent Motion from Internet Videos for Scalable Robot Learning

Unsupervised learning of latent motion from Internet videos is crucial for robot learning. Existing discrete methods generally mitigate the shortcut learning caused by extracting excessive static backgrounds through vector quantization with a small codebook size. However, they suffer from information loss and struggle to capture more complex and fine-grained dynamics. Moreover, there is an inherent gap between the distribution of discrete latent motion and continuous robot action, which hinders the joint learning of a unified policy. We propose CoMo, which aims to learn more precise continuous latent motion from internet-scale videos. CoMo employs an early temporal difference (Td) mechanism to increase the shortcut learning difficulty and explicitly enhance motion cues. Additionally, to ensure latent motion better captures meaningful foregrounds, we further propose a temporal contrastive learning (Tcl) scheme. Specifically, positive pairs are constructed with a small future frame temporal offset, while negative pairs are formed by directly reversing the temporal direction. The proposed Td and Tcl work synergistically and effectively ensure that the latent motion focuses better on the foreground and reinforces motion cues. Critically, CoMo exhibits strong zeroshot generalization, enabling it to generate effective pseudo action labels for unseen videos. Extensive simulated and real-world experiments show that policies co-trained with CoMo pseudo action labels achieve superior performance with both diffusion and auto-regressive architectures.

12.
arXiv (CS.CV) 2026-06-17

RT-Counter: Real-Time Text-Guided Open-Vocabulary Object Counting

Text-guided open-vocabulary object counting (TOOC) aims to count objects belonging to the categories specified by natural language descriptions. Although vision-language pre-trained models have been successful applied to TOOC tasks, they still struggle with fine-grained spatial understanding and real-time inference requirements in counting scenarios. To address these limitations, this paper proposes a real-time TOOC framework, called the Real-Time Counter (RT-Counter), that achieves not only good counting accuracy but also high computational efficiency. RT-Counter designs a novel Visual Prototype Textualization (VPT) module that can project learned visual features into a text feature space and then generate features containing the abstract information that is hard to capture with visual prototypes and the detailed prototype information that is difficult to describe in text, enhancing the object-level visual-language model's counting capabilities. Additionally, RT-Counter incorporates our Weaving Transformer (Weaformer) layers, maintaining high descriptive power at a fraction of the computational cost. The Weaformer layer adopts a novel hybrid attention mechanism that can efficiently weave together local and global visual features. Extensive experiments on three public datasets show that RT-Counter successfully breaks the accuracy-speed trade-off in TOOC. While achieving a competitive MAE of 13.30 on FSC147, RT-Counter operates at 112.48 FPS, making it 7.4x faster and over 4$\times$ more parameter-efficient than the existing leading methods in TOOC. Our work aims at balancing high accuracy and real-time performance in TOOC. Code is available at: https://github.com/Jason-Mar1/RT-Counter.

13.
arXiv (CS.CL) 2026-06-12

Does AI Reviewer See the Full Picture? Attacking and Defending Multimodal Peer Review

The integration of Large Language Models (LLMs) and Multimodal LLMs (MLLMs) into scientific peer-review workflows introduces novel and significant risks for adversarial manipulation, especially given the multimodal nature of scientific papers where figures, not just text, convey core evidence. This creates a significant gap: current robustness studies on AI peer-review are overwhelmingly text-only. Moreover, the problem is distinct from standard jailbreaking, as a peer-review attack seeks to induce a domain-specific, targeted failure (e.g., "inflate this score") rather than a general safety policy violation, for which no practical defenses exist. To address this, we introduce PaperGuard, the first comprehensive benchmark designed to systematically evaluate and defend AI-generated peer-review against these domain-specific, cross-modal attacks. Our framework is built on three pillars: (1) a new multimodal peer-review dataset spanning multiple scientific domains; (2) a unified suite of attacks, including black-box prompt injections and white-box perturbations, specifically designed to target both text (GCG) and figures (PGD); and (3) a practical defense, motivated by the long-context challenge of academic papers, that uses chunk-based embedding search to efficiently localize and mitigate harmful instructions. Our extensive experiments, conducted across state-of-the-art models, confirm that AI reviewers are pervasively vulnerable. PaperGuard establishes the foundational benchmark, protocols, and actionable defense necessary to pioneer trustworthy, attack-resilient AI-assisted scholarly reviewing.

14.
arXiv (CS.CV) 2026-06-12

Learning Task-Aware Sampling with Shared Saliency through Density-Equalizing Mappings

In image and surface-based learning tasks, convolutional features are typically extracted using receptive fields that are sampled uniformly across the entire domain. However, informative structures are rarely distributed uniformly in practice and are often concentrated in localized regions. Such phenomena are particularly common in medical imaging, where pathological changes are spatially confined. Consequently, uniform convolution allocates equal computational effort to both informative and uninformative regions, resulting in inefficient feature extraction and suboptimal utilization of model capacity. To address this issue, we propose a framework for task-adaptive sampling that dynamically redistributes computational attention according to the spatial importance of the data. Specifically, we introduce the Density-Equalizing Convolutional Neural Network (DECNN), which employs density-equalizing mappings to guide convolution through a learned density function. The density function encodes the relative importance of different regions and induces a transformation that enlarges informative areas while compressing less relevant ones. As a result, convolutional receptive fields are redistributed non-uniformly over the domain, enabling denser sampling in task-relevant regions. By coupling this importance-driven transformation with convolution, DECNN performs adaptive feature extraction that focuses computational resources on informative structures. This leads to more efficient use of model capacity, yielding a lightweight yet expressive architecture while simultaneously producing an interpretable saliency map. Experiments on image classification and craniofacial surface analysis demonstrate that DECNN achieves competitive or superior performance with fewer parameters, accurately identifies task-relevant regions, and remains robust under complex geometric variations.

15.
arXiv (CS.CL) 2026-06-11

Agent Skill Evaluation and Evolution: Frameworks and Benchmarks

The growth of agent skills has transformed how agentic systems are built, evaluated, and deployed. As skill libraries continue to scale, rigorous evaluation becomes critical to ensuring their utility, quality, and safety in real-world applications. Consequently, the field is undergoing an emerging paradigm shift from isolated skill creation to automated, evaluation-driven skill evolution. In this survey, we systematically examine the landscape of skill evolution and evaluation beyond foundational skill creation. We categorize evolution into four distinct paradigms, spanning execution feedback, trajectory distillation, compression, and reinforcement learning, showing how each element contributes to improving skill utility and reliability. We also provide an analysis of six skill-centric benchmark categories, identifying structural gaps in benchmark coverage, trade-offs, and metric richness to advance skill research. Finally, we identify open directions for building skill ecosystems that are generalizable, efficient, and verifiably safe. The project URL is https://github.com/Cassie07/AgentSkill_Survey

16.
arXiv (CS.CL) 2026-06-11

Lius: Translation Model Based Instructional Lingustic Using Continual Instruction Tuning In Kupang Malay

Large Language Models (LLMs) offer new potential for translation tasks but often experience performance degradation when handling low-resource languages. To address this limitation, we propose an approach for fine-tuning LLMs on a low-resource language, Kupang Malay. Our approach involves designing a set of instructions by leveraging explicit lexical and semantic features from a bilingual dictionary, and introducing Continual Instruction Tuning (CIT), a training paradigm that enables iterative instruction-based training. Experimental results demonstrate that our model, named Lius, yields notable improvements over standard instruction-tuned models by outperforming 4-6 points, and surpassing both Neural Machine Translation (NMT) and Multilingual LLM models by 10-13 points on several evaluation metrics. These findings highlight the potential of our approach to mitigate the reliance on large-scale parallel data in low-resource language translation.

17.
arXiv (CS.AI) 2026-06-19

Reward as An Agent for Embodied World Models

arXiv:2606.19990v1 Announce Type: new Abstract: While RL has become a promising tool for refining world models, existing methods largely rely on conservative rollouts near the training distribution, limiting exploration, behavioral diversity, and richer dynamic discovery. In this work, we challenge this conservative paradigm. We argue that the core limitation is not exploration itself, but the lack of reliable verification strategies to support broader exploration. Without reliable verification, expanded exploration becomes highly susceptible to reward hacking, where policies exploit imperfect rewards without achieving genuine improvement. To evaluate this motivation, we instantiate our method in embodied world models, where physical plausibility, and task completion provide a rigorous testbed for scalable RL under complex dynamics. On the verification side, we introduce Reward as an Agent, an agentic reward framework that actively evaluates generated behaviors to provide robust reward signals and mitigate reward hacking under distribution shifts. On the exploration side, we introduce Dynamic-Aware Rollout Diversification through DynDiff-GRPO, which explicitly expands action-space exploration to diversify trajectories, broaden state-action coverage, and encourage richer embodied behaviors beyond conservative rollout regimes. By unifying Reward as an Agent with DynDiff-GRPO, we enable RL on a more reliable reward foundation with substantially diversified sampling, effectively mitigating reward hacking while yielding significant accuracy gains across multiple open-source world models, thereby demonstrating that broader exploration can scale successfully when grounded in robust verification.

18.
arXiv (CS.LG) 2026-06-18

P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for Deep Spatiotemporal Super-resolution

arXiv:2606.19303v1 Announce Type: new Abstract: High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs. Traditional data-driven methods often lack physical constraints, and simple physics-informed learning struggles with irregular spatial geometries and intricately evolving temporal dynamics. To tackle these challenges, we propose a Physics-augmented Koopman-enhanced Graph Convolutional Network (P-K-GCN) for spatiotemporal super-resolution on irregular geometries. Specifically, a continuous spline-based GCN is first designed to extract spatial dependencies directly from coarse graph, and Koopman operator theory is incorporated to project the nonlinear dynamics into a compact latent space where temporal progression is linearized. Second, we augment the optimization objective with a physics-based loss to force the data-driven reconstructions to adhere to physical laws for improving predictive fidelity and robustness. Finally, we provide a rigorous theoretical analysis, establishing that the physics augmentation and Koopman regularization mathematically guarantees a reduction in super-resolution error by diminishing Rademacher complexity and tightening generalization bounds. We evaluate our framework on reconstructing spatially high-resolution cardiac electrodynamics across a 3D heart geometry from sparse low-resolution measurements. Numerical experiments demonstrate that our method achieves superior accuracy compared to baseline models.

19.
arXiv (CS.CV) 2026-06-16

FlexPooling with Simple Auxiliary Classifiers in Deep Networks

In computer vision, the basic pipeline of most convolutional neural networks consists of multiple feature extraction layers, where the input signal is downsampled to a lower resolution in each subsequent layer. This downsampling process is commonly referred to as pooling, which is an essential operation in CNNs. Pooling improves robustness against transformations, reduces the number of trainable parameters, increases the receptive field, and lowers computation time. Since pooling is a lossy process but remains important for extracting high-level information from low-level representations, it is important to preserve the most prominent information from previous activations to improve network discriminability. Standard pooling is usually performed using dense pooling methods, such as max pooling or average pooling, or through strided convolutional kernels. In this paper, we propose a simple yet effective adaptive pooling method, called FlexPooling, which generalizes average pooling by learning a weighted average over activations jointly with the rest of the network. We further show that attaching Simple Auxiliary Classifiers (SAC) to the CNN improves performance and demonstrates the effectiveness of the proposed method compared with standard pooling methods. Experiments on multiple popular image classification datasets show that FlexPooling consistently outperforms baseline networks, achieving approximately 1 to 3 percent improvement in accuracy.

20.
arXiv (CS.LG) 2026-06-16

InfoNCE Induces Gaussian Distribution

arXiv:2602.24012v2 Announce Type: replace Abstract: Contrastive learning has become a cornerstone of modern representation learning, allowing training with massive unlabeled data for both task-specific and general (foundation) models. A prototypical loss in contrastive training is InfoNCE and its variants. In this work, we show that the InfoNCE objective induces Gaussian structure in representations that emerge from contrastive training. We establish this result in two complementary regimes. First, we show that under certain alignment and concentration assumptions, projections of the high-dimensional representation asymptotically approach a multivariate Gaussian distribution. Next, under less strict assumptions, we show that adding a small asymptotically vanishing regularization term that promotes low feature norm and high feature entropy leads to similar asymptotic results. We support our analysis with experiments on synthetic and CIFAR-10 datasets across multiple encoder architectures and sizes, demonstrating consistent Gaussian behavior. This perspective provides a principled explanation for commonly observed Gaussianity in contrastive representations. The resulting Gaussian model enables principled analytical treatment of learned representations and is expected to support a wide range of applications in contrastive learning.

21.
arXiv (math.PR) 2026-06-11

Patterned matrices with random walk entries

arXiv:2512.04612v3 Announce Type: replace Abstract: It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their time-changed versions, in a non-commutative probability framework. For the Wigner link function, the limits are free Brownian motion and its time-changed version driven by an inverse stable subordinator. For the symmetric circulant and the circulant with CTRW entries, we use their explicit eigenvalue expressions to define some empirical processes that converge weakly to a Brownian motion and a complex Brownian motion, respectively. For matrices with iid entries, and for elliptic matrices, the algebraic limits are equal in $*$-distribution to processes whose marginals are circular and elliptic variables, respectively. A random time-changed variant of these results is also established.

22.
arXiv (math.PR) 2026-06-15

Real-order moments, tail representations, and logarithmic means

arXiv:2606.14019v1 Announce Type: cross Abstract: This paper develops a unified framework for the study of real-order moments of arbitrary random variables. General integral representations are established in terms of cumulative distribution functions and survival functions, covering continuous, discrete, and mixed distributions supported on the whole real line. These formulas extend the classical tail-integral identities for nonnegative random variables and provide a common treatment of positive, fractional, and negative moments. For discrete distributions, explicit series representations are derived in terms of cumulative probabilities, yielding simple criteria for the existence of moments. Applications are presented for the zeta and Skellam distributions, illustrating how tail behavior determines moment finiteness and how moments can be represented geometrically through cumulative distribution functions. In addition, a representation for logarithmic moments is obtained, linking logarithmic means, Laplace transforms, and the classical Frullani identity. The results provide a unified perspective on moment representations and establish useful connections between tail probabilities, distribution functions, Laplace transforms, and moment existence.

23.
arXiv (math.PR) 2026-06-11

On multidimensional infinite dihedral group extensions of Gibbs Markov maps

arXiv:2601.08961v2 Announce Type: replace-cross Abstract: We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the random walks on groups, we cannot use the convolution of measures on the group and instead we resort to an approach based on irreducible representations. Depending on the dimension of the group, we obtain either mixing, and thus ergodicity, or dissipativity. Also, we obtain the asymptotics of the first return time of the group extension to the origin.

24.
arXiv (CS.LG) 2026-06-16

Quantization Robustness of Monotone Operator Equilibrium Networks

arXiv:2603.10562v2 Announce Type: replace-cross Abstract: Monotone operator equilibrium networks are implicit-layer models whose output is the unique equilibrium of a monotone operator, guaranteeing existence, uniqueness, and convergence. When deployed on low-precision hardware, weights are quantized, potentially destroying these guarantees. We analyze weight quantization as a spectral perturbation of the underlying monotone inclusion. Convergence of the quantized solver is guaranteed whenever the spectral-norm weight perturbation is smaller than the monotonicity margin; the displacement between quantized and full-precision equilibria is bounded in terms of the perturbation size and margin; and a condition number characterizing the ratio of the operator norm to the margin links quantization precision to forward error. MNIST experiments confirm a phase transition at the predicted threshold: three- and four-bit post-training quantization diverge, while five-bit and above converge. The backward-pass guarantee enables quantization-aware training, which recovers provable convergence at four bits.

25.
arXiv (CS.CL) 2026-06-11

ICA Lens: Interpreting Language Models Without Training Another Dictionary

Finding interpretable directions in language-model representations is critical for understanding and controlling model behavior. Sparse autoencoders (SAEs) have become the standard tool for this purpose, but using them as the default first lens often requires training, storing, and evaluating large overcomplete dictionaries. This bottleneck limits rapid exploration and raises a fundamental question: how much interpretable structure is already visible from activation geometry before training another neural dictionary? Our intuition is simple: many interpretable directions are selective on tokens, and these directions should look less Gaussian than random directions. We therefore revisit independent component analysis (ICA), a classical method for finding non-Gaussian directions, as a compact lens for language-model interpretability. We find that ICA has been underestimated for LLM interpretability, because prior uses often relied on off-the-shelf ICA implementations that are brittle on LLM activations and lacked systematic tools for inspecting and evaluating the recovered directions. To bridge these gaps, we introduce ICALens, the first practical workflow for stable, efficient, and auditable ICA analysis of LLM representations. It combines an optimized GPU-parallel FastICA pipeline with LLM-specific stability recipes and better fitting diagnostics, enabling efficient and reliable layer-wise analysis. Across GPT-2 Small, Gemma 2 2B, and Qwen 3.5 2B Base, ICALens efficiently recovers compact, human-interpretable directions without per-layer gradient-based dictionary training. On SAEBench, ICA is competitive with public SAEs in sparse probing and outperforms them in targeted probe perturbation under small-to-medium budgets. These results suggest that ICA should not be viewed as a weak baseline, but as an efficient and complementary first lens for exploring language-model representations.