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01.
arXiv (CS.LG) 2026-06-12

Crossing the Validation Crisis: Cross-Validation Reduces Benchmarking Variance Surprisingly Well

arXiv:2606.12552v1 Announce Type: new Abstract: Modern machine learning progresses through empirical work, benchmarking new methods to evaluate relative performance. However, the statistical variability inherent to evaluation - exacerbated by the stochastic nature of many algorithms - often makes performance estimation unreliable due to the limited test samples available, leading to a validation crisis in which genuine advances are difficult to discern. In this work, we show that cross-validation improves markedly confidence when evaluating and comparing learning algorithm performances. We introduce the concept of sample gain, which quantifies the virtual data augmentation achieved by using multiple cross-validation splits to reduce benchmarking variance. Experiments on both synthetic and real-world datasets (histopathologic scans and NLP fine-tuning) demonstrate that multiple splits can substantially improve the reliability and stability of performance estimates, with diminishing returns often setting in later than expected. We also introduce a procedure to dynamically early-stop cross-validation by estimating from the first few folds if subsequent folds will bring large sample gains. Our findings highlight the value of pushing cross-validation on available samples to achieve robust and reliable benchmarking.

02.
arXiv (math.PR) 2026-06-17

Absolute continuity, supports and idempotent splitting in categorical probability

arXiv:2308.00651v5 Announce Type: replace Abstract: Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like conditional probability and almost sure equality, as well as proofs of fundamental results such as the Hewitt–Savage 0/1 Law, the de Finetti Theorem and the Ergodic Decomposition Theorem. In this work, we develop additional relevant notions from probability theory in the setting of Markov categories. This comprises improved versions of previously introduced definitions of absolute continuity and supports, as well as a detailed study of idempotents and idempotent splitting in Markov categories. Our main result on idempotent splitting is that every idempotent measurable Markov kernel between standard Borel spaces splits across another standard Borel space, and we derive this as an instance of a general categorical criterion for idempotent splitting in Markov categories.

03.
arXiv (quant-ph) 2026-06-17

Photon anti-bunching in high harmonic generation

arXiv:2606.17620v1 Announce Type: new Abstract: Photon anti-bunching is the direct evidence for the existence of photons without having a classical counterpart. Unlike bunching of photons, which can have a semi-classical description, the effect of photon anti-bunching can only be understood with quantized electromagnetic fields. However, for the process of high harmonic generation (HHG), where many photons of the driving field are upconverted to a single photon of higher energy, there is yet no clear evidence for the presence of individual photon emission. The key result of this work is the prediction of photon anti-bunching in the process of HHG, marking it the first theoretical discovery of non-classicality in the temporal correlations of HHG photons. While other non-classical signatures in HHG, such as sub-Poissonian statistics or squeezing, have been discussed for an ensemble of photons, the anti-bunching signature reported here is a signature of a single photon. This is achieved by using the recently developed Heisenberg picture approach for quantum optical HHG, revealing clear anti-bunching signatures in the intensity correlation function across the entire harmonic spectrum.

04.
arXiv (CS.LG) 2026-06-16

Near-Optimal Regret for Distributed Adversarial Bandits: A Black-Box Approach

arXiv:2602.06404v2 Announce Type: replace Abstract: We study distributed adversarial bandits, where $N$ agents cooperate to minimize the global average loss while observing only their own local losses. We show that the minimax regret for this problem is $\tilde{\Theta}(\sqrt{(\rho^{-1/2}+K/N)T})$, where $T$ is the horizon, $K$ is the number of actions, and $\rho$ is the spectral gap of the communication matrix. Our algorithm, based on a novel black-box reduction to bandits with delayed feedback, requires agents to communicate only through gossip. It achieves an upper bound that significantly improves over the previous best bound $\tilde{O}(\rho^{-1/3}(KT)^{2/3})$ of Yi and Vojnovic (2023). We complement this result with a matching lower bound, showing that the problem's difficulty decomposes into a communication cost $\rho^{-1/4}\sqrt{T}$ and a bandit cost $\sqrt{KT/N}$. We further demonstrate the versatility of our approach by deriving first-order and best-of-both-worlds bounds in the distributed adversarial setting. Finally, we extend our framework to distributed linear bandits in $R^d$, obtaining a regret bound of $\tilde{O}(\sqrt{(\rho^{-1/2}+1/N)dT})$, achieved with only $O(d)$ communication cost per agent and per round via a volumetric spanner.

05.
arXiv (quant-ph) 2026-06-15

Scaling native entanglement generation in layered semiconductors with quasi-phase matching

arXiv:2606.14553v1 Announce Type: new Abstract: Efficient generation of entangled photons typically relies on spontaneous parametric down-conversion (SPDC) in phase-matched macroscopic nonlinear media. However, generating entanglement under phase-matching constraints requires additional bulk optics or interferometers. In contrast, ultrathin van der Waals semiconductors - such as transition metal dichalcogenides (TMDs) - exhibit strong enough optical nonlinearities for SPDC to be observed from subwavelength-thick media, thereby bypassing conventional phase-matching constraints. In this microscopic domain, the intrinsic crystal symmetry governs the nonlinear optical response, enabling the native generation of polarization-entangled photon pairs. However, generating these states efficiently has been fundamentally restricted by the material's coherence length ($L_c$), which limits the attainable conversion efficiency. Here, we investigate periodically-poled TMDs (PPTMDs) designed to scale up this interaction via quasi-phase matching. We demonstrate that mechanically flipping the sign of the nonlinearity at precise intervals of $L_c$ introduces quasi-phase matching, that scales the pair-production rate while preserving the pristine, symmetry-generated polarization entanglement, with fidelities exceeding 99%. Backed by a rigorous theoretical model, our work clarifies the interplay between crystal symmetry and propagation effects in thin nonlinear media, providing a new avenue for engineering quantum light in nanophotonic systems.

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

Characterizing Software Aging in GPU-Based LLM Serving Systems

arXiv:2606.11916v1 Announce Type: cross Abstract: This paper proposes an empirical methodology to study software aging in GPU-based LLM serving systems. Traditional aging studies focus on CPU-centric software with relatively regular workloads; LLM serving is different, spanning a Python host and a CUDA device, handling requests whose cost varies by orders of magnitude, and relying on rapidly evolving software stacks. We run a 216-hour campaign across six co-located deployments under identical stress conditions, monitor host, device, and client metrics in parallel, and apply a statistical pipeline that accounts for autocorrelation and multiple testing. Our results reveal statistically significant memory aging in all deployments, with leak rates strongly dependent on the serving runtime and deployment configuration. Beyond these findings, we provide a reproducible framework that opens a research direction at the intersection of the software aging and rejuvenation and LLM serving communities.

07.
arXiv (CS.AI) 2026-06-12

SAIGuard: Communication-State Simulation for Proactive Defense of LLM Multi-Agent Systems

arXiv:2606.12474v1 Announce Type: cross Abstract: LLM-based multi-agent systems (MAS) solve complex tasks through inter-agent collaboration, but their communication-driven nature also allows security risks to spread across agents and trigger system-wide failures. Existing MAS defenses mainly follow a reactive paradigm after execution by detecting and isolating harmful agents, which may cause irreversible damage and degrade collaborative utility. To address this, we propose a proactive defense framework for MAS security, namely a Simulation-aware Interception Guard (SAIGuard). SAIGuard performs communication-state simulation over the MAS interaction graph, estimates the impact of incoming messages on local agent states and the global MAS state, and detects risky messages via reconstruction deviations from benign communication patterns. Instead of isolating agents, SAIGuard sanitizes or regenerates suspicious messages before it propagation into system. Experiments across diverse topologies and attack scenarios show that SAIGuard reduces attack success rates while maintaining MAS utility, outperforming reactive defenses.

08.
arXiv (CS.CV) 2026-06-11

FreqKD: Frequency-Decoupled Cross-Modal Knowledge Distillation for Infrared Object Detection

Transfer learning from large-scale RGB foundation models to infrared (IR) imagery through knowledge distillation (KD) remains challenging due to fundamental differences in image formation physics. We investigate the spectral structure of the RGB–IR modality gap and observe that feature divergence is not uniform across spatial frequencies: low-frequency components (shape, layout) show greater cross-modal alignment than high-frequency components (texture, fine edges), which reflect modality-specific characteristics. Based on this analysis, we propose FreqKD, a frequency-decoupled distillation framework that applies asymmetric supervision adapted to each band's cross-modal consistency. The method employs strict mean squared error (MSE) on the low-frequency band to preserve shared structural information and a relaxed log-MSE loss (weighted at 0.1) on the high-frequency band to provide edge guidance while tolerating texture differences. Spectral divergence analysis on 500 paired samples shows that high-frequency divergence exceeds low-frequency divergence by a factor of 2.4x on average across all analysed transformer layers. On KAIST multispectral pedestrian detection, FreqKD achieves 64.1 mAP50, improving 2.4 points over the DINOv2 baseline. The learned representation transfers across datasets (FLIR ADAS, +2.1 mAP50), tasks (MFNet segmentation, +1.85 mean intersection-over-union), and architectures (ResNet-50, +1.0 mAP50). Code is available at: https://anonymous.4open.science/r/freq_decoupled_kd-5E5A

10.
Nature (Science) 2026-06-10

Daily briefing: Ancient ground squirrels ate like ‘zombies of the Pleistocene’

作者:

Evidence from fossilized poo reveals the diverse diet of ancient ground squirrels. Plus, the science behind the peptide craze and our innate tendency to wander anticlockwise. Evidence from fossilized poo reveals the diverse diet of ancient ground squirrels. Plus, the science behind the peptide craze and our innate tendency to wander anticlockwise.

11.
arXiv (CS.CV) 2026-06-12

Measurement Plasticity: Sensor-Level Adaptation for Vision-Language Models

We propose Multi-View Physical-prompt (MVP) for Test-Time Adaptation (TTA), a forward-only framework that moves TTA from tokens to photons by treating the camera exposure triangle (i.e., ISO, shutter speed, and aperture) as physical prompts. At inference, MVP acquires selected multiple physical views using a source-affinity score, evaluates digitally augmented variants of each retained view and filters the lowest-entropy predictions, and aggregates predictions with hard voting. This selection-then-vote design is simple, calibration-friendly, and requires no gradients or model modifications. On ImageNet-ES and ImageNet-ES-Diverse, MVP outperforms digital-only TTA on both Auto-Exposure and a combination with conventional sensor control. MVP remains effective under reduced parameter candidates that lower capture latency, demonstrating its practicality.

12.
arXiv (CS.CV) 2026-06-16

The Vision Encoder as a Privacy Boundary: Visual-Token Side Channels in Encoder-Free Vision-Language Models

A vision encoder compresses image pixels into semantic embeddings, implicitly acting as a privacy boundary by preserving semantic content while attenuating pixel-local detail required for exact text recovery. Encoder-free vision-language models (VLMs) remove this boundary by routing image patches directly into the language-model token stream, thereby exposing an architectural privacy attack surface: intermediate visual tokens become a pre-output side channel. Under a token-access adversary, decoders invert visual-token streams from two encoder-free VLMs, Gemma4 and Fuyu, recovering recognizable image structure and readable held-out access codes, whereas matched encoder-based controls localize target regions but recover no exact strings. Within-model ablations show that the operative factor is spatial sampling fidelity of the visual-token grid, especially character-direction sampling density, rather than token or value count. The leakage is not limited to exported tokens: Gemma4 layer-0 key-value cache tensors are directly invertible, placing the side channel within KV caches commonly persisted by production serving stacks for decoding efficiency. The attack survives clutter, realistic document degradation, and zero-shot transfer to public document images, and it resists value-level defenses such as additive noise and quantization. Effective mitigation must therefore reduce spatial sampling, making removal of the vision encoder a first-class privacy decision in VLM deployment.

13.
PLOS Computational Biology 2026-06-09

Multi-stable oscillations in cortical networks with two classes of inhibition

by Arnab Dey Sarkar, Bard Ermentrout In the classical view of cortical rhythms, interactions between excitatory pyramidal neurons (E) and inhibitory parvalbumin-expressing interneurons (I) are sufficient to generate gamma- and beta-band oscillations. However, it is now well established that multiple inhibitory interneuron subtypes exist and that they play important roles in the generation and modulation of these rhythms. In this paper, we develop a spiking network model consisting of populations of E, I, and an additional interneuron type, somatostatin-expressing neurons (S), which receive excitation from the E cells and inhibit both the E and I populations. The S cells are further modulated by a third inhibitory subtype, vasoactive intestinal peptide (VIP) neurons, which receive inputs from other cortical areas. We reduce the spiking network to a system of nine differential equations that describe the mean membrane potential, firing rate, and synaptic conductance for each population. Using this reduced model, we identify a wide range of parameters that exhibit multiple coexisting rhythms. Employing tools from nonlinear dynamics, we then explore the roles of the two classes of inhibition, as well as VIP modulation, in shaping the properties of these rhythms.

14.
arXiv (quant-ph) 2026-06-16

Interaction-enabled topological pumping of Rydberg electrons

arXiv:2606.15126v1 Announce Type: cross Abstract: Topological pumping is a paradigmatic realization of quantized transport in band systems, yet its fate in strongly correlated regimes, especially with long-range interactions, remains largely unexplored. Here we report the experimental observation of interaction-enabled topological pumping of correlated Rydberg electrons in a synthetic lattice. We show that dipolar exchange interactions induce a controllable shift of the underlying topological singularity in parameter space, such that a fixed pumping trajectory can be driven through successive topological transitions by tuning the interaction strength alone. This leads to the emergence and breakdown of quantized transport. The observations are consistent with an effective Rice-Mele description with interaction-renormalized onsite potentials and are supported by characterizing the adiabaticity and robustness to control trajectory imperfections. Our results establish a platform for exploring interaction-controlled topological transport beyond perturbative regimes and open a route toward engineering correlated topological matter in synthetic quantum systems.

15.
arXiv (CS.CV) 2026-06-16

Are Neuro-Inspired Multi-Modal Vision-Language Models Resilient to Membership Inference Privacy Leakage?

In the age of agentic AI, the growing deployment of multi-modal models (MMs) has introduced new attack vectors that can leak sensitive training data in MMs, causing privacy leakage. This paper investigates a black-box privacy attack, i.e., membership inference attack (MIA) on multi-modal vision-language models (VLMs). State-of-the-art research analyzes privacy attacks primarily to unimodal AI-ML systems, while recent studies indicate MMs can also be vulnerable to privacy attacks. While researchers have demonstrated that biologically inspired neural network representations can improve unimodal model resilience against adversarial attacks, it remains unexplored whether neuro-inspired MMs are resilient against privacy attacks. In this work, we introduce a systematic neuroscience-inspired topological regularization (tau) framework to analyze MM VLMs resilience against image-text-based inference privacy attacks. We examine this phenomenon using three VLMs: BLIP, PaliGemma 2, and ViT-GPT2, across three benchmark datasets: COCO, CC3M, and NoCaps. Our experiments compare the resilience of baseline and neuro VLMs (with topological regularization), where the tau > 0 configuration defines the NEURO variant of VLM. Our results on the BLIP model using the COCO dataset illustrate that MIA attack success in NEURO VLMs drops by 24% mean ROC-AUC, while achieving similar model utility (similarities between generated and reference captions) in terms of MPNet and ROUGE-2 metrics. This shows neuro VLMs are comparatively more resilient against privacy attacks, while not significantly compromising model utility. Our extensive evaluation with PaliGemma 2 and ViT-GPT2 models, on two additional datasets: CC3M and NoCaps, further validates the consistency of the findings. This work contributes to the growing understanding of privacy risks in MMs and provides evidence on neuro VLMs privacy threat resilience.

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

YTClickbait21K: Human-Annotated Multimodal Dataset for YouTube Clickbait Detection Across Diverse Channels and Content Categories

Clickbait content on video-sharing platforms poses a significant challenge to information reliability, yet progress in automated detection has been constrained by the lack of large-scale, high-quality multimodal datasets. We present YTClickbait21K, a human-annotated YouTube clickbait dataset comprising 21,238 videos collected from 40 channels across 29 countries, covering diverse content categories such as news, entertainment, education, and gaming. Each sample includes structured metadata (title, description, engagement statistics) along with associated thumbnail images, enabling comprehensive multimodal analysis. To ensure annotation quality, every video was independently labeled by three annotators using a standardized decision framework that incorporates textual, visual, and cross-modal consistency cues, with final labels determined through majority voting. The dataset exhibits substantial inter-annotator agreement (k=0.65), confirming reliable labeling despite the inherent subjectivity of clickbait detection. By combining scale, annotation rigor, and multimodal richness, this dataset provides a robust benchmark for developing and evaluating machine learning models, facilitating research in cross-modal semantic understanding, and advancing automated content moderation systems.

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

Surflo: Consistent 3D Surface Flow Model with Global State

Geometry is invariant to viewpoint, which makes any collection of images a redundant encoding of a single 3D state. Existing feed-forward reconstruction models fail to exploit this: per-view methods emit overlapping, unaligned pointmaps that grow linearly with input count, while global-latent methods commit to a fixed, low-resolution output. We introduce Surflo, which compresses a variable number of unposed RGB views into K latent tokens-one global state-and decodes oriented 3D surface points by independently transporting them from noise onto the surface via flow matching. This frees the output from any fixed grid or token budget: the same latent yields from a few thousand to a million points in a single forward pass. To suppress the local inconsistencies inherent to independent per-point decoding, an inference-time guidance term correlates nearby points by injecting a photometric gradient during ODE integration. Surflo matches or surpasses feed-forward baselines on surface metrics, runs an order of magnitude faster than optimization-based methods that require hundreds of views, and is the only feed-forward approach to combine a global latent with arbitrary-resolution decoding.

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

CAMEO: A Conditional and Quality-Aware Multi-Agent Image Editing Orchestrator

Conditional image editing aims to modify a source image according to textual prompts and optional reference guidance. Such editing is crucial in scenarios requiring strict structural control (i.e., anomaly insertion in driving scenes and complex human pose transformation). Despite recent advances in large-scale editing models (i.e., Seedream, Nano Banana, etc), most approaches rely on single-step generation. This paradigm often lacks explicit quality control, may introduce excessive deviation from the original image, and frequently produces structural artifacts or environment-inconsistent modifications, typically requiring manual prompt tuning to achieve acceptable results. We propose CAMEO, a structured multi-agent framework that reformulates conditional editing as a quality-aware, feedback-driven process rather than a one-shot generation task. CAMEO decomposes editing into coordinated stages of planning, structured prompting, hypothesis generation, and adaptive reference grounding, where external guidance is invoked only when task complexity requires it. To overcome the lack of intrinsic quality control in existing methods, evaluation is embedded directly within the editing loop. Intermediate results are iteratively refined through structured feedback, forming a closed-loop process that progressively corrects structural and contextual inconsistencies. We evaluate CAMEO on anomaly insertion and human pose switching tasks. Across multiple strong editing backbones and independent evaluation models, CAMEO consistently achieves 20\% more win rate on average compared to multiple state-of-the-art models, demonstrating improved robustness, controllability, and structural reliability in conditional image editing.

19.
arXiv (math.PR) 2026-06-18

On two overlooked stick-breaking constructions of the normalized inverse Gaussian process

arXiv:2606.19306v1 Announce Type: new Abstract: We shed light on two alternative stick-breaking constructions of the normalized inverse Gaussian (NIG) random discrete distribution which appear to have been overlooked so far in the Bayesian nonparametric setting. The first is derived from a result in Aldous and Pitman (1998) for the conditional Brownian excursion partition, mixing over the local time at zero up to time one. The second arises as a particular case of a result in James (2013) for priors obtained by a random spatial and temporal change of the normalized generalized Gamma subordinator. Both constructions are in terms of straightforward transformations of standard random variables and can be easily generalized to provide the stick-breaking construction of any element, respectively, in a) the family of mixed Poisson-Kingman models driven by the $1/2$ stable Lévy measure and b) the family of Poisson-Gamma processes driven by the Inverse Gaussian subordinator.

20.
arXiv (CS.AI) 2026-06-18

DRIFT: Refining Instruction Data via On-Policy Data Attribution

arXiv:2606.18307v1 Announce Type: cross Abstract: Optimizing the training data distribution for Supervised Fine-Tuning (SFT) dictates the capability of Large Language Models (LLMs). While existing data curation methods excel at accelerating training under constrained budgets, they are less suited to elevating the capability upper bound. The challenge here is no longer to identify a smaller subset that preserves performance, but to refine the data distribution toward instances most capable of improving the final model. To address this problem, we explore instance-level data attribution using Influence Functions (IF). We identify that standard IF formulations struggle in this setting due to two structural limitations: a proximity gap caused by off-policy validation targets, and a severe bias towards gradient norm. We propose DRIFT (Data Refinement via On-Policy Influence Functions for Supervised Fine-Tuning). Instead of relying on external reference data, DRIFT utilizes the model's on-policy rollouts as validation targets, which empirically minimizes the parameter proximity gap and better aligns with the local neighborhood assumption of IF. It further applies signed weighting based on trajectory correctness and debiases influence scores against the gradient hacking issue, allowing a small set of validation queries to act as reliable anchors for attributing the full dataset. Experiments on 7B-parameter instruction and reasoning models show that DRIFT consistently raises the performance ceiling on both, outperforming existing data curation baselines.

21.
arXiv (CS.CL) 2026-06-11

Rewrite to Translate, Translate to Reward: Reinforcement Learning for Source Rewriting in Machine Translation

Rewriting source text with large language models (LLMs) before translation has been shown to improve machine translation (MT) quality. However, we find that prompt-based rewriting can degrade translation quality rather than improve it, particularly when smaller LLMs, such as 4B-parameter models, are used. We argue that this limitation stems from the difficulty of controlling rewriting behavior through natural-language prompts alone: a rewrite is useful only if it improves downstream translation, yet existing prompt-based methods do not explicitly optimize for this signal. To address this issue, we propose RLSR (Reinforcement Learning for Source Rewriting), a reinforcement learning framework that trains the rewriting model with a reward based on the downstream translation-quality improvement produced by each rewrite. Experiments across six MT systems and 16 language pairs show that our 4B RLSR-trained rewriting models significantly outperform both the no-rewriting baseline and prompt-based rewriting baselines at the same model scale, while remaining competitive with baselines that use a 235B LLM.

22.
arXiv (CS.LG) 2026-06-17

From Drift to Coherence: Stabilizing Beliefs in LLMs

arXiv:2606.17832v1 Announce Type: new Abstract: Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition, the martingale property of predictive beliefs, has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

23.
arXiv (math.PR) 2026-06-12

The Lov\'{a}sz Local Lemma: Foundations and Applications

作者:

arXiv:2603.07245v5 Announce Type: replace-cross Abstract: The Lov\'{a}sz Local Lemma (LLL) is a central tool in probabilistic combinatorics, providing a sufficient condition under which a finite collection of undesirable events with limited dependencies can be simultaneously avoided with positive probability. This paper offers a self-contained expository treatment of the lemma and its strengthened versions, emphasizing mathematical foundations, conceptual clarity, and applications. We begin with a pedagogically motivated proof of the LLL based entirely on unconditional probability inequalities. Particular attention is given to the symmetric form of the lemma and several subsequent strengthenings. The paper also discusses a variety of classical applications of both the symmetric and asymmetric forms of the LLL in combinatorics and graph theory, including bounds for the edge-disjoint paths problem, satisfiability of Boolean formulas in conjunctive normal form, lower bounds on diagonal and off-diagonal Ramsey numbers, hypergraph coloring results, structural properties of directed graphs, and acyclic graph colorings. Additional observations and refinements are provided throughout. We also introduce the algorithmic framework of Moser and Tardos, highlighting its constructive counterpart to the LLL, together with an introduction to the entropy-compression principle. The lopsided LLL, a refinement of the LLL, is presented along with an application to the Latin transversal problem. We further discuss the cluster-expansion lemma and its relation to the LLL, and present an alternative treatment of the Latin transversal problem from the cluster-expansion perspective that yields an improved result. The paper concludes with a high-level overview of the iterated LLL, also known as the semi-random method.

24.
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.

25.
arXiv (CS.CV) 2026-06-16

HiRo: A Compact Four-Directional Hierarchical Reservoir Token-Mixer for Efficient Image Classification

Recent image classification models must balance local feature modeling, cross-window interaction, and parameter efficiency. Many high-performing architectures rely on fully trainable token-mixers, which improve representation learning but increase parameter count, optimization complexity and computational cost. We propose a parameter-efficient image classification model called HiRo that integrates shifted-window partitioning with multi-directional hierarchical reservoir computing. Images are divided into non-overlapping patches (treated as tokens), linearly projected, normalized, and enriched with 2D sinusoidal positional encodings, then processed within local windows. Inside each window, tokens are scanned in four directions and passed through a two-stage slice-and-mix reservoir module. In the first stage, directional sequences are split into contiguous slices, each processed by its own fixed reservoir with a trainable closed-loop readout. The resulting slice outputs are summarized using the start, end, and mean representations, and then mixed by a second-stage fixed reservoir for each direction. The mixed slice representations are expanded back to the token level and fused with the first-stage outputs, after which the four directional outputs are realigned and averaged. Consecutive blocks alternate between regular and shifted windows to enable cross-window interaction, followed by layer normalization, a residual feed-forward network, and global pooling for classification. This design combines regular and shifted window partitioning with hierarchical multi-directional reservoirs to make an efficient local-to-cross-window token-mixing framework for image classification. Despite using under 1M trainable parameters and significantly lower memory and time than transformer-style baselines, HiRo also achieves 99.46%, 85.57%, and 59.10% accuracy on MNIST, CIFAR-10, and CIFAR-100, respectively.