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01.
arXiv (CS.CV) 2026-06-17

ERQA-Plus: A Diagnostic Benchmark for Reasoning in Embodied AI

Generalist embodied agents require more than object recognition: they must reason about spatial relations, actions, procedures, human intentions, environmental constraints, and commonsense consequences from situated visual observations. Yet existing visual and embodied question answering benchmarks often provide limited control over the reasoning dependencies being tested, making it difficult to distinguish grounded embodied reasoning from shortcut-driven visual or linguistic pattern matching. We present ERQA-Plus, a diagnostic benchmark for reasoning in embodied AI. ERQA-Plus contains 1,766 question-answer instances grounded in 711 robot-centric images and organized according to a structured taxonomy spanning perceptual, action-centric, social-interaction, navigation-environmental, and contextual commonsense reasoning. The dataset is constructed using a multi-stage generation and validation pipeline that combines taxonomy-guided question generation, automatic quality judging, iterative revision, and human assessment to improve visual grounding, answer validity, and reasoning quality. We benchmark representative general-purpose vision-language models and embodied models, including LLaVA-NeXT-8B, Prismatic-7B, MiniCPM-V-4.5-8B, Qwen3-VL, RoboRefer-8B, and RoboBrain2.5-8B. Although the strongest model, Qwen3-VL-32B, achieves 83.4% overall accuracy and 61.4 SBERT score, category-level results reveal persistent weaknesses in spatial reasoning, procedural reasoning, event prediction, and intention inference. ERQA-Plus therefore provides a fine-grained evaluation framework for measuring not only whether embodied agents answer correctly, but also which forms of embodied reasoning they can and cannot perform reliably. The dataset is available https://huggingface.co/datasets/huggingdas/erqa-plus and the project page at https://github.com/LUNAProject22/erqa-plus.

02.
arXiv (CS.AI) 2026-06-11

SirenFNO: Efficient and Full Frequency Learning of Fourier Neural Operators

arXiv:2606.11518v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations. However, owing to the reliance on frequency truncation to maintain learning efficiency of FNOs, empirical studies suggest that FNOs exhibit spectral bias toward low-frequency information, which may hinder the learning capability especially for certain PDEs with strong high-frequency oscillations. To address this limitation, we propose SirenFNO, a novel framework that leverages sinusoidal representation networks (SIRENs) to learn implicit neural representations and performs mode-wise kernel parameterization. Our SIREN parameterization learns a full-grid spectrum with a constant and discretization-independent parameter count, thereby eliminating the need for frequency truncation. We further extend SirenFNO with functional tensor decompositions to enhance parameter and learning efficiency. Empirical results show that our SirenFNO consistently outperforms FNO with approximately $4$ to $15$ times parameter reductions with preserved discretization invariance, and our functional decomposition variants obtain performance improvements with a maximum of $73$ times fewer parameters across multiple PDE benchmarks.

03.
arXiv (CS.CL) 2026-06-15

Dialogue SWE-Bench: A Benchmark for Dialogue-Driven Coding Agents

AI coding agents have rapidly transformed software engineering, powering widely used interactive coding assistants. Despite their interactive real-world use, existing benchmarks evaluate them as fully-autonomous systems. In this work, we introduce Dialogue SWE-Bench, an automatic benchmark dataset for evaluating the ability of coding agents to resolve real-world software engineering problems through dialogue with a user. We design a novel, persona-grounded user simulator to support our task evaluation, and augment our task evaluation with automatic evaluations of dialogue quality. We also propose a new schema-guided agent, aimed at improving the dialogue capabilities of off-the-shelf coding agents, which improves over strong baselines by 3-14%. Our results indicate that better coding models do not always correspond to better dialogue models, suggesting that dialogue capability is a distinct and currently understudied dimension of coding agent performance.

04.
arXiv (CS.CV) 2026-06-24

UniRED: Unified RGB-D Video Frame Interpolation with Event Guidance

High frame-rate RGB-D videos are crucial for a variety of downstream tasks, including motion analysis, dynamic scene understanding, and 3D reconstruction. However, due to hardware and sensing constraints, practical RGB-D cameras are typically limited to low frame rates, making it difficult to capture rapid scene dynamics. Existing video interpolation methods have achieved strong performance on RGB data, but they are not readily applicable to RGB-D scenarios, where they often yield blurry boundaries, visible artifacts, and degraded geometric consistency. Furthermore, motion estimation from only two boundary frames is inherently under-constrained in complex dynamic scenes. Event cameras, by contrast, provide asynchronous measurements with ultra-high temporal resolution, offering dense motion cues. In this paper, we propose a unified multimodal framework for RGB-D video interpolation that jointly exploits RGB appearance, depth geometry, and event-based temporal cues. Specifically, it first extracts and fuses RGB, depth and event cues, then estimates bidirectional flow with motion basis refinement for RGB and Z-axial refinement for depth, and finally synthesizes the target RGB-D frame via bidirectional warping and soft blending. In addition, we construct a new RGB-D-Event dataset to alleviate the scarcity of tri-modal training data. Extensive experiments on a public benchmark and the proposed dataset demonstrate that our method achieves superior photometric fidelity for RGB interpolation and stronger geometric accuracy for depth interpolation than existing approaches.

05.
arXiv (CS.CV) 2026-06-11

MARIC: Multi-Agent Reasoning for Image Classification

Image classification has traditionally relied on parameter-intensive model training, requiring large-scale annotated datasets and extensive fine tuning to achieve competitive performance. While recent vision language models (VLMs) alleviate some of these constraints, they remain limited by their reliance on single pass representations, often failing to capture complementary aspects of visual content. In this paper, we introduce Multi Agent based Reasoning for Image Classification (MARIC), a multi agent framework that reformulates image classification as a collaborative reasoning process. MARIC first utilizes an Outliner Agent to analyze the global theme of the image and generate targeted prompts. Based on these prompts, three Aspect Agents extract fine grained descriptions along distinct visual dimensions. Finally, a Reasoning Agent synthesizes these complementary outputs through integrated reflection step, producing a unified representation for classification. By explicitly decomposing the task into multiple perspectives and encouraging reflective synthesis, MARIC mitigates the shortcomings of both parameter-heavy training and monolithic VLM reasoning. Experiments on 4 diverse image classification benchmark datasets demonstrate that MARIC significantly outperforms baselines, highlighting the effectiveness of multi-agent visual reasoning for robust and interpretable image classification.

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

Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs

arXiv:2606.23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradients, and Hessians of the value function, where Hessian information is obtained from a matrix Riccati equation along optimal trajectories. These quantities augment a weighted least-squares regression over sparse polynomial bases on hyperbolic cross index sets, with gradients and Hessians contributing additional linear equations per sample and substantially reducing sample complexity compared to value-only regression. Feedback laws are recovered analytically from the learned value function. In high dimensions, a partial Hessian strategy controls the cost of data generation. The approach is validated on problems of increasing state dimension, where second-order data augmentation is shown to improve approximation accuracy and closed-loop performance, with up to an order-of-magnitude reduction in the number of training samples required relative to lower-order methods.

07.
arXiv (CS.AI) 2026-06-24

Reinforcement Learning for Computer-Use Agents with Autonomous Evaluation

arXiv:2606.24515v1 Announce Type: new Abstract: Computer-Use Agents (CUAs) execute high-level user goals by perceiving and acting directly within graphical user interfaces. However, reinforcement learning for CUAs remains difficult because open-ended desktop environments rarely provide scalable, machine-readable reward signals: task success is often visually grounded and hard to specify with handcrafted reward functions or dense manual labels. We propose an RL fine-tuning framework that uses autonomous vision-language evaluation as a scalable supervision signal for GUI agents. Given a final screenshot and the original instruction, a Vision-Language Model judges task completion and provides terminal feedback without task-specific heuristics or manual labels during policy optimization. Because autonomous evaluators are imperfect, we model their feedback as a noisy binary reward channel and derive a noise-corrected reward estimator for Proximal Policy Optimization. Experiments across macOSWorld, Windows Agent Arena, and OSWorld show that corrected evaluator rewards outperform both zero-shot baselines and raw evaluator rewards, improving success rates by an average of 12.6 percentage points over zero-shot performance and 5.1 points over raw evaluator fine-tuning. These results suggest that autonomous evaluation can serve as a practical reward signal for RL in GUI environments when evaluator noise is explicitly modeled and corrected.

08.
arXiv (CS.AI) 2026-06-16

Discovering Symmetry Groups with Flow Matching

arXiv:2512.20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries automatically is challenging. We propose LieFlow, a novel framework that reframes symmetry discovery as a distribution learning problem on Lie groups. Instead of searching for the symmetry generators, our approach operates directly in group space, modeling a symmetry distribution over a large hypothesis group $G$. The support of the learned distribution reveals the underlying symmetry group $H \subseteq G$. Unlike previous works, LieFlow can discover both continuous and discrete symmetries within a unified framework, without assuming a fixed Lie algebra basis or a specific distribution over the group elements. Experiments on synthetic 2D and 3D point clouds, ModelNet10 and a real-world MI-Motion dataset show that LieFlow accurately discovers continuous and discrete subgroups, significantly outperforming a state-of-the-art baseline, LieGAN, in identifying discrete symmetries.

09.
arXiv (CS.AI) 2026-06-11

CRUMB: Efficient Prior Fitted Network Inference via Distributionally Matched Context Batching

arXiv:2606.11473v1 Announce Type: cross Abstract: Prior-fitted networks (PFNs) are a promising class of tabular foundation models that perform in-context learning, whereby the entire labelled training set is supplied as context, and predictions for test queries are produced in a single forward pass. However, the quadratically scaling self-attention mechanism in many PFN architectures makes inference prohibitive for very large training datasets. We propose CRUMB (Clustered Retrieval Using Minimised-MMD Batching), a three-stage inference wrapper that (i) clusters the test queries, (ii) selects a small, distributionally matched training subset for each cluster by greedily minimising the maximum mean discrepancy (MMD), and (iii) runs exact PFN inference on each reduced-context batch. CRUMB is architecture-agnostic and requires no retraining. On the 51-dataset TabArena benchmark, evaluated across three PFN architectures (TabPFNv2, TabICLv1, TabICLv2), we show that CRUMB outperforms similar state-of-the-art context selection strategies. We also show that CRUMB is resilient to covariate drift, as the MMD-minimisation step naturally helps align the training context distribution to match the current test batch distributions.

10.
arXiv (CS.AI) 2026-06-24

Does Mixture-of-Experts Actually Help Inference on Consumer and Edge Hardware? An Empirical Study

arXiv:2606.21428v2 Announce Type: replace-cross Abstract: Mixture-of-Experts (MoE) language models are often described as ideal for resource-constrained inference. Each token activates only a small subset of experts, so the per-token compute cost, in floating-point operations (FLOPs), resembles that of a much smaller dense model. Whether that FLOP advantage survives in practice is far less clear. We ask whether MoE models actually run faster and cheaper than comparable dense models on consumer-grade and edge hardware. We benchmark OLMoE-1B-7B (1.3 B active of 6.9 B total) against three dense baselines on an Apple M2 Pro and an NVIDIA Jetson Orin Nano 8 GB through \texttt{llama.cpp}, measuring throughput, memory, and on-device energy. The answer is device-dependent: OLMoE's active-parameter advantage is only partly realised on the laptop (~10% behind the same-active Llama-3.2-1B) and erodes on the edge device (~31% behind, at 2.1$\times$ the energy per token, with peak memory at the 8 GB ceiling). Patching \texttt{llama.cpp} to time the decode graph node-by-node shows routing accounts for under 9% of MoE-block compute on the cleaner edge backend, so the gap reflects total-parameter memory footprint, expert dispatch, and KV-cache pressure rather than routing. The implication is that on bandwidth-bound edge hardware, inference cost tracks total parameters, not active ones, and sparse activation does not buy back what the device is constrained on. These findings are bounded to one MoE model at this parameter scale and two devices, and we release the full measurement harness and per-run data.

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

Scaling Adaptive Depth with Norm-Agnostic Residual Networks

arXiv:2606.16112v1 Announce Type: cross Abstract: Residual architectures are ubiquitous in deep learning, but they suffer from a subtle structural limitation: the norm of the residual stream can grow rapidly with depth. As a result, updates from later layers become small relative to the accumulated residual state. This reduces their impact on the representation and limits the benefits of scaling models in depth. To address this, we introduce NAG, a norm-agnostic residual architecture that separates magnitude from directional information in the residual stream, preserving meaningful layer contributions throughout depth and preventing later updates from being systematically suppressed by residual-norm growth. Importantly, NAG introduces only a negligible number of additional parameters and relies on simple operations that are easily kernel-fusible, preserving training efficiency in practice. We show that this architecture outperforms baseline Transformers, with gains that increase substantially as depth grows, enabling effective training of much deeper models. The norm-agnostic formulation also leads to an interpretable Mixture-of-Depths (MoD) mechanism that adaptively skips both attention and MLP layers. Beyond serving as a post-training accuracy-compute tradeoff, this mechanism can be used as a pretraining-time scaling strategy: under iso-FLOP training, compute saved by reducing per-token forward-pass cost can be reinvested into training on more tokens while keeping the total parameter count and KV-cache budget fixed. In our experiments, moderate Mixture-of-Depths rates of approximately 20%-25% match full-depth baseline performance under equal training compute while substantially reducing the number of executed layer parameters and forward-pass FLOPs. These results identify sparsity in depth as a new scaling axis for fixed-compute training, enabling very deep yet FLOP-efficient models.

12.
arXiv (CS.CL) 2026-06-25

Introducing corpora Hlava Cor and Hlava AD: Human Label Variation in Coreference and Discourse Relations

As previous research on annotator disagreement in discourse phenomena has shown, understanding text coherence varies considerably from one individual to another. To explore this phenomenon, we created two corpora with multiple annotations of Czech texts, accompanied by annotators' explanations of their choices. The first corpus consists of 1,024 contexts annotated in parallel by three annotators. It captures differences in the identification of coreference across various text types and grammatical-semantic categories, including pronouns, full noun phrases, and anaphoric adverbials. The second corpus comprises 512 contexts, annotated in parallel by five annotators, and focuses on identifying discourse relations in attributive and non-attributive constructions. Both corpora achieve a comparable inter-annotator agreement of approximately 60-65%. For coreference annotation, agreement tends to be lower in cases where automatic coreference resolution models disagree, suggesting that when the models disagree, the examples tend to be more difficult or ambiguous for human annotators to interpret. The annotators' comments, both for coreference and discourse relations, further reveal differences in interpretation, varying levels of confidence in text understanding, and individual reading strategies.

13.
arXiv (CS.AI) 2026-06-11

A Five-Plane Reference Architecture for Runtime Governance of Production AI Agents

作者:

arXiv:2606.12320v1 Announce Type: new Abstract: Enterprise security was built to govern data boundaries: the protected surface was data at rest and in transit, and the controls – access control, data-loss prevention, perimeter inspection – governed crossings of that boundary. Production AI agents dissolve this assumption. An agent reads context, calls tools, invokes connectors, and modifies systems of record on an enterprise's behalf, so risk moves inside the workflow, into sequences of individually-permitted actions that may transform a business process no one authorized. Existing policy engines do not extend to this regime: they evaluate request-time decisions against atomic principals, where agentic systems require stateful evaluation against composite principals whose authority attenuates through delegation chains. We present a reference architecture for the runtime governance of production agents, built from four composable primitives: a five-plane decomposition (a reasoning plane that adjudicates intent, and four enforcement planes – network, identity, endpoint, data – that realize the decision), stop-anywhere mediation, composite principals with capability attenuation, and audit as a structured evidence substrate. We define a taxonomy of six interruption primitives that generalize allow and deny, state and argue for four correctness invariants, and demonstrate the foreclosure of seven production-agent threats across five concrete workflows. A reference implementation of the policy-engine core supplies measured evidence: attenuation correctness and evidence reconstructability hold on every trial, adjudication runs in single-digit microseconds, and the audit substrate's tamper-evidence behaves exactly as designed. We are explicit about scope: the architecture governs delegated action, not model behavior, and a full-system evaluation against a live agent benchmark is the invited next step.

14.
arXiv (quant-ph) 2026-06-25

Resource-state Quantum RAM for Fast and Error-Correctable Queries

arXiv:2503.19172v2 Announce Type: replace Abstract: Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading datasets onto the quantum processor. However, a realisation of this building block is still outstanding due to its formidable resource requirements, which become even more demanding in quantum error-correction schemes. Here we show that the challenge of implementing QRAM can be entirely reduced to a state-preparation problem: since such resource-state is independent on the memory, our approach allows one to prepare it offline, opening the door to new design strategies. As an example, we introduce a heralded 'QRAM factory' which enables improved fidelities with high acceptance rate. More broadly, our results introduce the concept of resource-state QRAM: we study its performance in noisy settings, showing that it preserves the noise-resilience of standard QRAM, and discuss how it can be efficiently combined with quantum error-correction. Finally, we propose an implementation with neutral-atom hardware, where our analysis suggests that high-fidelity and low-latency queries can be implemented.

15.
arXiv (CS.LG) 2026-06-17

Accelerated Convex Optimization via Hamiltonian Dynamics with Deterministic Integration Time

arXiv:2606.17260v1 Announce Type: cross Abstract: We develop Hamiltonian dynamics-based algorithms for smooth convex optimization that achieve accelerated rates of convergence. By exploiting contraction of averaged Hamiltonian flow trajectories rather than requiring contraction at trajectory endpoints, we show that Hamiltonian dynamics-based optimization methods admit deterministic and accelerated convergence guarantees, extending prior work that is limited to quadratic objectives or holds only in expectation. We analyze an idealized continuous-time algorithm and derive practical discrete-time implementations with optimal first-order complexity, thereby establishing Hamiltonian dynamics as a useful algorithmic primitive for deterministic accelerated convex optimization.

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

LSTM-Based Detection of Structural Breaks in Property Insurance Loss Reserving: A Climate-Informed Approach

arXiv:2606.11463v1 Announce Type: cross Abstract: Accurate loss reserving is foundational to insurer solvency, yet accelerating climate driven catastrophes systematically violate the stability assumptions on which traditional actuarial methods depend. This white paper presents a research program testing whether Long Short Term Memory (LSTM) neural networks can detect and adapt to these structural breaks faster and more accurately than Chain Ladder, Bornhuetter Ferguson, and Cape Cod methods. Using 15 plus years of regulatory development triangle data from Florida and Louisiana, enriched with NOAA hurricane intensity indices and sea surface temperatures, we hypothesize a targeted improvement of 15, 20% in reserve accuracy for catastrophe exposed years, a threshold grounded both in the prior neural network reserving literature and in the formal convergence results developed here. Beyond empirical validation, we develop a theoretical framework grounding LSTM structural break detection in probabilistic terms, providing formal performance guarantees that compensate for the limited number of catastrophe events in the test period. We document the research design, methodology, expected contributions, and a candid assessment of limitations.

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

Online LLM Selection via Constrained Bandits with Time-Varying Demand

arXiv:2606.17489v1 Announce Type: cross Abstract: Large Language Models (LLMs) are increasingly deployed in edge-cloud inference systems to handle diverse user tasks with heterogeneous accuracy, latency, and cost profiles. Selecting the appropriate LLM for each incoming task is critical for ensuring service quality and efficient resource utilization. However, model heterogeneity, stochastic and unknown performance characteristics, and time-varying task demands make static selection strategies inadequate. Real-world deployments often impose hard resource budgets such as monetary expenditure limits, along with soft service-level requirements such as latency guarantees. These constraints introduce additional challenges for online decision-making. We formulate this problem as a constrained stochastic bandit learning task, where the learner sequentially selects models under both packing-type (hard) and covering-type (soft) constraints, while adapting to time-varying task demand. The learner operates without access to the underlying reward, cost, or latency distributions and must rely on partial feedback. We develop a novel online learning algorithm that leverages confidence-bound estimates and demand predictions to balance reward maximization with long-term constraint satisfaction. We provide theoretical guarantees showing sublinear regret and sublinear covering constraint violations compared to an offline benchmark with full information. Experimental results on synthetic workloads demonstrate the effectiveness and robustness of our approach in dynamic, resource-constrained environments.

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

Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection

arXiv:2606.18833v1 Announce Type: new Abstract: This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection. We address the challenge of robust cluster definition in noisy environments – a task where partitioning algorithms often over-assign outliers and density-based methods remain sensitive to heuristic global parameters. Drawing on a-contrario statistical reasoning and Gestalt proximity principles, we define a cluster as a maximal subset of data points containing no anomalies relative to a null hypothesis of uniform randomness. Central to this approach is the Perception algorithm, which utilises a principled expectation-based threshold ($\mathbb{E} < 1$) to identify outliers without manual parameter tuning. By treating clustering as the dual of anomaly detection, we employ an iterative ``clustering-by-exclusion'' mechanism. The algorithm is seed-guided, leveraging minimal user-provided labels to initialise robust cluster medians and form initial groups, which are subsequently expanded by admitting non-anomalous points. This approach naturally isolates fringe points, isolated noise, and emerging unknown clusters. We evaluate the method on synthetic and real-world benchmarks, including image and text datasets represented through raw, linear-reduced, and neighbourhood-preserving embeddings. Results demonstrate that with as few as 10–30 seeds per cluster, the proposed method achieves competitive and often very strong performance under a practical low-tuning benchmarking protocol, while maintaining linear scalability with respect to both observations and dimensionality for a fixed number of seeded clusters and iterations.

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

Adaptive inference and function vectors in deep transformers

arXiv:2606.16694v1 Announce Type: cross Abstract: Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious. We introduce a theory of a deep transformer as a mean-field interacting system that implements distributed inference, subject to constraints on communication, locality and depth. We show that such a system can exploit internal state representations ('function vectors') to infer a latent context variable at increasingly finer scales over its layers. In an in-context regression task, the theory predicts a non-trivial relationship between non-Gaussian, hierarchical structure in the latent context variable, and transformer depth. Predictions are tested using constrained linear attention transformers and demonstrate adaptive inference in deep architectures. Feedforward blocks and depth enable transformers to implement a much richer class of in-context learning algorithms than previously described.

20.
arXiv (CS.CL) 2026-06-11

SoftMatcha 2: A Fast and Soft Pattern Matcher for Trillion-Scale Corpora

We present SoftMatcha 2, an ultra-fast and flexible search algorithm that enables search over trillion-scale natural language corpora in under 0.3 seconds while allowing semantic variations in the form of substitution, insertion, and deletion. Our approach employs string matching based on suffix arrays that scales well with corpus size, and represents words as vectors, which underpin its semantic flexibility. To mitigate the combinatorial explosion induced by the semantic relaxation of queries, our method is built on two key algorithmic ideas: dynamic corpus-aware pruning and fast exact lookup enabled by a disk-aware design. We theoretically analyze the efficiency of the proposed method, indicating that it can mitigate exponential growth in the search space. Empirically, on FineWeb-Edu (Lozhkov et al., 2024) (1.4T tokens), it attains substantially lower search latency than existing methods: infini-gram (Liu et al., 2024), infini-gram mini (Xu et al., 2025), and SoftMatcha (Deguchi et al., 2025). As a practical application, our method uncovers benchmark contamination in training corpora that existing approaches miss, and it also benefits information retrieval and paraphrase detection. We also provide an online demo of fast, soft search across corpora in seven languages.

21.
arXiv (CS.LG) 2026-06-16

Scalable and Interpretable Representation Alignment with Ordinal Similarity

arXiv:2606.16379v1 Announce Type: new Abstract: Evaluating representation similarity is fundamental to representation learning. However, existing metrics suffer from significant limitations: they lack interpretability due to shifting baselines, lack robustness to outliers, and are computationally intractable for large datasets, forcing reliance on heuristic approximations. To address this, we develop an ordinal-similarity framework, instantiated by the Triplet (TSI) and Quadruplet (QSI) Similarity Indices, which measure alignment by quantifying the consistency of ordinal relationships. We theoretically demonstrate this formulation is inherently interpretable, robust to outliers, and computationally efficient. Finally, we establish a formal equivalence between TSI and local neighborhood alignment, measured by Mutual Nearest Neighbors. Empirically, we validate these properties and show that ordinal similarity offers a scalable approach to measuring alignment, enabling practitioners to better understand and design representations.

22.
arXiv (CS.AI) 2026-06-11

The Power of Test-Time Training for Approximate Sampling

arXiv:2606.11437v1 Announce Type: cross Abstract: Efficiently sampling from a complex probability distribution is a fundamental problem which has become increasingly pertinent in recent years with the rise of generative AI, as sophisticated sampling procedures from LLMs have been proposed to solve challenging reasoning problems. The efficacy of such sampling algorithms is limited, however, by the relationship between the LLM and the particular sampling task at hand, which has motivated the framework of test-time training (TTT). TTT works by updating a model's weights in response to partial generations and reward feedback received at inference time, thus adapting to the particular problem. In this work, we propose a formalization for TTT as the problem of producing a sample from a given probability measure $\mu^\star$ belonging to a known class ${F}$ of distributions, given an oracle $\hat \mu$ which yields approximate density estimates for $\mu^\star$. This is closely related to the problem of reducing sampling to approximate counting studied in seminal works of Jerrum, Valiant & Vazirani (1986) and Jerrum & Sinclair (1989): namely, when ${F}$ is the class of all distributions, it coincides exactly with the aforementioned counting-to-sampling reduction. In this paper, we first show a quadratic lower bound on the query complexity of sampling from $\mu^\star$ given query access to $\hat \mu$ (for sufficiently large classes ${F}$), thus showing that the random walk approach proposed by Jerrum & Sinclair (1989) and refined by Hayes & Sinclair (2010), is optimal. This answers an open question posed by Hayes & Sinclair. We then show that this lower bound can be circumvented if the size of ${F}$ is bounded appropriately. As we discuss, this latter result can be viewed as an abstraction of TTT, and thus represents a starting point for the development of a principled theoretical framework for TTT.

23.
arXiv (math.PR) 2026-06-24

Perron–Frobenius theorem for a general tree-valued growth-fragmentation-isolation process

arXiv:2606.24599v1 Announce Type: new Abstract: A general tree-valued dynamics is considered in continuous time: new vertices are added, and the percolation happens on the links, and the connected components can be frozen. The model is an infinite-type branching process. The main result establishes the Perron–Frobenius type theorem on this model, which extends the previous work [Ann. Appl. Probab. 33 (6B) 5233 - 5278]. The proof does not rely on any property of the uniform random recursive tree.

24.
arXiv (quant-ph) 2026-06-16

Twisted (co)homology of non-orientable Weyl semimetals

arXiv:2511.22303v3 Announce Type: replace-cross Abstract: The quasi-particle excitations in Weyl semimetals, known as Weyl fermions, are usually forced to emerge in charge-conjugate pairs by the Nielsen–Ninomiya theorem. When the Brillouin zone is non-orientable, this constraint is replaced by a $\mathbb{Z}_2$ charge cancellation, as a result of the chirality becoming ill-defined on such manifolds; this results in configurations with seemingly non-zero total chirality. Here, we set out to explain this behaviour from a purely topological perspective, and provide a classification of non-orientable Weyl semimetal topology in terms of exact sequences of twisted (co)homology groups. This leads to several discoveries of direct physical importance: in particular, we recover the $\mathbb{Z}_2$ charge cancellation in a coordinate-independent way, allowing meaningful limits to be set on its physical interpretation. A detailed discussion is provided on a specific Klein bottle-like topology induced by a momentum-space glide symmetry, including a full review of the insulating and semimetallic invariants of the system and a classification of the surface states on the non-orientable boundary. Beyond this, we provide a complete survey of all possible non-orientable Brillouin zones and their associated invariants, and extend our formalism into the realm of non-Hermitian topological physics and inversion-symmetric Weyl semimetals. Our work exemplifies the vast potential of fundamental mathematical descriptions to not only aid the corresponding physical intuition, but also predict novel and hitherto overlooked phenomena of great relevance throughout the physics research forefront.

25.
arXiv (CS.CL) 2026-06-17

OpenLID-v3: Improving the Precision of Closely Related Language Identification – An Experience Report

Language identification (LID) is an essential step in building high-quality multilingual datasets from web data. Existing LID tools (such as OpenLID or GlotLID) often struggle to identify closely related languages and to distinguish valid natural language from noise, which contaminates language-specific subsets, especially for low-resource languages. In this work we extend the OpenLID classifier by adding more training data, merging problematic language variant clusters, and introducing a special label for marking noise. We call this extended system OpenLID-v3 and evaluate it against GlotLID on multiple benchmarks. During development, we focus on three groups of closely related languages (Bosnian, Croatian, and Serbian; Romance varieties of Northern Italy and Southern France; and Scandinavian languages) and contribute new evaluation datasets where existing ones are inadequate. We find that ensemble approaches improve precision but also substantially reduce coverage for low-resource languages. OpenLID-v3 is available on https://huggingface.co/HPLT/OpenLID-v3.