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

EurekAgent: Agent Environment Engineering is All You Need For Autonomous Scientific Discovery

LLM-based agents have shown increasing potential in automating scientific discovery. Given an optimizable metric and an execution environment, they can propose, validate, and iterate scientific solutions, and have produced results that outperform human-designed approaches. As model capabilities continue to improve, we argue that the bottleneck for autonomous scientific discovery is shifting from prescribing agent workflows to designing agent environments: the resources, constraints, and interfaces that shape agent behavior. We frame this as environment engineering: building environments that amplify productive behaviors, such as open-ended exploration, systematic artifact management, and inter-agent collaboration, while suppressing harmful behaviors, such as reward hacking and high-friction human oversight. We present EurekAgent, an environment-engineered agent system for metric-driven autonomous scientific discovery. EurekAgent engineers the environment along four dimensions: permissions engineering for bounded agent execution and isolated evaluation; artifact engineering for filesystem and Git-based collaboration; budget engineering for budget-aware exploration; and human-in-the-loop engineering for easy human supervision and intervention. EurekAgent sets new state-of-the-art results on multiple mathematics, kernel engineering, and machine learning tasks, including new state-of-the-art 26-circle packing results discovered with less than $11 in total API cost. We open-source our code and results, and call for environment engineering as a core research direction for developing reliable autonomous research agents.

02.
arXiv (CS.CL) 2026-06-24

When Retrieval Metrics Mislead: Measuring Policy Signal in Long-Horizon Tool-Use Agents

Exact-match retrieval recall is often used as a proxy for whether a retriever supplies useful policy context to a downstream decision model. We test this proxy for pre-action policy classification in tau-bench using Qwen2.5-3B/7B classifiers. Under gold-policy conditioning, a compact structured state improves macro-F1 over raw trajectories by 0.13-0.17 after tuning. We then replace the benchmark-designated policy clause with the top-ranked clause retrieved from decision-time context. Although the exact governing clause is retrieved at rank 1 for only 7% of airline states, the primary 3B classifier obtains macro-F1 0.58 with retrieved clauses versus 0.60 with gold clauses (Delta=-0.02, task-cluster 95% CI [-0.23,+0.21]); mismatched-policy and no-policy controls score 0.32 and 0.21. We do not detect a macro-F1 difference between retrieved and gold clauses in this configuration, although the interval remains too wide to establish non-inferiority. The same qualitative pattern appears with a second retriever and at 7B, while varying across fine-tuning configurations. These results indicate that exact-match clause recall can underestimate downstream policy utility in this benchmark setting, motivating evaluation with retrieved policies in the classification loop rather than recall alone.

04.
arXiv (CS.CL) 2026-06-18

BCL: Bayesian In-Context Learning Framework for Information Extraction

Existing information extraction (IE) tasks increasingly adopt in-context learning (ICL) with large language models. However, current approaches either show inconsistent performance across model scales or lack systematic optimization and generalizability. Building on this, we propose BCL (Bayesian In-Context Learning Framework for Information Extraction), the first optimization framework that uses particle filtering with Bayesian updates to systematically refine label representations across IE tasks. Through four steps initialization, observation, weight update, and resampling, BCL generalizes to both sequence labeling and relation classification paradigms. Extensive experiments demonstrate substantial and consistent improvements over existing approaches.

05.
arXiv (CS.CL) 2026-06-19

Where to Place the Query? Unveiling and Mitigating Positional Bias in In-Context Learning for Diffusion LLMs via Decoding Dynamics

While In-Context Learning (ICL) is extensively studied in Autoregressive (AR) LLMs, its mechanism within Diffusion Large Language Models (dLLMs) remains largely unexplored. Unlike AR models restricted by unidirectional causal masking, dLLMs intrinsically utilize bidirectional attention, offering extensive spatial flexibility for query placement. Unfortunately, current practices conventionally inherit AR-style trailing-query templates, often overlooking the structural paradigm shift. This paper presents a comprehensive analysis unveiling that query position is actually a first-order variable in dLLMs. Through empirical decoupling, we demonstrate that positional variance impacts generation quality on par with example semantic quality. Internally, this positional sensitivity stems from a spatial ``Recency Effect'' in attention flow and task-dependent shifts in decoding trajectories. To mitigate this instability without ground-truth labels, we reveal that traditional single-step confidence ($C_{decoded}$) fails in dLLMs. Instead, we propose Average Confidence ($\overline{C}$), a novel metric tracking the iterative decoding process. By establishing the foundational spatial ICL baselines, we introduce Auto-ICL, a training-free adaptive routing strategy that dynamically optimizes query placement, robustly approaching oracle performance across heterogeneous reasoning and perception tasks.

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

DifFRACT: Diffusion Feature Reconstruction and Attribution for Circuit Tracing

Mechanistic interpretability seeks to explain neural network behavior by decomposing model computations into interpretable features and circuits. While transcoder-based circuit tracing has recently enabled detailed causal analyses of large language models, multimodal diffusion transformers for image generation remain comparatively opaque. We still lack tools for understanding how semantic information propagates across denoising steps and how text and image representations interact within double-stream MM-DiT architectures. Existing methods provide only partial insight: attention maps expose a limited view of token interactions, while sparse autoencoders can discover interpretable features but do not directly reveal how these features are transformed and composed through nonlinear MLP layers. In this work, we extend transcoder-based circuit tracing to multimodal diffusion transformers. We train timestep-conditioned transcoders that faithfully approximate the input-output behavior of MLP sublayers in FLUX.1[schnell]. By replacing MLPs with transcoders and linearizing the remaining computation, we obtain exact feature-to-feature attribution and recover compact, interpretable circuits. Empirically, our transcoders match or slightly outperform sparse autoencoders on the sparsity-faithfulness tradeoff. The resulting circuits reveal mechanisms underlying attribute binding and cross-stream semantic propagation, and provide causal explanations for systematic generation errors. Moreover, circuit-guided interventions are substantially more precise and effective than standard SAE-based steering. Our results demonstrate that transcoder-based circuit analysis is feasible for state-of-the-art diffusion transformers and provides a powerful framework for understanding and controlling multimodal generative models. The code is available at https://github.com/Artalmaz31/DifFRACT

07.
arXiv (CS.AI) 2026-06-18

Maturing Markov Decision Processes: Decision Making under Increasing Information and Shrinking Action Sets

arXiv:2606.18820v1 Announce Type: cross Abstract: Sequential decision problems often exhibit an asymmetric evolution of information and decision flexibility: as a decision cycle unfolds, the agent receives richer information while feasible actions expire due to operational cutoffs, commitments, or resource constraints. Standard MDP formulations typically flatten this structure into stage-dependent state descriptions and action masks, thereby obscuring the nested information–action asymmetry that determines which decisions are urgent and which can be deferred. We introduce Maturing Markov Decision Processes (MMDPs), a formulation built around this information–action asymmetry. We characterize one of its key consequences through an expiring-action priority principle, which identifies the actions that must be resolved before the next stage. Motivated by this structure, we develop a structure-aware reinforcement learning framework with stage-aware policy design, expiring-action abstraction, and search-augmented learning with distillation. Experiments on a controlled multi-supplier replenishment problem, simplified cash-management environments of increasing complexity, and a production-scale simulator show that explicitly modeling this asymmetry improves learning efficiency and becomes increasingly valuable as decision problems scale.

08.
arXiv (CS.AI) 2026-06-24

Scaling Laws for Task-Specific LLM Distillation

arXiv:2606.24747v1 Announce Type: new Abstract: Large Language Models (LLMs) achieve strong performance across a growing range of domains, yet their scale poses deployment challenges in applications where latency and cost constraints are critical. This paper derives empirical scaling laws for domain-specific LLM compression, quantifying how in-domain and general knowledge performance scale with dataset size, compression ratio, supervision format, and iterative pruning schedule. Using quantitative finance as our application domain, we compare logit-based and LoRA-based distillation under iterative structural pruning, introducing a blended chain-of-thought supervision loss that stabilizes KL-divergence distillation over reasoning traces. In-domain task quality degrades predictably under compression while general-knowledge benchmarks collapse well before the same point; supervision format is the key driver of this tradeoff, with chain-of-thought supervision actively recovering general knowledge that pruning erases. We release the headline dataset FinHeadlineMix, scaling law results, and practical recommendations to provide a reusable framework for domain-specific compression decisions.

09.
arXiv (quant-ph) 2026-06-15

On-site interactions in quantum thermal machines: efficiency, rectification and entanglement beyond local and global master equations

arXiv:2606.14593v1 Announce Type: new Abstract: Advances in experimental techniques have opened new routes for harnessing non-equilibrium dynamics in mesoscopic quantum systems. In this context, we study the impact of on-site interactions on the transport properties of a continuous quantum thermal machine composed of two coupled oscillators connected to two thermal reservoirs. In the weak system-reservoir coupling regime, where a long-standing debate concerns which reduced description should be preferred, we first show that the Redfield master equation (RME) provides an accurate and unifying framework that interpolates between two well-known limits: the local and global master equations. By relying on the Hierarchy of Pure States (HOPS), a numerically exact stochastic method, we then explore the full parameter space and show that interactions can be leveraged to tune the efficiency of the thermal machine at high temperatures (while leaving it essentially unchanged at low temperatures), induce non-reciprocal transport under asymmetric reservoir couplings, and generate steady-state entanglement within the junction. We derive expressions for system-bath correlators, such as heat and particle currents, consistently across different frameworks. Our work features on-site interactions to enhance the versatility of quantum thermodynamic junctions and clarifies the role of non-Markovianity and non-linearities in quantum transport.

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

From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models

Authors:

arXiv:2606.08956v2 Announce Type: replace Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs – forces, fluxes, or heat sources – to outputs, such as displacement, velocity, concentration, and temperature. These models rely on deep domain knowledge to determine the form of the governing differential equation, which is then calibrated with data by solving an inverse problem. In recent years, the field of Scientific Machine Learning has introduced a variety of alternative modeling strategies for physical systems. A method called Sparse Identification of Nonlinear Dynamics learns the governing equation as a sparse linear combination of terms in a user-defined library. Neural Ordinary Differential Equations construct the governing equation by taking in the state and its derivatives at the input layer of a neural network. Entirely foregoing the modeling framework of differential equations, neural operators directly learn a non-linear mapping between the system inputs and outputs. From inverse problems to neural operators, all of these modeling strategies can be conceptualized as data-driven machinery to predict a system's response over a range of inputs. It is then natural to wonder how exactly these various strategies relate to each other, and whether they can be neatly taxonomized. Drawing from the philosophical literature on scientific models, we argue that many model types have a common structure, differing only in the assumed model class of the input-output relation they define. Connecting to philosophical ideas on mechanism, and arguing that data from physical systems arises from solutions to parsimonious differential equations, we propose that only certain models are capable of mechanism discovery, and thus generalization. Our analysis is intended to unite apparently disparate modeling strategies and provide insight into their appropriate use cases.

11.
arXiv (CS.LG) 2026-06-24

Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems

arXiv:2606.24769v1 Announce Type: cross Abstract: Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonlinear parametrizations such as neural networks or mixture models. We propose to add inertia to the Dirac-Frenkel dynamics and show that this allows useful parameter velocity information to persist from the past trajectory in directions that are weakly informed, while well-informed parameter velocity directions continue to follow the Dirac-Frenkel dynamics. We prove that the inertial formulation yields well-posed parameter dynamics and provide a posteriori error bounds. After time discretization, the method requires the solution of the same type of regularized linear least-squares problem as standard Dirac-Frenkel dynamics, but with the previous velocity appearing as an anchor. Numerical experiments demonstrate the increased robustness obtained with inertia.

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

Probabilistic Salary Prediction with Graph Attention Networks and a Mixture Density Network

arXiv:2606.11663v1 Announce Type: cross Abstract: Accurate salary prediction is critical for bridging the information gap between employers and job seekers in modern labor markets. Existing approaches predominantly yield a single point estimate and treat job attributes such as location, occupation, and industry as independent categorical features, ignoring both the inherent uncertainty and multi-modality of real-world compensation data and the rich hierarchical and semantic-similarity relationships that govern pay norms. In this paper we propose GAT-MDN, a unified framework that addresses both limitations simultaneously. For each of the three attribute domains we construct a domain-specific graph whose edges encode (i) hierarchical parent-child containment and (ii) weighted similarity links derived from a pre-trained Sentence-Transformer. Parallel Graph Attention Networks (GATs) with edge-feature-aware attention learn rich, context-sensitive node representations from these multi-relational graphs. A priority-based hierarchical selection module then assembles a composite feature vector that gracefully handles missing or coarse attributes, and a Mixture Density Network (MDN) head maps this vector to the parameters of a Gaussian Mixture Model (GMM), yielding a full conditional salary distribution. Extensive experiments on a real-world Dutch job-posting dataset of over 1 million records demonstrate that GAT-MDN significantly outperforms a non-graph MLP-MDN baseline in both Negative Log-Likelihood (NLL) and Mean Squared Error (MSE).

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

Harness In-Context Operator Learning with Chain of Operators

arXiv:2606.12318v1 Announce Type: cross Abstract: Neural operators approximate mappings between function spaces, but often generalize poorly to other operators and usually require fine-tuning or retraining. In-Context Operator Networks (ICON) addresses this issue by prompting the model with numerical context so that the model learns specific operators from prompts and adapt to different operators without fine-tuning. However, ICON may still fail to generalize to out-of-distribution (OOD) operator tasks. Inpired by the success of harness engineering of Large Language models (LLMs), we introduce Chain of Operators (CHOP), a framework that harness a frozen ICON to OOD operator tasks without updating its parameters. Specifically, CHOP constructs a chain of operators consisting of explicit elementary transformations and the frozen ICON. Experiments on a scalar conservation law and a mean-field control problem show that CHOP reduces relative inference error over direct ICON evaluation, while each operator in the chain remains interpretable and in closed form. A chain constructed on one PDE family further generalizes to a different family, indicating shared mechanisms across harness systems.

14.
arXiv (CS.CV) 2026-06-15

Interpretable Alzheimer's Diagnosis via Multimodal Fusion of Regional Brain Experts

Accurate and early diagnosis of Alzheimer's disease (AD) is critical for effective intervention and requires integrating complementary information from multimodal neuroimaging data. However, conventional fusion approaches often rely on simple concatenation of features, which cannot adaptively balance the contributions of biomarkers such as amyloid PET and MRI across brain regions. In this work, we propose MREF-AD, a Multimodal Regional Expert Fusion model for AD diagnosis. It is a Mixture-of-Experts (MoE) framework that models mesoscopic brain regions within each modality as independent experts and employs a gating network to learn subject-specific fusion weights. Utilizing tabular neuroimaging and demographic information from the Alzheimer's Disease Neuroimaging Initiative (ADNI), MREF-AD achieves competitive performance over strong classic and deep baselines while providing interpretable, modality- and region-level insight into how structural and molecular imaging jointly contribute to AD diagnosis. The source code is available at https://github.com/PennShenLab/mref-ad.

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

LLMs Infer Cultural Context but Fail to Apply It When Responding

Recent work has shown that LLMs overrepresent dominant cultures, particularly Western ones, while marginalizing others. We investigate whether this affects models' ability to generate culturally adapted responses by evaluating their use of local measurement units based on the user's perceived cultural background. We introduce Cultural and Pragmatic Response Inference (CAPRI), a dataset of conversations with varying levels of cultural cues. Experiments with state-of-the-art LLMs show that models can infer cultural background and recall relevant conventions, but often fail to utilize the information to adapt their answers to the relevant cultural conventions, unless explicitly prompted to perform the tasks sequentially. We further evaluate adaptation to the interpretation of time and quantity expressions, two subjective language grounding dimensions that are affected by culture. We find that models increasingly adapt their answers as cultural cues accumulate, but their priors are not culture-neutral, sometimes aligning with the model's country of origin. Overall, CAPRI provides a resource for future research aimed at narrowing the gap between cultural knowledge and culturally adaptive language generation.

16.
bioRxiv (Bioinfo) 2026-06-15

SMLMFlow: Improving Structural Resolution in Single Molecule Localization Microscopy with Flow Matching

While Single Molecule Localization Microscopy (SMLM) aims to generate precise coordinates of molecular targets in cells, the resulting point clouds are inherently blurred by additive noise sources across the experimental, imaging, and processing workflow. This blurring often limits SMLM's ability to accurately quantify complex assembled structures required to address biological issues, despite reported localization precision down to a couple of nanometers. Here, we present SMLMFlow, a machine learning framework for improving structural resolution in SMLM datasets that combines a graph neural network and a hierarchical transformer with flow matching. We show that SMLMFlow improves structural resolution and downstream quantification across different structures, including filaments and protein nano-clusters, and generalizes to new unseen photophysics models.

17.
arXiv (math.PR) 2026-06-12

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

Authors:

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.

18.
arXiv (CS.AI) 2026-06-12

Topical Phase Transitions in Artificial Intelligence Research: Large-Scale Evidence and an Early-Warning Signature for Emerging Topics

arXiv:2606.12828v1 Announce Type: new Abstract: Do research topics in artificial intelligence grow gradually, or do they advance through abrupt, detectable jumps? Analyzing 80,814 accepted main-track papers from five premier AI conferences (ACL, CVPR, ICLR, ICML, NeurIPS) spanning 2017 to 2025, we show major AI topics advance through topical phase transitions: remaining marginal for years, then surging across venues within one to three years. Large language models became the dominant cross-venue topic by 2025, diffusion models rose with comparable abruptness, and language-model methods crossed into computer vision via vision-language models, whereas reinforcement learning compounded smoothly, distinguishing genuine phase transitions from ordinary growth. This structure is our primary contribution: a large-scale, cross-venue characterization of how AI research reorganizes. We then ask whether a transition leaves a detectable footprint before it peaks. We define an early-warning signature, four publication-dynamics criteria frozen on 2017-2021 data, and evaluate it out of sample on 2023-2025 transitions, obtaining a precision of 27% and recall of 63% against a 13.5% base rate. Applied to 2025 data, the signature flags reasoning and test-time compute, agentic AI, multimodal LLMs, retrieval-augmented generation, and world models as topics to monitor over 2026-2028. The source code is also publicly available on GitHub at https://github.com/KurbanIntelligenceLab/ai-phase-transitions.

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

LIBERO-Occ: Evaluating and Improving Vision-Language-Action Models under Scene-Induced Occlusion via Viewpoint Imagination

Vision-Language-Action (VLA) models achieve strong performance on standard manipulation benchmarks, but most evaluations assume that task-relevant objects are fully visible. This assumption often fails in realistic settings, where occlusion makes manipulation partially observable. In this paper, we study scene-induced occlusion as a fundamental challenge for VLA models and introduce LIBERO-Occ, an occlusion-oriented extension of LIBERO. Experiments show that state-of-the-art VLAs suffer substantial performance degradation under occlusion. To address this issue, we propose Viewpoint Imagination (VIM), which generates a complementary view from an occluded primary observation and conditions action prediction on both observed and imagined evidence. VIM improves robustness across task suites, occlusion types, and severity levels without requiring additional cameras at deployment time, suggesting that viewpoint imagination is an promising mechanism for perception completion in partially observable manipulation. Our benchmark and corresponding code are available at: \href{https://github.com/litsh/Libero-Occ}{https://github.com/litsh/Libero-Occ}.

20.
arXiv (CS.AI) 2026-06-24

Decentralised AI Training and Inference with BlockTrain

Authors:

arXiv:2606.24722v1 Announce Type: new Abstract: Frontier AI training is increasingly shaped by access to dense, centrally controlled accelerator clusters. This creates a structural advantage for hyperscalers and large centralized laboratories, and makes open or independent AI efforts depend on scarce capital, privileged infrastructure, and data-center geography. We present Spheroid BlockTrain, a decentralized training protocol in which a model is partitioned into independently trainable blocks, each optimized on a local objective derived from the same global target and composed at inference into one model. On byte-level WikiText, BlockTrain reaches cross entropy 1.359 (perplexity 3.89), within about 0.04 CE of a same-setup end-to-end Transformer reference, while each active worker trains only one block and avoids full-model optimizer state. A shared six-worker block training run reaches CE 1.385 by averaging same-block updates into one assembled model. HTTP/TCP transport experiments move real serialized checkpoints and updates, including a public-IP three-host run that improves CE from 5.580 to 1.811 while moving 15.22 GB. For inference, the current BlockTrain path uses one block-stack traversal per full output and serves over direct TCP across three public-network GPU hosts up to a 75.80B-parameter logical fp16 shape, outperforming a matched plain-autoregressive TCP pipeline baseline because it emits a full sequence per WAN pipeline traversal rather than one token per traversal.

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

A Practical Evaluation Method for Long-Form Simultaneous Speech-to-Speech Translation

Simultaneous speech-to-speech translation (SimulS2ST) enables real-time cross-lingual communication, but existing evaluation has focused largely on short or pre-segmented speech rather than long-form, continuous input. Prior approaches are difficult to reproduce and make assumptions that do not hold for end-to-end systems. We present a practical evaluation method for long-form SimulS2ST. Given source speech, pre-segmented source transcripts, and reference translations, we run automatic speech recognition (ASR) and forced alignment on the generated target speech to recover token-level timestamps, then apply a sentence-embedding-based aligner to match the target text to its corresponding source sentences. This enables sentence-level computation of latency and quality metrics, including YAAL and xCOMET, which are then aggregated into final system-level scores. Experiments on representative SimulS2ST systems show that the method is effective in practice and reveal that current systems suffer from substantial latency accumulation on long speech.

22.
arXiv (CS.LG) 2026-06-24

The Cost Geometry of Belief: finite-resource inference under noisy observation

arXiv:2606.21585v2 Announce Type: replace Abstract: A finite machine's digital twin of a system observes the territory through finite, noisy sensors; we model its coherent output as a belief, a probability density over states, the Bayes posterior, never a point. Certainty, the perfect twin, is denied twice, by observation and by physics, both read off the Fisher information. To make this finiteness geometric, we model what it costs to change a belief: a belief-cost geometry, optimal transport in Wasserstein space reweighted conformally by Fisher information. The framework rests on two posed commitments: that revision cost is a scalar price on transport (the arena), and that the price is honest: one nat costs the same length everywhere. Honesty selects the Fisher reweighting because transport demotes the Fisher information from the metric ruler of distinguishability to the slope of entropy, the move that sets transport apart from Fisher-Rao. From these two postulates, three results follow on the conformal class (essentially location-scale), all invariants of one change of cost unit. A wall: a well-posed inference rejects certainty to infinite distance as soon as the cost dominates the Fisher information (necessity conjectured beyond power laws). An honest family: the eikonal price where each nat the same length everywhere, is equivalent to proportionality U=cJ, the Fisher family. A rigidity: these geometries are hyperbolic, and the Stam bound crowns the Gaussian, the most hyperbolic location-scale belief; -1/4 is one image of a relativity of cost. The cost of reaching a given precision then has a geometric cost floor diverging at certainty. Thermodynamics fixes the cost unit and motivates the framework; the results are geometric, in nats.

23.
arXiv (CS.LG) 2026-06-15

On the Geometry and Optimization of Polynomial Convolutional Networks

arXiv:2410.00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions. Specifically, we prove that their parameterization map is regular and is an isomorphism almost everywhere, up to rescaling the filters. By leveraging on tools from algebraic geometry, we explore the geometric properties of the image in function space of this map - typically referred to as neuromanifold. In particular, we compute the dimension and the degree of the neuromanifold, which measure the expressivity of the model, and describe its singularities. Moreover, for a generic large dataset, we derive an explicit formula that quantifies the number of critical points arising in the optimization of a regression loss.

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

Federated Medical Image Segmentation under Real-World Label Noise: A Benchmark Suite for Noisy Label Learning Method Selection

While federated learning (FL) enables collaborative medical image segmentation without centralizing sensitive data, real-world deployment is frequently complicated by cross-site label imperfections such as contour disagreement, missing or additional structures, and confused labels. Federated noisy label learning (FNLL) aims to mitigate these effects, yet remains underused in practice as existing evidence is largely based on synthetic noise, simplified settings, and limited real-world noisy evaluation. We address this gap by introducing a benchmark suite that combines diverse real-world noisy datasets, deployment-relevant client-noise scenarios, and label-noise-targeted evaluation to support systematic FNLL assessment and informed method selection. The suite combines curated real-world noisy medical image segmentation datasets from diverse sources with a comprehensive federated segmentation framework including various client-noise scenarios and noise-targeted evaluation. The presented suite provides a realistic and discriminative basis for FNLL evaluation in medical image segmentation and establishes a reusable foundation for fair benchmarking, dataset-specific label-noise characterization, and future method development under realistic federated settings. Code is available at https://github.com/MIC-DKFZ/FedSegNoiseBench.

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

Open-World Video Segmentation

While video segmentation has advanced rapidly on short clips and closed-set benchmarks, open-world video segmentation remains largely unexplored. The challenge is twofold: (1) existing methods are not designed to support object discovery and identity maintenance in long videos of dynamic ego-motion, and (2) existing evaluation protocols rely on a rigid 1:1 matching that unfairly penalizes semantically valid predictions with mismatched granularity. To address both gaps, we introduce Savvy, a practical and strong system for zero-shot open-world long-horizon video segmentation. Savvy combines hierarchical mask discovery, deferred admission, and track consolidation to support persistent object discovery, safe track promotion, and stable long-range identity maintenance. We further propose OGA, a granularity-aware evaluation suite for open-world video segmentation. Built on a Granularity-Agnostic (GA) matching protocol, OGA relaxes conventional 1:1 matching to an n:1 mapping, but still enforces temporal rigor by detecting support discontinuities through sever points and scoring each reference object through its dominant coherent fragment. This prevents fragmented or flickering support from being over-rewarded while enabling GA-adapted metrics and structural diagnostics: identity persistence (IP), and identity concentration (IC). On VIPSeg, we show that standard 1:1 evaluation substantially underestimates open-world methods, whereas GA evaluation recovers much of their suppressed performance. On the more realistic long-horizon benchmarks: ScanNet and HM3D, Savvy consistently outperforms strong baselines across both classical and proposed metrics, including STQ, VPQ$_\infty$, IP and IC. Together, these results establish a practical benchmark and a strong baseline for open-world long-horizon video segmentation.