# Research Papers — 2026-05 · bundle page 253 of 326

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### mHC-SSM: Manifold-Constrained Hyper-Connections for State Space Language Models with Stream-Specialized Adapters

Authors: Abdulvahap Mutlu, Şengül Doğan, Türker Tuncer
Published: 2026-05-08
Categories: cs.LG, cs.AI, cs.CL
arXiv: https://arxiv.org/abs/2605.08300v1

Manifold-Constrained Hyper-Connections (mHC) introduce a stability-motivated variant of multi stream residual mixing by constraining residual stream mixing matrices to the manifold of doubly stochastic matrices via Sinkhorn-Knopp projection. In his work, we study whether mHC-style constrained multi-stream residual topology transfers effectively to state space model (SSM) language modeling. We implement a static mHC mechanism around an SSM block by expanding the residual stream into multiple parallel streams, aggregating streams into a single SSM input through simplex-constrained pre-mixing, scattering the SSM output back to streams through simplex-constrained post-mixing, and applying Sinkhorn-projected residual stream mixing at each layer. We further introduce stream-specialized adapters that add lightweight stream-specific capacity through a shared bottleneck with per-stream scaling, applied both before stream aggregation and after the SSM output prior to scattering. We evaluate baseline single-stream SSM, static mHC SSM, and mHC SSM with adapters on WikiText-2 using identical training settings and report checkpoint-based validation loss, perplexity, throughput, and peak GPU memory. Under the reported fair checkpoint evaluation, static mHC improves validation loss from 6.3507 to 6.2448 and reduces perplexity from 572.91 to 515.35, while mHC with adapters further improves validation loss to 6.1353 and perplexity to 461.88. These gains are accompanied by modest throughput reductions from 1025.52 to 964.81 and 938.90 tokens per second, and increased peak memory from 2365 MB to 2568 MB and 3092 MB. The results suggest that mHC-inspired constrained multi-stream residual mixing can yield measurable quality improvements in SSM language models and that stream-specialized adapter capacity can further enhance performance with predictable efficiency tradeoffs.

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### Do not copy and paste! Rewriting strategies for code retrieval

Authors: Andrea Gurioli, Federico Pennino, Maurizio Gabbrielli
Published: 2026-05-08
Categories: cs.SE, cs.AI
arXiv: https://arxiv.org/abs/2605.08299v1

Embedding-based code retrieval often suffers when encoders overfit to surface syntax. Prior work mitigates this by using LLMs to rephrase queries and corpora into a normalized style, but leaves two questions open: how much representational shift helps, and when is the per-query LLM call justified? We study a hierarchy of three rewriting strategies: stylistic rephrasing, NL-enriched PseudoCode, and full Natural-Language transcription, under joint query-corpus (QC, online) and corpus-only (C, offline) augmentation, across six CoIR benchmarks, five encoders, and three rewriters spanning independent model families (Qwen, DeepSeek, Mistral). We are the first to evaluate NL-enriched PseudoCode and snippet-level Natural Language as direct retrieval representations, rather than as transient intermediates. Full NL rewriting with QC yields the largest gains (+0.51 absolute NDCG@10 on CT-Contest for MoSE-18), while corpus-only rewriting degrades retrieval in 56 of 90 configurations, about 62%. We introduce two diagnostics, Delta H, token entropy, and Delta s, embedding cosine, and show that Delta H predicts retrieval gain under QC across all three rewriter families: pooled Spearman rho = +0.436, p &lt; 0.001 on DeepSeek+Codestral; rho = +0.593 on Codestral alone; rho = +0.356 on Qwen. This establishes Delta H as a cheap, rewriter-agnostic proxy for deciding when rewriting pays off before running retrieval. Our analysis reframes LLM rewriting as a cost-benefit decision: it is most effective as a remediation layer for lightweight encoders on code-dominant queries, with diminishing returns for strong encoders or NL-heavy queries.

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### What Cohort INRs Encode and Where to Freeze Them

Authors: Vasiliki Sideri-Lampretsa, Sophie Starck, Robbie Holland, Julian McGinnis, Daniel Rueckert
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08298v1

Reusing the early layers of cohort-trained INRs as initialization for new signals has been shown to accelerate and improve signal fitting, yet it remains unclear which layers of the shared encoder learn transferable representations and what those representations encode. We address both questions for two standard backbones, SIREN and Fourier-feature MLPs (FFMLP). First, sweeping the freeze depth across the shared encoder at test time, we find that the optimum coincides with the layer of highest weight stable rank. Moreover, freezing at this depth matches or improves on the standard fine-tuning recipe across all our experiments. Second, identifying which layer transfers does not characterize what that layer encodes. To address this we adopt sparse autoencoders (SAEs), the dominant tool in mechanistic interpretability, and present the first SAE decomposition of INR activations into sparse dictionary atoms. Interestingly, SIREN and FFMLP achieve comparable cohort-fitting quality, but learn qualitatively different dictionaries. Cohort SIREN's atoms are localized, tiling the coordinate plane such that each atom fires in a confined region independent of cohort content. Cohort FFMLP's atoms are image-spanning, tracing the contours of memorized cohort signals. Single-atom ablations confirm causal use of these dictionaries: a single FFMLP atom out of 4096 can drop PSNR by up to 10.6 dB across the image, while SIREN ablations remain confined to where the atom fires. Together, these results give the first mechanistic account of what transfers in cohort-trained INRs and turn their activations into inspectable dictionary atoms. These tools open a path towards characterizing what INRs encode and towards architectures designed for generalization rather than memorization.

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### A Qualitative Test-Risk Mechanism for Scaling Behavior in Normalized Residual Networks

Authors: Daning Cheng, Zeyu Liu, Jun Sun, Fen Xia, Boyang Zhang, Dongping Liu, Yunquan Zhang
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08297v1

The scaling behavior, in which test performance often improves as model size and data increase, is a central empirical phenomenon in modern deep learning, yet its theoretical basis remains incomplete. In this paper, we study depth expansion in normalized residual networks: starting from a trained model in an old hypothesis class, we insert a new residual block at an intermediate layer and ask when such an expansion can yield a provable improvement in test risk. We develop a unified framework that decomposes this question into representational gain, optimization gain, and generalization transfer. First, under a first-order descent condition near zero initialization, we prove that the expanded hypothesis class contains an auxiliary jumpboard model with strictly smaller population risk than the original model. Second, under norm control tailored to post-normalized residual architectures, we establish a norm-based Rademacher complexity bound for the expanded model class. These ingredients lead to two complementary test-risk guarantees: one route passes through population risk and is tighter when a positive population margin is available, while the other works directly at the train/test level, avoids Hoeffding transfer, and is more robust in degenerate regimes. Together, these results provide a theorem-driven mechanism under which residual depth expansion can improve test performance in normalized residual networks. More broadly, they suggest that scaling is inherently joint: depth creates new improving directions, width enhances the finite-sample observability of weak signals, and data determines whether the statistical cost of expansion can be controlled.

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### BenchHAR: Benchmarking Self-Supervised Learning for Generalizable Sensor-based Activity Recognition

Authors: Yize Cai, Rui Feng, Anlan Yu, Baoshen Guo, Zhiqing Hong
Published: 2026-05-08
Categories: cs.CV, eess.SP
arXiv: https://arxiv.org/abs/2605.08296v1

Human Activity Recognition (HAR) from wearable sensors supports broad healthcare and behavior science applications. However, data heterogeneity and the scarcity of labeled data limit its real-world generalization. Recent advances in self-supervised learning (SSL) in vision and language domains have shown strong capability for learning generalizable representations from unlabeled data. Yet, few studies have systematically compared the generalization performance of SSL methods or explored how to adapt them for generalizable HAR. To address these gaps, we present BenchHAR, a unified framework for evaluating the generalization capability of SSL methods for sensor-based HAR on unseen target distributions. BenchHAR curates a large-scale dataset (~258K samples) and evaluates eight representative SSL methods across 12 encoder-classifier architectures. Our results reveal that existing SSL methods struggle to achieve satisfactory generalization performance. We find that: (1) For HAR models, the hybrid paradigm (combining reconstruction and contrastive pretraining) achieves the best overall performance. The CNN encoder exhibits the strongest ability to learn generalizable representations, while more expressive classifier architectures further improve generalization. (2) For data scale, increasing the amount of pretraining data from downstream activity classes consistently improves generalization, while adding more labeled data yields limited gains. Interestingly, incorporating unlabeled data from non-downstream activity classes does not improve generalization. (3) Sensor data collected from custom-grade devices generalizes better than that from research-grade devices, and data from limb transfers more effectively to trunk positions. BenchHAR provides a unified benchmark and actionable insights for generalizable sensor-based HAR systems. Our code is available at https://github.com/saiketa/HAR-Bench.

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### In-Context Fixation: When Demonstrated Labels Override Semantics in Few-Shot Classification

Authors: Ming Liu
Published: 2026-05-08
Categories: cs.LG, cs.AI, cs.CL
arXiv: https://arxiv.org/abs/2605.08295v1

While random demonstration labels barely hurt in-context learning (Min et al., 2022), we show that homogeneous labels--even semantically valid ones--collapse accuracy to &lt;=12% across six models (Pythia, Llama, Qwen; 0.8B--8B) and four tasks. The trigger is label-slot content: the model treats tokens occupying the label position as an exhaustive answer vocabulary, with homogeneity as the maximally collapsed case. A novel set-level fixation finding confirms this: when demonstrations carry varied nonsense tokens from {foo,bar,vex,nit,orb}, the model places 42--67% of probability on the demonstrated set while P(dog) remains below 0.2%. This is inconsistent with latent-concept Bayesian accounts (Xie et al., 2022) and reveals that ICL output is constrained vocabulary retrieval--the model binds its output to the demonstrated token inventory regardless of semantic plausibility. The effect generalizes to 4-way classification (0% accuracy across three models, 1B--8B) and multi-token verbalizers ("very positive"), where we decompose fixation into format-level (template adoption) and content-level (polarity override) components that are experimentally dissociable. Mechanistically, per-item paired activation patching on Pythia-1B recovers 98.4% of the gap (95% CI (84%, 112%)), localizing fixation to a layer-7-centered circuit (rank 2/560, 99.8th percentile; 4-fold CV mean 103%). Cross-architecture logit lens on Llama-3.2-1B replicates the encode-then-override trajectory with causal confirmation (top-5 layers: 89% recovery).

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### Distill, Diffuse, Segment: Unsupervised 3D Semantic Segmentation for Autonomous Driving Based on Multi-Level Distillation and Graph Diffusion

Authors: Yijing Wang, Ruonan Li, Qilin Wang, Rongqiang Zhao, Jie Liu
Published: 2026-05-08
Categories: cs.CV
arXiv: https://arxiv.org/abs/2605.08293v3

LiDAR-based semantic segmentation is essential for autonomous-driving perception, yet dense point-wise annotations are costly, and long-tailed outdoor scenes make small safety-critical objects difficult to discover without supervision. Existing unsupervised methods face three key challenges: they struggle to preserve small and sparsely observed objects under substantial scale variation, have difficulty enforcing intra-region consistency and inter-region discrimination during cross-modal transfer, and lack an efficient feature-preserving mechanism for contextual propagation over superpoint graphs. We therefore propose DDS, an unsupervised 3D semantic segmentation framework. First, a coarse-to-fine multi-granularity mask cascade provides complementary 3D region cues for objects across different scales, improving the preservation of small and sparsely observed objects. Second, region-guided multi-level distillation transfers self-supervised visual knowledge through point-level alignment, mask-level prototype alignment, and prototype-level contrastive learning, enhancing intra-region consistency and inter-region discrimination. Third, restart-based graph diffusion efficiently propagates contextual information among superpoints while anchoring the refined representation to the initial distilled features and avoiding explicit graph eigendecomposition. Experiments on real-world driving datasets show that DDS outperforms representative unsupervised baselines, improving oAcc, mAcc, and mIoU by up to 2.9%, 9.7%, and 4.1%, respectively. These results demonstrate the effectiveness and transferability of DDS for unsupervised 3D scene understanding in autonomous-driving scenarios.

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### Hierarchical Mixture-of-Experts with Two-Stage Optimization

Authors: Gleb Molodtsov, Alexander Miasnikov, Aleksandr Beznosikov
Published: 2026-05-08
Categories: cs.LG, cs.AI, math.OC
arXiv: https://arxiv.org/abs/2605.08292v1

Sparse Mixture-of-Experts (MoE) models scale capacity by routing each token to a small subset of experts. However, their routers exhibit a fundamental trade-off: strong load balancing can suppress expert specialization, while aggressive diversity often causes routing collapse. We propose Hi-MoE, a grouped MoE framework that decomposes routing control into two coupled levels: (i) inter-group balancing that enforces fair traffic across expert groups, and (ii) intra-group specialization that promotes complementary expert behaviors while preventing within-group collapse. Our analysis provides a principled explanation of how our hierarchical objectives reshape the router, thereby promoting stable specialization and mitigating collapse. We observe consistent improvements over recent sparse-routing and grouped-MoE baselines across NLP and vision benchmarks, and confirm robustness via scaling studies (model size, expert count) and targeted ablations. In large-scale pre-training on 58B tokens, Hi-MoE-7B achieves a 5.6% perplexity reduction and a 40% improvement in expert balance over OLMoE-7B across diverse evaluation domains.

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### Graph Computation Meets Circuit Algebra: A Task-Aligned Analysis of Graph Neural Networks for Electronic Design Automation

Authors: Hyunmog Kim
Published: 2026-05-08
Categories: cs.LG, cs.AI, cs.AR
arXiv: https://arxiv.org/abs/2605.08291v1

EDA problems are graph-structured, but not all graph-structured problems call for the same GNN computation. We argue that successful GNN-for-EDA methods are those whose propagation, aggregation, and supervision align with the native algebra of the target task. Concretely: static timing analysis is a max-plus/min-plus recurrence on a topologically ordered DAG, structurally aligned with asynchronous DAG-GNNs; placement is governed by hypergraph wirelength and density penalties and is exploited by differentiable placers rather than by message-passing GNNs alone; routing congestion is a sparse demand-supply field over a layout grid; switching-activity propagation is a probabilistic recurrence on a directed netlist; IR drop is a linear system on the power-delivery network; and analog symmetry extraction is a discrete constraint-prediction problem on schematic graphs. Through these task-by-task alignments we (i) review the GNN architectural toolkit relevant to circuits, (ii) formalize how circuit graphs differ from generic graphs (directed, heterogeneous, multi-scale, with sequential and clock structure), (iii) characterize where current methods succeed and where the algebra-architecture mismatch limits them, and (iv) identify failure modes--stage leakage, proxy-to-signoff gap, calibration, and design-distribution shift--that we believe are likely to dominate the next phase of work. We position the paper as a GNN-for-EDA, task-aligned analysis rather than a comprehensive AI-for-chip-design survey. Continuous SE(3)-equivariant geometric GNNs are usually mismatched to Manhattan digital layout, and LLM-for-RTL, HLS, and RL/diffusion-based topology generation are outside our scope.

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### Toward Optimal Regret in Robust Pricing: Decoupling Corruption and Time

Authors: Kalana Kalupahana, Francesco Emanuele Stradi, Matteo Castiglioni, Alberto Marchesi
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08290v1

We design the first regret guarantees for robust dynamic pricing that decouple the dependence on the corruption $C$ and the time horizon $T$. In dynamic pricing, a seller with unlimited supply of a good interacts with a stream of buyers over \( T \) rounds, with the goal of maximizing revenue. At each round $t$, the seller posts a price $p_t$, and the buyer purchases the good only if their unknown valuation $v^\star$ exceeds this price. The seller observes only the binary feedback $\mathbb{I} \left\{ p_t \leq v^\star \right\}$, indicating whether a sale occurred. In the \emph{robust} pricing setting, a malicious adversary is allowed to corrupt this feedback in at most $C$ rounds. Even if the learner knows the corruption $C$, the best known regret bound is $\mathcal{O}(C\log\log T)$ by Gupta et al. (2025). This leaves as an open problem to ``decouple'' the dependence on $C$ and $T$. In this work, we resolve this open problem. In particular, we develop a robust variant of binary search that achieves regret $\mathcal{O}(C+\log T)$ when the corruption $C$ is known and $\mathcal{O}(C+\log^2 T)$ when the corruption is unknown.

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### What If We Let Forecasting Forget? A Sparse Bottleneck for Cross-Variable Dependencies

Authors: Fan Zhang, Shiming Fan, Hua Wang
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08289v1

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from "more interaction" to "more effective interaction".

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### UMEDA: Unified Multi-modal Efficient Data Fusion for Privacy-Preserving Graph Federated Learning via Spectral-Gated Attention and Diffusion-Based Operator Alignment

Authors: Shih-Yu Lai, Hirozumi Yamaguchi, Shang-Tse Chen, Yu-Lun Liu, Bing-Yu Chen
Published: 2026-05-08
Categories: cs.LG, cs.AI, cs.CR, cs.DC
arXiv: https://arxiv.org/abs/2605.08288v1

Device-free localization trains models from heterogeneous wireless and visual sensors (e.g., Wi-Fi, LiDAR) distributed across edge devices. Federated learning offers a privacy-respecting framework, but is brittle when clients differ in sensor modality and resolution, when their data distributions drift, and when privacy noise destroys the structural signal needed for localization. We propose UMEDA, a graph federated learning framework in which clients form nodes of a global graph that share a continuous integral operator, and aggregation is reformulated as spectral signal processing on this operator. Each client encodes its local sensors with a linear-attention layer whose kernel spectrum is low-rank filtered, suppressing modality-specific residuals so clients with different sensors align in a common low-rank subspace. The server then aggregates client updates via a diffusion model over the kernel's spectral coefficients, treating updates as discretizations of a shared operator rather than topology-bound weights -- this absorbs varying graph sizes and missing modalities without node-wise correspondence. To balance privacy and utility, we add an anisotropic differential-privacy mechanism that projects noise preferentially into the null space of the signal subspace, preserving dominant eigendirections while ensuring formal $(ε, δ)$-DP under gradient clipping. On MM-Fi and the RELI11D out-of-distribution benchmark, UMEDA outperforms state-of-the-art federated baselines in accuracy, convergence, and communication efficiency, particularly under high modality heterogeneity and tight privacy budgets.

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### Multi-Armed Bandits With Best-Action Queries

Authors: Francesco Bacchiocchi, Matteo Castiglioni, Alberto Marchesi, Francesco Emanuele Stradi
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08287v1

We study \emph{multi-armed bandits} (MABs) augmented with \emph{best-action queries}, in which the learner may additionally query an oracle that reveals the best arm in the current round. This setting was recently characterized by Russo et al. (2024) in the \emph{full-feedback} model, where the learner observes the rewards of all arms after each round. They show that, in both \emph{stochastic} and \emph{adversarial} environments, $k$ best-action queries reduce the optimal $\widetilde{\mathcal{O}}(\sqrt{T})$ regret to $\widetilde{\mathcal{O}}(\min\{T/k,\sqrt{T}\})$. Whether this improvement extends to the more realistic \emph{bandit-feedback} model -- where the learner observes only the reward of the played arm -- was left as an open problem. We fully resolve this question. When rewards are stochastic but correlated among arms, we show that the full-feedback result does not carry over: any algorithm must incur regret at least $Ω(\sqrt{T-k})$. This lower bound directly extends to adversarial environments. On the positive side, we show that $\widetilde{\mathcal{O}}(\min\{T/k,\sqrt{T-k}\})$ regret is still achievable when rewards are stochastic and i.i.d., and establish a matching lower bound, up to logarithmic factors. Together, these results provide a complete characterization of the benefits of \emph{best-action queries} in the \emph{bandit-feedback} model.

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### Diagnosing Spectral Ceilings in Equivariant Neural Force Fields

Authors: Hyunmog Kim
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08286v1

We introduce a spectral-injection diagnostic for measuring which angular frequencies a trained equivariant force-field backbone preserves: inject a controlled angular-frequency perturbation into a molecular force field, attach a lightweight Spectral Prediction Network (SPN) to the frozen backbone, and read off which frequencies are recoverable. On aspirin, a quadratic SPN attached to an L = 2 NequIP backbone recovers the boundary signal at l = 4 but collapses at l = 5: a 11.7x cliff at the predicted drL boundary, with p dropping from 0.913 to 0.078. The same boundary-vs-above contrast persists across n = 4 independently trained backbones (raw-gain delta contrast, hierarchical cluster bootstrap) and is corroborated by a denominator-free injected-residual metric (R2_inj(4) = 0.374 versus R2_inj(5) = 0.006). A finite-degree span theorem calibrates the diagnostic: for a single marked direction, degree-d polynomials of degree-L spherical-harmonic features span exactly H less than or equal to dL with multiplicity-one saturation at the boundary (scoped to single-direction degree-bounded probes, not a function-class upper bound on multi-atom MPNNs). A synthetic C5 calibration plus capacity, activation, and cross-architecture controls rule out parameter count alone as the explanation.

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### Exactness Matters for Physical Rule Enforcement

Authors: Bum Jun Kim
Published: 2026-05-08
Categories: cs.LG, cs.CE
arXiv: https://arxiv.org/abs/2605.08285v1

Autoregressive scientific forecasters often enforce physical or structural constraints by repairing each predicted state before feeding it back into the model. However, it remains unclear when stronger physical rule enforcement becomes reliable and when it becomes a source of distribution shift. We study this question through operator exactness, meaning whether the repair map is the identity on the target manifold and is aligned with the target geometry. We compare raw forecasting, post hoc repair, and in-loop repair across periodic incompressible Navier--Stokes, non-periodic CFDBench flows, and a hierarchical-forecasting support task. In the exact periodic regime, Fourier projection substantially improves rollout accuracy. On the NS-128 benchmark, a strong Raw-FNO has a final-step rollout MSE at horizon 100 of $(9.390 \pm 6.290)\times 10^{-5}$, and post hoc and in-loop projection reduce it to $(1.130 \pm 0.165)\times 10^{-6}$ and $(5.370 \pm 0.113)\times 10^{-7}$. However, once an exact projection is unavailable and only approximate boundary-preserving cleanup is available, the ordering changes. Across cavity, tube, dam, and cylinder flow, stronger Poisson-based cleanup can reduce divergence while worsening rollout error; target-distortion MSE predicts this harm far better than a linear-system residual. Controlled mismatch, screened cleanup, adaptive gating, and external-backbone checks show that the best approximate-regime operating point can be raw or near-identity. Hierarchical forecasting gives the same broader pattern. Exact forecast reconciliation is a stable baseline, whereas blended top-down repair, a validation-tuned interpolation toward historical-proportion top-down reconciliation, is dataset-dependent. Thus, constraint enforcement should be benchmarked by operator--data alignment before enforcement strength.

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### HTPO: Towards Exploration-Exploitation Balanced Policy Optimization via Hierarchical Token-level Objective Control

Authors: Xincheng Yao, Ruoqi Li, Cheng Chen, Daoxin Zhang, Yi Wu, Yao Hu, Chongyang Zhang
Published: 2026-05-08
Categories: cs.LG, cs.AI, cs.CL
arXiv: https://arxiv.org/abs/2605.08283v1

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a pivotal technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, the de facto practice of mainstream RL algorithms is to treat all tokens of one response equally and assign the same optimization objective to each token, failing to provide granular guidance for the reasoning process. While in Chain-of-Thought (CoT) reasoning, different tokens usually play distinct roles. Therefore, the current RL algorithms lack an effective mechanism to dynamically balance the exploration-exploitation trade-off during learning. To this end, we propose Hierarchical Token-level Objective Control Policy Optimization (HTPO), a novel RL algorithm that takes the divide-and-conquer idea to hierarchically partition the response tokens into specific functional groups from three aspects (i.e., prompt difficulty, answer correctness, and token entropy). Within each group, according to the contributions to exploration or exploitation, we design specialized optimization objectives to facilitate the effective execution of each token's expected functionality. In this way, HTPO can achieve a more balanced exploration-exploitation trade-off. Extensive experiments on challenging reasoning benchmarks validate the superiority of our HTPO algorithm, which significantly outperforms the strong DAPO baseline (e.g., +8.6% and +6.7% on AIME'24 and AIME'25, respectively). When scaling test-time compute, the HTPO-trained model maintains a consistent performance advantage over the DAPO baseline, and the gap widens as the sampling budget increases, validating that our adaptive token-level control method fosters effective exploration without sacrificing exploitation performance. Code will be at https://github.com/xcyao00/HTPO.

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### A Paired Point-of-Care Ultrasound Dataset for Image Quality Enhancement and Benchmarking via a cGAN Baseline

Authors: Lennard M. van Karnenbeek, Hilde G. A. van der Pol, Mark Wijkhuizen, Eva Poelman, Caroline A. Drukker, Theo Ruers, Freija Geldof, Behdad Dashtbozorg
Published: 2026-05-08
Categories: eess.IV, cs.AI, cs.CV
arXiv: https://arxiv.org/abs/2605.08282v1

Purpose: We aim to enhance the image quality of point-of-care ultrasound (POCUS) devices using deep learning and a novel paired dataset of POCUS and high-end ultrasound images. Approach: We collected the first accurately paired dataset using a custom-built automated gantry system of low-end POCUS and high-end ultrasound images. A conditional generative adversarial network (cGAN) was utilized based on the pix2pix architecture, with a U-Net generator that incorporates both L1 and structural similarity index (SSIM) losses to improve perceptual quality. Pretraining on a simulation dataset further boosts performance. Evaluation was performed on 1064 paired ex vivo tissue and phantom ultrasound image sets. Results: Our approach improves the SSIM from 0.29 to 0.54 and PSNR from 19.16 dB to 22.41 dB. No-reference metrics also indicate substantial enhancement, with the Natural Image Quality Evaluator (NIQE) and Perception-based Image Quality Evaluator (PIQE) scores dropping from 7.95 to 4.44 and 31.12 to 19.99, respectively. Conclusions: This work presents the first publicly available accurately paired dataset of low-end POCUS to high end ultrasound images. Additionally, our results demonstrate the potential of the proposed framework to overcome hardware limitations of handheld POCUS, enhancing its diagnostic value in low-resource and point-of-care settings. The POCUS-IQ Dataset is publicly available at https://github.com/NKI-MedTech-AI/POCUS-IQ.

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### Is Class Signal Clustered or Routed in Task-Induced Implicit Neural Representation Weight Spaces?

Authors: Xinyi Guo, Mingyi He, Haobin Ding, Weiming Chen, Xinrui Chen, Jiawen Li, Di Zhang, Minxi Ouyang, Yizhi Wang, Xitong Ling
Published: 2026-05-08
Categories: cs.CV
arXiv: https://arxiv.org/abs/2605.08281v1

Implicit neural representations (INRs) encode images as neural-network weights, making image classification a problem of weight-space classifiability. A natural geometric hypothesis is that classifier feedback should make image-specific weights cluster by class in the shared-anchor coordinate. We test this hypothesis in the SIREN-based Meta Weight Transformer (MWT) regime, where end-to-end training meta-learns a shared initialization and inner-loop update schedule for fitting image-specific SIRENs. We find that this prediction fails. Exposed weight-space geometry and supervised clustering pressure do not reliably track trained-reader accuracy; clustering can even make local neighborhoods more class-consistent while making the trained reader worse. Crucially, the reader constructs rather than inherits class-aligned geometry: token-flow diagnostics show that class-aligned neighborhoods become strongly predictive of trained-reader accuracy only after late reader interactions, not in the input coordinate. We further identify the native SIREN bias column in the augmented weight token as a low-dimensional, sample-dependent causal readout route for the trained reader; targeted controls rule out generic scalar-column and marginal-distribution artifacts. The diagnosis motivates interventions that strengthen reader routing, add an explicit bias route, or use denser inner-loop fitting; under the lane-specific training conventions used here, route-directed variants often outperform the shared-anchor baseline but interact non-additively. Task-induced INR weights are classifiable not because they form raw geometric clusters, but because their class signal is routed through the reader.

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### Beyond the False Trade-off: Adaptive EWC for Stealthy and Generalizable T2I Backdoors

Authors: Lu Bowen, Xinyu Tang, Yin Yin Low, Shu-Min Leong
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08280v1

Preserving model fidelity is essential for stealthy text-to-image (T2I) backdoor attacks. Existing methods such as Learning without Forgetting (LwF) rely on output-based distillation, which provides limited regularization. We introduce Elastic Weight Consolidation (EWC) as a parameter-based alternative for preserving fidelity in backdoor learning. While stronger in principle, we show that standard static EWC with a fixed regularization weight lambda and mean-squared utility loss creates an artificial trade-off between attack success rate (ASR) and fidelity, particularly degrading performance on weak triggers. To address this, we propose Cosine-Aware Adaptive EWC, which dynamically adjusts EWC regularization using a cosine-based semantic utility and adaptive scheduling. This approach transforms EWC from a fixed penalty into a context-sensitive constraint, maintaining high ASR while preserving model fidelity. Experiments demonstrate improved ASR-fidelity balance and enhanced robustness on out-of-domain (OOD) datasets compared to existing baselines.

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### LaWM: Least Action World Models for Long-Horizon Physical Consistency from Visual Observations

Authors: Qixin Xiao, Maani Ghaffari
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08279v1

Learning predictive world models from visual observations is a core problem in embodied AI, with applications to model-based reinforcement learning and robotic planning. Existing latent world models typically generate future states with unconstrained neural transition functions, while modern video generation systems often prioritize perceptual plausibility or introduce physical structure through auxiliary losses, external guidance, or separate dynamics modules. As a result, long-horizon rollouts can remain weakly grounded in the physical principles that govern real dynamics, leading to compounding error, energy drift, and physically inconsistent futures. We propose Least Action World Models (LaWM), a latent world-modeling framework that operationalizes the Principle of Least Action in learned visual latent space: future rollouts are governed by a learned Lagrangian action functional rather than produced only by an unconstrained transition predictor. Our main technical realization is a latent variational integrator: LaWM encodes observations into learned generalized coordinates, learns a latent discrete Lagrangian over consecutive latent states, constructs a discrete action functional, and advances prediction by solving the corresponding discrete integration condition. Thus, physical structure is not merely used to score, regularize, or constrain a completed trajectory; it defines the latent transition rule itself. Because the transition is induced by a discrete variational principle, LaWM provides a structure-preserving bias for long-horizon visual prediction. Across physics-clean synthetic dynamics and embodied robot interaction benchmarks, LaWM improves physical invariance, background consistency, motion smoothness, and appearance and geometric prediction metrics over video-generation and world-model baselines.

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### Trapping Attacker in Dilemma: Examining Internal Correlations and External Influences of Trigger for Defending GNN Backdoors

Authors: Fan Yang, Binyan Xu, Di Tang, Kehuan Zhang
Published: 2026-05-08
Categories: cs.LG, cs.AI, cs.CR
arXiv: https://arxiv.org/abs/2605.08278v2

GNNs have become a standard tool for learning on relational data, yet they remain highly vulnerable to backdoor attacks. Prior defenses often depend on inspecting specific subgraph patterns or node features, and thus can be circumvented by adaptive attackers. We propose PRAETORIAN, a new defense that targets intrinsic requirements of effective GNN backdoors rather than surface-level cues. Our key observation is that flipping a victim node's prediction requires substantial influence on the victim: attackers tend to either inject many trigger nodes or rely on a small set of highly influential ones. Building on this observation, PRAETORIAN (i) analyzes internal correlations within potential trigger subgraphs to detect abnormally large injected structures, and (ii) quantifies external node influence to identify triggers with disproportionate impact. Across our evaluations, PRAETORIAN reduces the average attack success rate (ASR) to 0.55% with only a 0.62% drop in clean accuracy (CA), whereas state-of-the-art defenses still yield an average ASR of &gt;20% and a CA drop of &gt;3% under the same conditions. Moreover, PRAETORIAN remains effective against a range of adaptive attacks, forcing adversaries to either inject many trigger nodes to achieve high ASR (&gt;80%), which incurs a &gt;10% CA drop, or preserve CA at the cost of limiting ASR to 18.1%. Overall, PRAETORIAN constrains attackers to an unfavorable trade-off between efficacy and detectability.

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### Mitigating Many-shot Jailbreak Attacks with One Single Demonstration

Authors: Kejia Chen, Jiawen Zhang, Boheng Li, Pengcheng Li, Jian Lou, Zunlei Feng, Mingli Song, Ruoxi Jia, Tianwei Zhang
Published: 2026-05-08
Categories: cs.CR, cs.AI
arXiv: https://arxiv.org/abs/2605.08277v1

Many-shot jailbreaking (MSJ) causes safety-aligned language models to answer harmful queries by preceding them with many harmful question-answer demonstrations. We study why this attack becomes stronger as the number of demonstrations increases. Empirically, we find that MSJ induces a progressive activation drift: the representation of a fixed harmful query moves step by step away from the safety-aligned region as more harmful demonstrations are added. Theoretically, we show that this drift can be interpreted as implicit malicious fine-tuning: conditioning on N harmful demonstrations induces SGD-style updates equivalent to optimizing on the corresponding N harmful samples. This view turns the attack mechanism into a defense principle. We append a fixed one-shot safety demonstration at inference time, which induces a counteracting safety-oriented update and restores refusal behavior. The resulting method improves the model's robustness to MSJ without modifying its parameters or requiring white-box access at deployment. Code is available at https://github.com/Thecommonirin/SafeEnd.

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### Beyond ViT Tokens: Masked-Diffusion Pretrained Convolutional Pathology Foundation Model for Cell-Level Dense Prediction

Authors: Weiming Chen, Xitong Ling, Zhenyang Cai, Xidong Wang, Jiawen Li, Tian Guan, Benyou Wang, Yonghong He
Published: 2026-05-08
Categories: cs.CV
arXiv: https://arxiv.org/abs/2605.08276v1

Cell-level dense prediction is central to computational pathology, but remains challenging due to fine-grained histological structures, strong domain shifts, and costly dense annotations. Existing ViT-based pathology foundation models rely on patch tokenization, which can disrupt spatial continuity and weaken local morphological details needed for cell-level prediction. To address this, we propose Masked-Diffusion Convolutional Foundation Models, termed ConvNeXt Masked-Diffusion (CMD), a self-supervised convolutional generative pretraining framework for dense pathology representation learning. CMD uses a fully convolutional ConvNeXt-UNet backbone, performs masked-diffusion pretraining in pixel space, and incorporates frozen pathology foundation model features through adaptive normalization. Experimental results demonstrate that CMD consistently outperforms existing ViT-based pathology foundation models and even surpasses state-of-the-art end-to-end segmentation methods while fine-tuning only a small number of task-specific parameters across multiple pathology dense prediction tasks. The advantage is particularly pronounced under limited annotation settings, where CMD exhibits stronger robustness and generalization ability. Our findings suggest that purely convolutional architectures can also serve as competitive pathology foundation models for cell-level dense prediction, achieving leading performance within the current ViT-dominated paradigm and providing a scalable, high-performance solution that better preserves histological structural priors for fine-grained pathology understanding.

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### Model-based Dynamic 3D MRI Reconstructions using Neural Fields and Tensor Product Expansions

Authors: Ray Sheombarsing, Max van Riel, David Heesterbeek, Nico van den Berg, Alessandro Sbrizzi
Published: 2026-05-08
Categories: eess.IV, cs.CV
arXiv: https://arxiv.org/abs/2605.08275v1

Conventional MRI reconstruction methods treat images and coil sensitivities as discrete objects, leading to high memory demands and limited structural awareness that hamper effective regularization. These limitations hinder accurate reconstruction in highly undersampled scenarios, such as dynamic 3D cardiac magnetic resonance (CMR). We introduce a discretization-free, memory-efficient, model-based framework for dynamic 2D and 3D MRI reconstruction from highly undersampled data. We represent magnetization and coil sensitivities as continuous objects -- differentiable functions -- using tensor products of univariate neural fields. This tensor product structure enables scalable optimization in high-dimensional spatiotemporal settings. Our method outperforms state-of-the-art model-based reconstructions in dynamic 2D and 3D MR settings, preserving structure and motion even under aggressive undersampling (e.g., acceleration factor 16).

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### Efficient Prompt Learning for Traffic Forecasting

Authors: Qianru Zhang, Xinyi Gao, Alexander Zhou, Reynold Cheng, Siu-Ming Yiu, Hongzhi Yin
Published: 2026-05-08
Categories: cs.LG, cs.AI
arXiv: https://arxiv.org/abs/2605.08273v1

Accurate traffic prediction is essential for optimizing transportation systems, enhancing resource allocation, and improving overall urban administration. Spatio-temporal graph neural networks (GNNs) have achieved state-of-the-art performance and have been widely used in various spatio-temporal prediction scenarios. However, these prediction methods often exhibit low generalization ability, struggling with distribution shifts caused by spatio-temporal dynamics. To address this challenge, we propose an approach to enhance the generalization and adaptation of spatio-temporal GNNs through efficient prompting. Specifically, we introduce a lightweight and model-agnostic prompt tuning framework for spatio-temporal GNNs, named SimpleST. It facilitates adapting pre-trained spatio-temporal GNNs to novel distributions while keeping the model parameters fixed. This prompt mechanism reduces the overhead and complexity of adaptation, enabling efficient utilization of pre-trained models for out-of-distribution generalization. Extensive experiments conducted on five real-world urban spatio-temporal datasets demonstrate the superiority of our approach in terms of prediction accuracy and computational efficiency.

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### Bridging Modalities, Spanning Time: Structured Memory for Ultra-Long Agentic Video Reasoning

Authors: Jiazheng Li, Chi-Hao Wu, Yunze Liu, Kaize Ding, Jundong Li, Chuxu Zhang
Published: 2026-05-08
Categories: cs.CV, cs.AI
arXiv: https://arxiv.org/abs/2605.08271v1

Understanding ultra-long videos such as egocentric recordings, live streams, or surveillance footage spanning days to weeks, remains a challenge. For current multimodal LLMs: even with million-token context windows, frame budgets cover only tens of minutes of densely sampled video, and most evidence is discarded before inference begins. Memory-augmented and agentic approaches help with scale, but their retrieval remains fragmented across modalities and lacks long-range narrative summaries that span days or weeks. We propose \textbf{MAGIC-Video}, a training-free framework built around a multimodal memory graph with interleaved narrative chain: the graph unifies episodic, semantic, and visual content through six typed edges and supports cross-modal retrieval, while the chain distils long-horizon entity biographies and recurring activity events. At inference time, an agentic loop interleaves graph retrieval with narrative fact injection, covering both the modality and time dimensions of ultra-long video in a single retrieval pipeline. On EgoLifeQA, Ego-R1 and MM-Lifelong, MAGIC-Video consistently outperforms strong general-purpose, long-video, and agentic baselines, with gains of 10.1, 7.4, and 5.9 points over the prior best agentic system on each benchmark. Code is available at https://github.com/lijiazheng0917/MAGIC-video.

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### SAFformer:Improving Spiking Transformer via Active Predictive Filtering

Authors: Zequan Xie, Weiming Zeng, Yunhua Chen, Sichang Ling, Tongyang Chen, Jinsheng Xiao
Published: 2026-05-08
Categories: cs.CV, cs.AI
arXiv: https://arxiv.org/abs/2605.08270v2

Spiking Neural Networks (SNNs) offer notable advantages in biological plausibility and energy efficiency, making them promising candidates for building low-power Transformers. However, existing Spiking Transformers largely adhere to a passive reactive paradigm, which struggles to focus on task-relevant information and incurs substantial computational overhead when processing redundant visual data. To overcome this fundamental yet underexplored limitation, we propose SAFformer, a novel Spiking Transformer architecture based on an active predictive filtering paradigm. Inspired by the brain's predictive coding mechanism, SAFformer actively suppresses predictable signals and focuses on salient visual features. Extensive experiments show that SAFformer establishes new state-of-the-art performance on CIFAR-10/100 and CIFAR10-DVS. Remarkably, on ImageNet-1K, it achieves 80.44% Top-1 accuracy with only 26.58M parameters and an energy consumption of 5.88 mJ, demonstrating an exceptional balance between accuracy and efficiency.

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### Insider Attacks in Multi-Agent LLM Consensus Systems

Authors: Xiaolin Sun, Zixuan Liu, Yibin Hu, Zizhan Zheng
Published: 2026-05-08
Categories: cs.MA, cs.AI
arXiv: https://arxiv.org/abs/2605.08268v1

Large language models (LLMs) are increasingly deployed in multi-agent systems where agents communicate in natural language to solve tasks jointly. A key capability in such systems is consensus formation, where agents iteratively exchange messages and update decisions to reach a shared outcome. However, most existing multi-agent LLM frameworks assume that all participating agents are aligned with the system objective. In practice, a malicious insider may participate as a legitimate member of the group while pursuing a hidden adversarial goal. In this work, we study insider manipulation in multi-agent LLM consensus systems. We formalize the problem as a sequential decision-making task in which a malicious agent seeks to delay or prevent agreement among benign agents. To make attack optimization tractable, we propose a world-model-based framework that learns surrogate dynamics over the latent behavioral states of benign agents and then trains an attacker using reinforcement learning based on this learned model. Preliminary results show that the trained attacker reduces the benign consensus rate and prolongs disagreement more effectively than the direct malicious-prompt baseline. These results suggest that combining latent world models with reinforcement learning is a promising direction for adaptive insider attacks in language-based multi-agent systems.

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### Execution Envelopes: A Shared Admission Contract for Backend AI Execution Requests

Authors: Krti Tallam
Published: 2026-05-08
Categories: cs.SE, cs.AI, cs.DC, cs.ET
arXiv: https://arxiv.org/abs/2605.08267v1

Enterprise AI backends increasingly admit heterogeneous execution requests across model deployment, inference, evaluation, data movement, and agentic workflows. In many systems, those requests arrive in service-specific shapes, which makes it difficult to attach shared admission-time behavior such as logging, governance hints, resource accounting, authorization-aware policy hooks, and later runtime review without rebuilding the same contract in each subsystem. This paper introduces the execution envelope, a normalized internal admission object that records who is asking for what kind of execution, what resources were requested, what policy-relevant scope accompanied the request, and what the backend ultimately granted. The proposal is intentionally narrow. It does not replace service-specific request models, perform scheduling, or introduce a new authority token. Instead, it defines a descriptive admission seam that can be threaded through real backend paths before backend-specific resolution begins. I formalize the distinction between requested and granted resources, specify the field families, invariants, and lifecycle of the envelope, work through POST /serving/deploy_model as an initial proving ground, and position the design relative to usage control, analyzable authorization, admission control, and cluster scheduling. The central claim is that a shared execution-admission contract is a useful missing primitive for modern AI backends because it creates one place to attach governance and observability without pretending to solve placement, policy, and runtime execution in a single step.

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### Coarse-to-Fine: Progressive Image Compression for Semantically Hierarchical Classification

Authors: Jungwoo Kim, Jun-Hyuk Kim, Jong-Seok Lee
Published: 2026-05-08
Categories: eess.IV, cs.CV
arXiv: https://arxiv.org/abs/2605.08266v1

Recent advances in learned image compression (LIC) have enabled practical deployments, spurring active research into image compression for machines and progressive coding schemes. However, their integration remains under-explored: prior works on progressive machine codec predominantly target sample-level difficulty adaptation (i.e., easy-to-hard), without considering semantic-level scalability. In this work, we introduce a semantic hierarchy-aware progressive codec that enables semantic scalability (i.e., coarse-to-fine) from a single bitstream. We first systematically categorize ImageNet-1K classes into CLIP embedding-based semantic hierarchies. Based on a channel-wise autoregressive framework, we decompose latent representations into hierarchically ordered channel blocks, each explicitly optimized for a corresponding semantic hierarchy. Extensive experiments demonstrate that our approach substantially improves coarse-level recognition at low bitrates while maintaining fine-grained accuracy at higher bitrates. By reframing progressive transmission through the lens of semantic scalability, our work provides an efficient and interpretable solution for task-adaptive image coding, outperforming existing progressive codecs under hierarchical evaluation.

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### 123D: Unifying Multi-Modal Autonomous Driving Data at Scale

Authors: Daniel Dauner, Valentin Charraut, Bastian Berle, Tianyu Li, Long Nguyen, Jiabao Wang, Changhui Jing, Maximilian Igl, Holger Caesar, Boris Ivanovic, Yiyi Liao, Andreas Geiger et al.
Published: 2026-05-08
Categories: cs.RO, cs.CV
arXiv: https://arxiv.org/abs/2605.08084v1

The pursuit of autonomous driving has produced one of the richest sensor data collections in all of robotics. However, its scale and diversity remain largely untapped. Each dataset adopts different 2D and 3D modalities, such as cameras, lidar, ego states, annotations, traffic lights, and HD maps, with different rates and synchronization schemes. They come in fragmented formats requiring complex dependencies that cannot natively coexist in the same development environment. Further, major inconsistencies in annotation conventions prevent training or measuring generalization across multiple datasets. We present 123D, an open-source framework that unifies such multi-modal driving data through a single API. To handle synchronization, we store each modality as an independent timestamped event stream with no prescribed rate, enabling synchronous or asynchronous access across arbitrary datasets. Using 123D, we consolidate eight real-world driving datasets spanning 3,300 hours and 90,000 kilometers, together with a synthetic dataset with configurable collection scripts, and provide tools for data analysis and visualization. We conduct a systematic study comparing annotation statistics and assessing each dataset's pose and calibration accuracy. Further, we showcase two applications 123D enables: cross-dataset 3D object detection transfer and reinforcement learning for planning, and offer recommendations for future directions. Code and documentation are available at https://github.com/kesai-labs/py123d.

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### LLMs Improving LLMs: Agentic Discovery for Test-Time Scaling

Authors: Tong Zheng, Haolin Liu, Chengsong Huang, Huiwen Bao, Sheng Zhang, Rui Liu, Runpeng Dai, Ruibo Chen, Chenxi Liu, Tianyi Xiong, Xidong Wu, Hongming Zhang et al.
Published: 2026-05-08
Categories: cs.CL
arXiv: https://arxiv.org/abs/2605.08083v2

Test-time scaling (TTS) has become an effective approach for improving large language model performance by allocating additional computation during inference. However, existing TTS strategies are largely hand-crafted: researchers manually design reasoning patterns and tune heuristics by intuition, leaving much of the computation-allocation space unexplored. We propose an environment-driven framework, AutoTTS, that changes what researchers design: from individual TTS heuristics to environments where TTS strategies can be discovered automatically. The key to AutoTTS lies in environment construction: the discovery environment must make the control space tractable and provide cheap, frequent feedback for TTS search. As a concrete instantiation, we formulate width--depth TTS as controller synthesis over pre-collected reasoning trajectories and probe signals, where controllers decide when to branch, continue, probe, prune, or stop and can be evaluated cheaply without repeated LLM calls. We further introduce beta parameterization to make the search tractable and fine-grained execution trace feedback to improve discovery efficiency by helping the agent diagnose why a TTS program fails. Experiments on mathematical reasoning benchmarks show that the discovered strategies improve the overall accuracy--cost tradeoff over strong manually designed baselines. The discovered strategies generalize to held-out benchmarks and model scales, while the entire discovery costs only $39.9 and 160 minutes. Our data, and code will be open-source at https://github.com/zhengkid/AutoTTS.

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### Normalizing Trajectory Models

Authors: Jiatao Gu, Tianrong Chen, Ying Shen, David Berthelot, Shuangfei Zhai, Josh Susskind
Published: 2026-05-08
Categories: cs.CV, cs.LG
arXiv: https://arxiv.org/abs/2605.08078v2

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

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### Conformal Path Reasoning: Trustworthy Knowledge Graph Question Answering via Path-Level Calibration

Authors: Shuhang Lin, Chuhao Zhou, Xiao Lin, Zihan Dong, Kuan Lu, Zhencan Peng, Jie Yin, Dimitris N. Metaxas
Published: 2026-05-08
Categories: cs.CL
arXiv: https://arxiv.org/abs/2605.08077v2

Knowledge Graph Question Answering (KGQA) offers grounded, interpretable reasoning, but existing methods often fail to provide reliable coverage guarantees over retrieved answers. While Conformal Prediction (CP) offers a principled framework for producing prediction sets with statistical guarantees, prior conformal KGQA methods suffer from two critical pitfalls: violated coverage guarantees due to invalid calibration, and weak score discriminability that yields excessively large prediction sets. We propose Conformal Path Reasoning (CPR), a novel trustworthy KGQA framework built on two key innovations. First, query-level conformal calibration over path-level scores preserves exchangeability to ensure valid coverage guarantees. Second, we introduce the Residual Conformal Value Network (RCVNet), a lightweight module trained via PUCT-guided exploration to learn discriminative path-level nonconformity scores. Extensive experiments show that CPR significantly improves the Empirical Coverage Rate by 45% while reducing prediction set size by 52% on average over conformal baselines across benchmark datasets, highlighting its effectiveness for reliable conformal reasoning over knowledge graphs.

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### Zero-Shot Imagined Speech Decoding via Imagined-to-Listened MEG Mapping

Authors: Maryam Maghsoudi, Shihab Shamma
Published: 2026-05-08
Categories: cs.LG, eess.AS
arXiv: https://arxiv.org/abs/2605.08075v1

Decoding imagined speech from non-invasive brain recordings is challenging because imagined datasets are scarce and difficult to align temporally across subjects and sessions In this work, we propose a new approach to the decoding of imagined speech that leverages the richer and more reliably labeled recordings during listening to speech. We collected paired listened and imagined MEG recordings to rhythmic melodic and spoken stimuli from trained musicians. Using trained musicians helped improve temporal alignment across conditions. We then developed a three-stage decoding pipeline that revealed consistent and meaningful relationships between neural activity evoked by imagining and listening to the same stimuli. First, we trained six linear and neural models to map imagined MEG responses to listened responses. We evaluated these models against a null baseline from unseen subjects to validate that the predicted-listening responses preserve stimulus-specific information. In the second stage, we trained a contrastive word decoder exclusively on the listened MEG responses, and evaluated it using four embedding strategies including semantic, acoustic, and phonetic representations. In the third stage, we process the imagined MEG responses from held-out subjects through the mapping pipeline to compute the corresponding listening responses that are then decoded by the listened decoder. Using rank-based analysis, we show that the imagined words are decodable significantly above chance. We shall report here the results of a proof-of-concept implementation to decode imagined speech, where all evaluations are performed on held-out subjects. We also demonstrate that performance improves with training data size, suggesting that this approach is scalable and can directly be made applicable to realistic brain-computer interface scenarios.

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### GRAPHLCP: Structure-Aware Localized Conformal Prediction on Graphs

Authors: Peyman Baghershahi, Fangxin Wang, Debmalya Mandal, Sourav Medya
Published: 2026-05-08
Categories: cs.LG
arXiv: https://arxiv.org/abs/2605.08074v1

Conformal prediction (CP) provides a distribution-free approach to uncertainty quantification with finite-sample guarantees. However, applying CP to graph neural networks (GNNs) remains challenging as the combinatorial nature of graphs often leads to insufficiently certain predictions and indiscriminative embeddings. Existing methods primarily rely on embedding-space proximity for localization, which can be unreliable for graphs and yield inefficient prediction sets. We propose GRAPHLCP, a proximity-based localized CP framework that explicitly incorporates graph topology and inter-node dependencies into localization and weighting. Our approach introduces a feature-aware densification step to mitigate locality bias in sparse graphs, followed by a Personalized PageRank-based kernel computation to model structural proximity. This enables topology-dependent anchor sampling and calibration weighting that captures both local and long-range dependencies. Extensive experiments on several regression and classification datasets demonstrate that GRAPHLCP guarantees marginal coverage with finite samples while efficiently attaining favorable test conditional coverage across various conditioning scenarios.

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### EmambaIR: Efficient Visual State Space Model for Event-guided Image Reconstruction

Authors: Wei Yu, Yunhang Qian
Published: 2026-05-08
Categories: cs.CV, cs.AI
arXiv: https://arxiv.org/abs/2605.08073v1

Recent event-based image reconstruction methods predominantly rely on Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) to process complementary event information. However, these architectures face fundamental limitations: CNNs often fail to capture global feature correlations, whereas ViTs incur quadratic computational complexity (e.g., $O(n^2)$), hindering their application in high-resolution scenarios. To address these bottlenecks, we introduce EmambaIR, an Efficient visual State Space Model designed for image reconstruction using spatially sparse and temporally continuous event streams. Our framework introduces two key components: the cross-modal Top-k Sparse Attention Module (TSAM) and the Gated State-Space Module (GSSM). TSAM efficiently performs pixel-level top-k sparse attention to guide cross-modal interactions, yielding rich yet sparse fusion features. Subsequently, GSSM utilizes a nonlinear gated unit to enhance the temporal representation of vanilla linear-complexity ($O(n)$) SSMs, effectively capturing global contextual dependencies without the typical computational overhead. Extensive experiments on six datasets across three diverse image reconstruction tasks - motion deblurring, deraining, and High Dynamic Range (HDR) enhancement - demonstrate that EmambaIR significantly outperforms state-of-the-art methods while offering substantial reductions in memory consumption and computational cost. The source code and data are publicly available at: https://github.com/YunhangWickert/EmambaIR

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### A Note on Non-Negative $L_1$-Approximating Polynomials

Authors: Jane H. Lee, Anay Mehrotra, Manolis Zampetakis
Published: 2026-05-08
Categories: stat.ML, cs.DS, cs.LG, math.ST
arXiv: https://arxiv.org/abs/2605.08072v1

$L_1$-Approximating polynomials, i.e., polynomials that approximate indicator functions in $L_1$-norm under certain distributions, are widely used in computational learning theory. We study the existence of \textit{non-negative} $L_1$-approximating polynomials with respect to Gaussian distributions. This is a stronger requirement than $L_1$-approximation but weaker than sandwiching polynomials (which themselves have many applications). These non-negative approximating polynomials have recently found uses in smoothed learning from positive-only examples. In this short note, we prove that every class of sets with Gaussian surface area (GSA) at most $Γ$ under the standard Gaussian admits degree-$k$ non-negative polynomials that $\eps$-approximate its indicator functions in $L_1$-norm, for $k=\tilde{O}(Γ^2/\varepsilon^2)$. Equivalently, finite GSA implies $L_1$-approximation with the stronger pointwise guarantee that the approximating polynomial has range contained in $(0,\infty)$. Up to a constant-factor, this matches the degree of the best currently known Gaussian $L_1$-approximation degree bound without the non-negativity constraint.

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### VecCISC: Improving Confidence-Informed Self-Consistency with Reasoning Trace Clustering and Candidate Answer Selection

Authors: James Petullo, Sonny George, Dylan Cashman, Nianwen Xue
Published: 2026-05-08
Categories: cs.AI
arXiv: https://arxiv.org/abs/2605.08070v1

A standard technique for scaling inference-time reasoning is Self-Consistency, whereby multiple candidate answers are sampled from an LLM and the most common answer is selected. More recently, it has been shown that weighted majority voting (e.g. Confidence-Informed Self Consistency (CISC)), which assigns a confidence value to each candidate answer and chooses the answer with the largest accumulated score, tends to be more accurate on a wide range of popular benchmarks. In practice, weighted majority voting necessitates calling a critic LLM on each candidate's reasoning trace to produce the answer's confidence score. This secondary series of LLM calls greatly increases the overhead and cost of weighted majority voting, despite its potential performance benefits. To reduce this expense, we propose VecCISC, a lightweight, adaptive framework that uses a measure of semantic similarity to filter reasoning traces that are semantically equivalent to others, degenerate, or hallucinated, thus decreasing the number of candidate answers that must be evaluated by the critic. To ensure adequate experimental thoroughness, we evaluate VecCISC on five challenging, widely-adopted datasets spanning the domains of mathematics, chemistry, biology, commonsense reasoning, and the humanities. Our results demonstrate that VecCISC reduces the total token usage by 47%, while maintaining or exceeding the accuracy of CISC.

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### Empirical Bayes Rebiasing

Authors: Wanyi Ling, Sida Li, Junming Guan, Nikolaos Ignatiadis
Published: 2026-05-08
Categories: stat.ME, stat.ML
arXiv: https://arxiv.org/abs/2605.08069v1

We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard debiasing approach, which subtracts the bias estimate from each biased estimate, inflates variance and yields long intervals. In this paper, we propose an empirical Bayes rebiasing strategy that starts from the fully debiased estimates and learns from data how much bias to reintroduce by estimating the unknown bias distribution. We provide convergence rates for the coverage of our intervals when the bias distribution is estimated using nonparametric maximum likelihood. Furthermore, we demonstrate substantial precision gains in prediction-powered inference, including pairwise LLM win-rate evaluations, as well as for inference of direct genetic effects in family-based GWAS.

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### Proxy3D: Efficient 3D Representations for Vision-Language Models via Semantic Clustering and Alignment

Authors: Jerry Jiang, Haowen Sun, Denis Gudovskiy, Yohei Nakata, Tomoyuki Okuno, Kurt Keutzer, Wenzhao Zheng
Published: 2026-05-08
Categories: cs.CV
arXiv: https://arxiv.org/abs/2605.08064v1

Spatial intelligence in vision-language models (VLMs) attracts research interest with the practical demand to reason in the 3D world.Despite promising results, most existing methods follow the conventional 2D pipeline in VLMs and use pixel-aligned representations for the vision modality. However, correspondence-based models with implicit 3D scene understanding often fail to achieve spatial consistency, and representation-based models with 3D geometric priors lack efficiency in vision sequence serialization. To address this, we propose a Proxy3D method with compact yet comprehensive 3D proxy representations for the vision modality. Given only video frames as input, we employ semantic and geometric encoders to extract scene features and then perform their semantic-aware clustering to obtain a set of proxies in the 3D space. For representation alignment, we further curate the SpaceSpan dataset and apply multi-stage training to adopt the proposed 3D proxy representations with the VLM. When using shorter sequences for vision information, our method achieves competitive or state-of-the-art performance in 3D visual question answering, visual grounding and general spatial intelligence benchmarks.

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### Flow-OPD: On-Policy Distillation for Flow Matching Models

Authors: Zhen Fang, Wenxuan Huang, Yu Zeng, Yiming Zhao, Shuang Chen, Kaituo Feng, Yunlong Lin, Lin Chen, Zehui Chen, Shaosheng Cao, Feng Zhao
Published: 2026-05-08
Categories: cs.CV, cs.AI
arXiv: https://arxiv.org/abs/2605.08063v5

Existing Flow Matching (FM) text-to-image models suffer from two critical bottlenecks under multi-task alignment: the reward sparsity induced by scalar-valued rewards, and the gradient interference arising from jointly optimizing heterogeneous objectives, which together give rise to a 'seesaw effect' of competing metrics and pervasive reward hacking. Inspired by the success of On-Policy Distillation (OPD) in the large language model community, we propose Flow-OPD, the first unified post-training framework that integrates on-policy distillation into Flow Matching models. Flow-OPD adopts a two-stage alignment strategy: it first cultivates domain-specialized teacher models via single-reward GRPO fine-tuning, allowing each expert to reach its performance ceiling in isolation; it then establishes a robust initial policy through a Flow-based Cold-Start scheme and seamlessly consolidates heterogeneous expertise into a single student via a three-step orchestration of on-policy sampling, task-routing labeling, and dense trajectory-level supervision. We further introduce Manifold Anchor Regularization (MAR), which leverages a task-agnostic teacher to provide full-data supervision that anchors generation to a high-quality manifold, effectively mitigating the aesthetic degradation commonly observed in purely RL-driven alignment. Built upon Stable Diffusion 3.5 Medium, Flow-OPD raises the GenEval score from 63 to 92 and the OCR accuracy from 59 to 94, yielding an overall improvement of roughly 10 points over vanilla GRPO, while preserving image fidelity and human-preference alignment and exhibiting an emergent 'teacher-surpassing' effect. These results establish Flow-OPD as a scalable alignment paradigm for building generalist text-to-image models. The codes and weights will be released in: https://github.com/CostaliyA/Flow-OPD .

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### Rubric-Grounded RL: Structured Judge Rewards for Generalizable Reasoning

Authors: Manish Bhattarai, Ismael Boureima, Nishath Rajiv Ranasinghe, Scott Pakin, Dan O'Malley
Published: 2026-05-08
Categories: cs.AI
arXiv: https://arxiv.org/abs/2605.08061v1

We argue that decomposing reward into weighted, verifiable criteria and using an LLM judge to score them provides a partial-credit optimization signal: instead of a binary outcome or a single holistic score, each response is graded along multiple task-specific criteria. We formalize \emph{rubric-grounded reinforcement learning (RL)}: a framework in which the policy is optimized against a structured, multi-criterion reward produced by a frozen LLM judge that conditions on auxiliary grounding the policy never sees. We instantiate the framework by deriving rubrics from an Office of Scientific and Technical Information (OSTI)-derived corpus of roughly 100,000 scientific and technical documents and training Llama-3.1-8B-Instruct with Group Relative Policy Optimization (GRPO). With GRPO-based training, the model achieves $71.7\%$ normalized reward on held-out rubric evaluation. The GRPO-tuned policy also improves over the base model on four reasoning benchmarks not derived from the training corpus -- GSM8K, MATH, GPQA Main, and GPQA Diamond. These results provide evidence that structured, document-grounded rewards can improve held-out rubric performance and induce transferable reasoning behaviors beyond the corpus used to construct the training environment.

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### The Memory Curse: How Expanded Recall Erodes Cooperative Intent in LLM Agents

Authors: Jiayuan Liu, Tianqin Li, Shiyi Du, Xin Luo, Haoxuan Zeng, Emanuel Tewolde, Tai Sing Lee, Tonghan Wang, Carl Kingsford, Vincent Conitzer
Published: 2026-05-08
Categories: cs.CL, cs.AI, cs.GT, cs.MA
arXiv: https://arxiv.org/abs/2605.08060v1

Context window expansion is often treated as a straightforward capability upgrade for LLMs, but we find it systematically fails in multi-agent social dilemmas. Across 7 LLMs and 4 games over 500 rounds, expanding accessible history degrades cooperation in 18 of 28 model--game settings, a pattern we term the memory curse. We isolate the underlying mechanism through three analyses. First, lexical analysis of 378,000 reasoning traces associates this breakdown with eroding forward-looking intent rather than rising paranoia. We validate this using targeted fine-tuning as a cognitive probe: a LoRA adapter trained exclusively on forward-looking traces mitigates the decay and transfers zero-shot to distinct games. Second, memory sanitization holds prompt length fixed while replacing visible history with synthetic cooperative records, which restores cooperation substantially, proving the trigger is memory content, not length alone. Finally, ablating explicit Chain-of-Thought reasoning often reduces the collapse, showing that deliberation paradoxically amplifies the memory curse. Together, these results recast memory as an active determinant of multi-agent behavior: longer recall can either destabilize or support cooperation depending on the reasoning patterns it elicits.

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### 6D Pose Estimation via Keypoint Heatmap Regression with RGB-D Residual Neural Networks

Authors: Ismail Aljosevic, Amir Masoud Almasi, Ana Parovic, Ashkan Shafiei
Published: 2026-05-08
Categories: cs.CV, cs.RO
arXiv: https://arxiv.org/abs/2605.08059v1

In this paper, we propose a modular framework for 6D pose estimation based on keypoint heatmap regression. Our approach combines YOLOv10m for object detection with a ResNet18-based network that predicts 2D heatmaps from RGB images. Keypoints extracted from these heatmaps are used to estimate the 6D object pose via the PnP RANSAC algorithm. We compare different keypoint selection strategies to assess their impact on pose accuracy. Additionally, we extend the baseline by incorporating depth data using a cross-fusion architecture, which enables interaction between RGB and depth features at multiple stages. We further explore general training improvements, such as experimenting with activation functions and learning rate scheduling strategies to improve model performance. Our best RGB-only model achieved a mean ADD-based accuracy of 84.50%, while the RGB-D fusion model reached 92.41% on the LINEMOD dataset. The code is available at https://github.com/ameermasood/HeatNet.

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### CA-SQL: Complexity-Aware Inference Time Reasoning for Text-to-SQL via Exploration and Compute Budget Allocation

Authors: James Petullo, Nianwen Xue
Published: 2026-05-08
Categories: cs.CL, cs.AI
arXiv: https://arxiv.org/abs/2605.08057v1

While recent advancements in inference-time learning have improved LLM reasoning on Text-to-SQL tasks, current solutions still struggle to perform well on the most challenging tasks in the Bird-Bench (BIRD) benchmark. This is due to inadequate solution space exploration, which is necessary to uncover promising candidate queries that can be further refined to produce the correct output. To address this challenge, we introduce CA-SQL, a novel Text-to-SQL pipeline that utilizes the estimated difficulty of a task to dynamically scale the breadth of the exploration for generating solution candidates. In addition, we use a custom prompt seeding method, based on principles of evolutionary search, to further elicit exploratory behavior from the base LLM and a novel voting method to select the best candidate solution at the end of the search. Experiments demonstrate that our solution achieves a state-of-the-art score of 51.72% on the "challenging" tier of BIRD development set problems, using only GPT-4o-mini, out-performing other in-context learning approaches, even those that leverage larger models. Overall, our method attains a competitive 61.06% execution accuracy and 68.77% Soft F1 score on the BIRD development dataset.

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### Towards Highly-Constrained Human Motion Generation with Retrieval-Guided Diffusion Noise Optimization

Authors: Hanchao Liu, Fang-Lue Zhang, Shining Zhang, Tai-Jiang Mu, Shi-Min Hu
Published: 2026-05-08
Categories: cs.CV
arXiv: https://arxiv.org/abs/2605.08054v1

Generating human motion that satisfies customized zero-shot goal functions, enabling applications such as controllable character animation and behavior synthesis for virtual agents, is a critical capability. While current approaches handle many unseen constraints, they fail on tasks with very challenging spatiotemporal restrictions, such as severe spatial obstacles or specified numbers of walking steps. To equip motion generators for these highly constrained tasks, we present a retrieval-guided method built on the training-free diffusion noise optimization framework. The key idea is to search within large motion datasets for guidance that can potentially satisfy difficult constraints. We introduce relational task parsing to group target constraints and identify the difficult ones to be handled by retrieved reference. A better initialization for diffusion noise is then obtained via a reward-guided mask that combines random noise with retrieved noise. By optimizing diffusion noise from this improved initialization, we successfully solve highly constrained generation tasks. By leveraging LLM for relational task parsing, the whole framework is further enabled to automatically reason for what to retrieve, improving the intelligence of moving agents under a training-free optimization scheme.

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### Reinforcement Learning for Exponential Utility: Algorithms and Convergence in Discounted MDPs

Authors: Gugan Thoppe, L. A. Prashanth, Ankur Naskar, Sanjay Bhat
Published: 2026-05-08
Categories: cs.LG
arXiv: https://arxiv.org/abs/2605.08053v1

Reinforcement learning (RL) for exponential-utility optimization in discounted Markov decision processes (MDPs) lacks principled value-based algorithms. We address this gap in the fixed risk-aversion setting. Building on the Bellman-type equation for exponential utility studied in \cite{porteus1975optimality}, we derive two Q-value-style extensions and show that the associated operators are contractions in the $L_\infty$ and sup-log/Thompson metrics, respectively. We characterize their fixed points and prove that the induced greedy stationary policy is optimal for the exponential-utility objective among stationary policies. These structural results lead to two model-free algorithms: a two-timescale Q-learning--style algorithm, for which we establish almost-sure convergence and provide finite-time convergence rates via timescale separation, and a one-timescale algorithm governed by a sublinear power-law operator. Since the latter does not admit a global contraction in standard metrics, we prove its convergence using delicate arguments based on local Lipschitzness, monotonicity, homogeneity, and Dini derivatives, and provide a scalar finite-time analysis that highlights the challenges in obtaining convergence rates in the vector case. Our work provides a foundation for value-based RL under exponential-utility objectives.

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### Period spacings and global seismic parameters for K2 red giants using deep learning

Authors: Nipun Ghanghas, Siddharth Dhanpal, Shravan Hanasoge, Praneeth Netrapalli, Karthikeyan Shanmugam
Published: 2026-05-08
Categories: astro-ph.SR, stat.ML
arXiv: https://arxiv.org/abs/2605.08051v2

Gravity-mode period spacings (DPi_1) of red giants probe the stellar core directly, constraining its structure, mass and evolutionary state. Their measurement requires resolving narrow, densely spaced mixed modes and has so far relied on the four-year baseline of Kepler. Recovering DPi_1 from the much shorter (~80-day) baselines typical of K2 remains largely unexplored at the ensemble scale. We develop an automated machine-learning technique to measure global asteroseismic parameters and gravity-mode period spacings for red giants from single-campaign K2 photometry. Two deep residual neural networks take the full-resolution power spectrum of an ~80-day light curve as input, without background fitting or mode identification, and return a probability distribution for each parameter, yielding a point estimate and asymmetric uncertainties. They are trained on ~8 million synthetic spectra and evaluated on held-out synthetics, on Kepler data degraded to K2-like resolution, and on K2 observations. On Kepler data at K2-like resolution, numax and Dnu are recovered for 96% and 91% of stars with robust dispersions of 3.6% and 1.2%; DPi_1 for 22%, with a dispersion of 0.9%. Applied to 18,704 K2 red giants, the inferred numax and Dnu agree with catalogue values to 5.8% and 1.9%, the additional scatter arising from known K2 artefacts. Among the 2,059 young red giants we obtain DPi_1 for 232 stars with a median fractional uncertainty of 1.3%, following the same Dnu-DPi_1 sequence as the Kepler sample although the training set carries no imprint of that relation. We show that numax, Dnu and - for a subset of young red giants - DPi_1 can be recovered from a single ~80-day K2 campaign within an automated, probabilistic machine-learning framework. This approach can also be extended to short-baseline samples from TESS and, in future, Roman and PLATO.

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### Inferring Asteroseismic Parameters from Short Observations Using Deep Learning: Application to TESS and K2 Red Giants

Authors: Nipun Ghanghas, Siddharth Dhanpal, Shravan Hanasoge, Praneeth Netrapalli, Karthikeyan Shanmugam
Published: 2026-05-08
Categories: astro-ph.SR, stat.ML
arXiv: https://arxiv.org/abs/2605.08051v1

Asteroseismology is the study of resonant oscillations of stars to infer their internal structure and dynamics. It is also a powerful tool for precisely determining stellar parameters such as mass, radius, surface gravity, and age. The ongoing TESS mission, with its nearly complete sky coverage, presents a unique opportunity to uniformly probe stellar populations across the Milky Way. TESS is estimated to have observed more than 300,000 oscillating red giants, most of which have one to two months of observations. Given the scale of this dataset, we need a fast, efficient, and robust way to analyse the data. In this work, our objective is to develop a machine learning (ML) based method to infer asteroseismic parameters from short-duration observations. Specifically, we focus on two global seismic parameters, the large frequency separation ($Δν$) and the frequency at maximum power ($ν_{\mathrm{max}}$), from one-month-long TESS observations of red giants. Meanwhile, for K2 data, our focus extends to inferring the period spacings of dipolar gravity modes ($ΔΠ_{1}$), in addition to $Δν$ and $ν_{\mathrm{max}}$. Our findings demonstrate that our machine learning algorithm can accurately infer $Δν$ and $ν_{\mathrm{max}}$ for approximately 50% of samples created by taking one-month Kepler and K2 observations. For TESS one sector data however, we recover reliable $Δν$ for only about 23% of the stars. Additionally, we get reliable $ΔΠ_{1}$ inferences for about 200 young red-giants from K2. For these $ΔΠ_{1}$ inferences, we see a good match with the well known $Δν-ΔΠ_{1}$ degenerate sequence observed in Kepler red-giants.

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