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01.
arXiv (CS.CL) 2026-06-16

Symbolic Informalization: Fluent, Productive, Multilingual

Authors:

Symbolic informalization enables a reliable conversion of formal mathematics to natural language. It has the potential to make machine-checked content human-readable without loss of precision. In a traditional proof system usage, symbolic informalization generalizes the limited mechanisms of syntactic sugar into the ordinary language of mathematics. In a setting where proofs are constructed by artificial intelligence and autoformalization, symbolic informalization can explain what precisely has been constructed. This paper outlines the project Informath, which aims to show how symbolic informalization can produce fluent text with a reasonable development effort and address multiple formal and natural languages. Informath is based on an interlingual architecture, where Dedukti works as a hub between different proof systems (Agda, Lean, Rocq) and Grammatical Framework (GF) takes care of linguistic correctness and variation in different natural languages.

02.
arXiv (CS.AI) 2026-06-15

Refusal Beyond a Single Direction: A Preliminary Comparison of Diff-in-Means and INLP

arXiv:2606.13720v1 Announce Type: new Abstract: Arditi et al. (2024) has shown that refusal in safety fine-tuned chat models is mediated by a single linear direction in the residual stream, recoverable by a difference-in-means (DiM) of harmful and harmless activations. We compare DiM-based interventions (activation addition and directional ablation) with two interventions derived from Iterative Nullspace Projection (INLP) – nullspace projection and counterfactual flipping – on five open-weight chat models, asking whether INLP can match DiM at steering refusal and whether its richer parameterisation yields more tweakable interventions. INLP counterfactual flipping is competitive with DiM directional ablation on refusal suppression, while nullspace projection is consistently weaker. Restricting INLP to the leading directions of the extracted subspace preserves most of the suppression effect at near-baseline perplexity, giving a tunable capability. Geometrically, the two INLP interventions land in qualitatively different regions of activation space: nullspace projection collapses transformed activations between the harmful and harmless clusters, while counterfactual flipping moves them into the opposite cluster, suggesting that the model encodes the absence of a concept differently from its opposite – an intriguing distinction that warrants further investigation in future work.

03.
arXiv (CS.LG) 2026-06-17

The Implicit Bias of Steepest Descent with Mini-batch Stochastic Gradient

arXiv:2602.11557v2 Announce Type: replace Abstract: A variety of widely used optimization methods like SignSGD and Muon can be interpreted as instances of steepest descent under different norm-induced geometries. In this work, we study the implicit bias of mini-batch stochastic steepest descent in multi-class classification, characterizing how batch size, momentum, and variance reduction shape the limiting max-margin behavior and convergence rates under general entry-wise and Schatten-$p$ norms. We show that, without momentum, worst-case convergence and successful classification can only be guaranteed with full-batch gradient. In contrast, momentum enables small-batch convergence to an approximate max-margin solution through a batch-momentum trade-off, though it slows convergence. This approach provides fully explicit, dimension-free rates that improve upon prior results. Moreover, we prove that variance reduction can recover the exact full-batch implicit bias for any batch size, albeit at a slower convergence rate. Finally, we further investigate the batch-size-one steepest descent without momentum, and reveal its convergence to a fundamentally different bias via a concrete data example, which reveals a key limitation of purely stochastic updates. Overall, our unified analysis clarifies when stochastic optimization aligns with full-batch behavior, and paves the way for perform deeper explorations of the training behavior of stochastic gradient steepest descent algorithms.

04.
medRxiv (Medicine) 2026-06-22

Paired plasma and EV-enriched plasma proteomics reveal nonredundant sepsis-associated host-response signatures in critical illness

Background: Plasma proteomics may identify host-response signatures in sepsis, but it is unclear whether extracellular vesicle (EV)-enriched plasma provides distinct or redundant information compared with plasma. We compared paired plasma and EV-enriched plasma proteomes in critically ill patients with sepsis and critically ill non-sepsis controls (CINS). Methods: In this prospective observational study, paired plasma and EV-enriched plasma samples were analyzed from 56 critically ill adults, including 40 patients with sepsis and 16 CINS patients. Protein abundance was quantified using liquid chromatography-tandem mass spectrometry. Analyses compared proteomic depth, protein overlap, global concordance between compartments, and differential protein abundance between CINS and sepsis. Exploratory Gene Ontology enrichment was performed as a supplementary analysis. Results: EV-enriched plasma expanded proteomic detection, identifying 2,476 filtered proteins compared with 506 in plasma. Only 386 proteins were detected in both compartments, while 2,090 were unique to EV-enriched plasma and 120 were unique to plasma. Among shared proteins, plasma and EV-enriched plasma showed modest global concordance across critically ill patients (Spearman coeff = 0.322, p = 9.19 x 10^-11), with similar findings in sepsis alone. Differential abundance analysis identified 11 sepsis-associated proteins in plasma and 22 in EV-enriched plasma. Only SAA1, SAA2, and IGFBP6 were significant in both compartments. Exploratory pathway analysis supported acute-phase and inflammatory enrichment in plasma sepsis-associated proteins, while EV-enriched signals were directionally plausible but did not meet prespecified FDR thresholds. Conclusion: Plasma and EV-enriched plasma proteomics capture related but nonredundant sepsis-associated host-response information in critically ill patients.

05.
arXiv (quant-ph) 2026-06-11

A post-selected quantum model of cosmic acceleration

arXiv:2606.12297v1 Announce Type: cross Abstract: The origin of cosmic acceleration remains a central problem in cosmology, commonly attributed to a cosmological constant within the $\Lambda$CDM model or to dynamical dark energy. Here, we develop an alternative approach in which acceleration emerges from quantum post-selection, a standard feature of quantum theory that is not usually incorporated into cosmological modelling. While quantum theory admits both pre-selected and post-selected ensembles, quantum cosmological models are almost exclusively formulated in terms of initial conditions. Building on previous work on post-selected quasiclassical dynamics, we construct a minimal predictive cosmological model in which post-selection and coarse-graining generate effective late-time acceleration without introducing a cosmological constant, dark energy, or modifications of general relativity. The resulting expansion history is highly constrained theoretically and depends on at most two parameters beyond standard Friedmann evolution. Confrontation with type Ia supernova and cosmic chronometer data yields statistically competitive fits while naturally avoiding the coincidence problem. The model also reproduces the standard radiation- and matter-dominated behaviour at early times and predicts a present-day jerk parameter significantly different from the $\Lambda$CDM value. These results suggest that cosmic acceleration may arise as a macroscopic quantum cosmological effect rather than from additional cosmological fluids or modified gravitational dynamics.

06.
arXiv (quant-ph) 2026-06-11

Consistent Evaluation of Operators Involving the Position Operator in the Bloch Representation: Application to the Orbital Moment

arXiv:2606.11679v1 Announce Type: cross Abstract: The position operator plays a central role in condensed-matter observables such as velocity, orbital moment, and electric polarization. In solid-state physics, the evaluation of operators incorporating the position operator has not reached a consensus, as observed in the operator-level discrepancy between the local circulation of Wannier functions and the self-rotation of wave packets. Here, to achieve a consistent evaluation of such operators, we propose three rules for evaluating operators involving the position operator in the Bloch representation. The rules are devised to satisfy physical conditions: independence from the choice of unit cell, preservation of Hermitian conjugacy for the product of operators, and recovery of the correct intraband velocity. We further address the gauge dependence of the position operator and introduce a scheme termed gauge filtration, which systematically removes gauge-dependent contributions from the operators containing the position operator. This methodology ensures that the quantities obtained from the operator evaluation correspond to observable physical phenomena. By applying our framework, we reconcile the results concerning the self-rotation of the wave packet and the local circulation of the Wannier function. We expect our proposal to establish a consistent framework for evaluating operators involving the position operator.

07.
arXiv (CS.LG) 2026-06-16

A spectral audit framework reveals task-dependent aperiodic reliance across EEG and ECG deep learning

arXiv:2606.08583v2 Announce Type: replace Abstract: Deep learning on physiological time series is interpreted through domain-specific features – oscillatory rhythms in EEG, morphological complexes in ECG – yet these signals sit atop a broadband aperiodic 1/f-like envelope that covaries with arousal, age, and pathology. We introduce a spectral audit framework combining aperiodic/periodic decomposition, phase-preserving Fourier interventions, sham controls, and simulation validation. Aperiodic reliance was task-dependent and architecture-general: across six neural architectures, flattening drops exceeded 0.42 balanced-accuracy points for sleep-wake classification, reached 0.07-0.13 for clinical abnormality detection, and remained minimal for motor imagery. Six of seven EEG foundation models showed FDR-significant aperiodic reliance on clinical EEG; age/sex and recording-era controls reduced but did not eliminate the effect. Applying the audit to PTB-XL ECG revealed neural drops of 0.32–0.36 persisting after demographic matching, confirming this confound class extends beyond EEG. Aperiodic controls should become standard for interpretable physiological time-series deep learning.

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

SheafStain: Sheaf-Theoretic Schrödinger Bridge for Spatially and Biologically Coherent Virtual Staining

Current virtual staining approaches offer the potential for time- and cost-efficient biomarker quantification in cancer diagnostics and prognostics. However, patch-wise inference for gigapixel whole slide images (WSIs) fails to maintain spatial continuity, yielding artifacts that cause catastrophic mismatches with ground-truth images. Although pathology Vision Foundation Models (VFMs) offer rich representations, their self-attention causes varying global contexts to produce inconsistent embeddings for the same physical region. We formalize and validate this ``context contamination'' as a sheaf-theoretic problem where these embeddings form a presheaf that violates the gluing axiom. To address this, we propose SheafStain, a new approach that reinterprets VFM features as sheaf-like sections for spatially and biologically coherent virtual staining. Specifically, SheafStain integrates class and patch tokens into a Schrödinger Bridge framework as sheaf-like sections. While the class token anchors biological consistency, patch tokens form a per-position spatial map. A backbone co-pretrained on Hematoxylin \& Eosin (H\&E) and Immunohistochemistry (IHC) yields non-degenerate cross-stain stalks, so a single VFM feature space supervises both input conditioning and output stain alignment. Departing from prior work that evaluates on isolated $256 \times 256$ patches and either random-crops or resizes the $1024 \times 1024$ ground truth, we translate at $256 \times 256$ and evaluate on the stitched $1024 \times 1024$ outputs across HER2, ER, PR, and Ki-67. SheafStain demonstrates promising results against six prior methods while mitigating patch-boundary stitching artifacts. Code will soon be released.

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

VERITAS: Verifier-Guided Proof Search for Zero-Shot Formal Theorem Proving

arXiv:2606.19399v1 Announce Type: cross Abstract: LLM-based formal provers often collapse rich verifier signals (syntax errors, type mismatches, partial goal progress) into a binary pass/fail bit. We present VERITAS, a zero-shot framework that routes every verifier signal back into proof search through a two-phase protocol: Best-of-N sampling first, then a critic-guided MCTS pass that ingests Phase 1 failures as explicit negative examples. The protocol preserves every theorem solved by its own Phase 1 sweep, so Phase 2's additional solves are attributable to feedback-driven exploration. VERITAS reaches 40.6% on miniF2F (vs. an independently run Best-of-5 at 36.9%, Portfolio 26.2%) and 7.3% on VERITAS-CombiBench, a 55-theorem combinatorics benchmark we release on which Best-of-5 (1.8%) falls below Portfolio (3.6%), exposing that unguided sampling hurts when correct lemma names must be recovered iteratively from verifier feedback. Artifacts are available on GitHub.

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

Preregistration for Experiments with AI Agents

arXiv:2606.11217v1 Announce Type: cross Abstract: The proliferation of large language models (LLMs) and autonomous AI agents has given rise to a rapidly growing methodological paradigm: "in silico" behavioral experiments. Originally conceived as a way to use AI agents as proxies for human participants in studies of cognition, decision-making, and social dynamics, this approach has taken on new significance – as AI agents increasingly negotiate, transact, and make consequential decisions on behalf of people and organizations, understanding their behavior has become a research priority in its own right. While these experiments with AI agents offer unprecedented advantages in terms of scalability, cost efficiency, and experimental control, they also inherit, and in some cases amplify, methodological vulnerabilities that have long plagued human subjects research. To address these issues, this paper argues that preregistration practices – central to improving the credibility of human subjects experiments – should now be extended to experiments with AI agents. We systematically catalog the researcher degrees of freedom that experiments with AI agents introduce – model selection, prompt wording, settings, and outcome-contingent redesign, for example – and show how the low cost of iteration and lack of reporting norms make these choices both easy to exploit and difficult to detect. We propose a preregistration template tailored to experiments with AI agents and call on conferences, journals, and funding agencies to make preregistration standard practice for this emerging research paradigm.

12.
arXiv (quant-ph) 2026-06-11

An iterative Ising decoder for quantum error correction codes

arXiv:2606.12301v1 Announce Type: new Abstract: The Ising framework maps the decoding problem in quantum error correction onto ground-state optimization of a classical Hamiltonian, in which $X$-$Z$ error correlations enter as cross terms. Under phenomenological depolarizing noise, the exact joint formulation contains up to 8-body interactions for the toric code and 10-body for the $6.6.6$ color code. These high-order terms degrade solver convergence, inflate runtime, and raise the auxiliary spin overhead when embedding into native 2-body Ising hardware. In this work, we propose the iterative low-order decoding (ILOD) algorithm, which alternates between $X$- and $Z$-type sub-Hamiltonians, approximating cross-type correlations through Bayesian priors that reweight each type's couplings using the other type's inferred error configuration. This halves the maximum body count of interaction terms in the Hamiltonian, accelerating the solver, restoring convergence at larger code distances, and reducing the total spin count for 2-body embedding by a factor of $2.5$. For the toric code, ILOD attains a threshold of $4.73%$ versus $4.83%$ for the joint formulation, with the empirical runtime ratio scaling as $(0.81)^d$. For the $6.6.6$ color code, their thresholds agree within statistical uncertainty for small code distances, and ILOD remains convergent for larger distances where the joint formulation fails to converge despite a larger annealing budget.

13.
arXiv (CS.CV) 2026-06-16

Null-Space Diffusion Distillation Unlocks Speed, Fidelity and Realism in Lensless Imaging

Lensless imaging reconstructs scenes from highly multiplexed measurements, resulting in a severely ill-posed inverse problem. In this work, we identify a fundamental trade-off between measurement consistency, perceptual quality, and inference speed across lensless reconstruction paradigms. Traditional methods favor consistency but produce perceptually degraded results, supervised approaches achieve high-quality reconstructions with fast inference but may violate physical constraints, and diffusion-prior methods achieve high perceptual quality and consistency–particularly when structured constraints such as range-null decomposition are used–but remain slow due to iterative sampling. Motivated by this observation, we propose Null-Space Diffusion Distillation (NSDD), a single-pass reconstruction model that distills structured diffusion-prior inference into an efficient feed-forward network. NSDD learns to produce high-quality reconstructions that preserve measurement consistency while avoiding costly iterative sampling. Experimental results demonstrate that NSDD achieves perceptual quality and consistency competitive with diffusion-prior methods, while providing significantly faster inference and offering a favorable balance across all three objectives. Furthermore, ablation experiments show that distilling the range–null decomposition improves reconstruction quality and robustness over unstructured full-reconstruction distillation, including on unseen real scenes. These results highlight the potential of structure-aware distillation for efficient lensless imaging. Code is available at github.com/JRCSAVSN/NullSpaceDiffusionDistillation.

14.
arXiv (CS.CL) 2026-06-16

AuAu: A Benchmark for Auditing Authoritarian Alignment in Large Language Models

The worldwide surge of authoritarianism, combined with the increasing central role in users' everyday lives, raises the question of to what extent specific models exhibit or promote authoritarian attitudes and characteristics. We introduce AuAu, a comprehensive benchmark that aims to assess the risk of LLMs generating responses with authoritarian tendencies. This benchmark combines three evaluation approaches: (i) psychometric questions from an extensive pool of 15 human validated instruments; (ii) contextual behavior vignettes probing intended actions in concrete situations; and (iii) responses to realistic user prompts. Unlike prior work, AuAu evaluates not only a general closeness towards authoritarianism but also the established sub-concepts Authoritarian Aggression, Authoritarian Submission, and Conventionalism. Evaluating 17 models from China, the EU, Russia, and the USA, we find that all tested models exhibit substantial authoritarian response rates under the psychometric evaluation, though rates drop significantly in increasingly more realistic downstream task. We further find that an authoritarian system prompt easily manipulates 15 out of 17 models to promote increased authoritarianism. Our results underscore the need for continued, systematic auditing of LLM-based AI systems to detect and ultimately mitigate undesired authoritarian tendencies in generated output. Our code and data are available at: https://github.com/andreaseinwiller/AuAu

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

Treatment Response Optimized Clinical Decision Support AI System via Digital Twin Simulation

arXiv:2606.17405v1 Announce Type: new Abstract: Clinical decision support AI systems (CDSASs) must adapt to evolving patient conditions in real-time while adhering to strict safety constraints. We present an online adaptive framework that integrates Treatment Effect (TE) estimation to quantify clinical benefits, a patient Digital Twin (DT) to simulate treatment trajectories, and Reinforcement Learning (RL) for sequential decision-making. The AI system is initially trained on historical medical records and operates in a continuous learning loop. To ensure safety, a rule-based module monitors vital signs and blocks contraindicated treatments. Cases with strong internal model disagreement are flagged for clinician review, simulated in our experiments via a pre-trained outcome model. We validate our framework using both a synthetic clinical simulator and a real-world ovarian cancer dataset from The Cancer Genome Atlas (TCGA). In both simulated and clinical settings, our method demonstrated superior effectiveness and stability in recommending treatments compared to standard computational baselines. Furthermore, the AI system maintains low latency and requires expert consultation for only a minority of cases in our experimental validation, demonstrating its potential as a safe, clinician-supervised tool for personalized medicine that continuously improves through practical use.

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

RAMAC: Multimodal Risk-Aware Offline Reinforcement Learning and the Role of Behavior Regularization

arXiv:2510.02695v3 Announce Type: replace-cross Abstract: In safety-critical domains where online data collection is infeasible, offline reinforcement learning (RL) is attractive only if policies achieve high returns without catastrophic lower-tail risk. Prior work on risk-averse offline RL achieves safety at the cost of either (i) value/model-based pessimism or (ii) restricted policy classes that limit expressiveness, whereas diffusion/flow-based expressive generative policies have largely been used in risk-neutral settings. We introduce Risk-Aware Multimodal Actor-Critic (RAMAC), a simple, modular, model-free framework that couples an expressive generative actor (e.g., diffusion/flow) with a distributional critic and optimizes a composite objective that combines Conditional Value-at-Risk (CVaR) with behavioral cloning (BC), enabling risk-sensitive learning in complex multimodal scenarios. Since out-of-distribution (OOD) actions are a major driver of catastrophic failures in offline RL, we further provide an objective-level analysis showing that controlling behavior divergence via BC suppresses OOD actions and stabilizes CVaR. Instantiating RAMAC with a diffusion actor, we illustrate these insights on a 2-D risky bandit and evaluate on Stochastic-D4RL, observing consistent gains in $\mathrm{CVaR}_{0.1}$ while maintaining strong returns. The code and experimental results are available on the \href{https://kaifukazawa.github.io/ramac-project/} {project website}

17.
medRxiv (Medicine) 2026-06-22

National trends and operational drivers of vaccine wastage in Uganda, 2020-2025: a descriptive analysis of four tracer antigens

Background Vaccine wastage reduces immunisation efficiency, increases costs, and complicates supply forecasting. Uganda routinely monitors vaccine use, but national evidence comparing observed wastage with World Health Organization (WHO) and Uganda-specific planning thresholds has been limited. We described national and sub-national trends for four tracer antigens to inform supply-chain planning and forecasting. Methods We conducted a retrospective descriptive analysis of routinely reported immunisation data from Ugandas District Health Information Software 2, 2020-2025. We analysed Bacille Calmette-Guerin (BCG), measles-rubella (MR), oral polio vaccine (OPV), and diphtheria-tetanus-pertussis-containing vaccine (DPT). Vaccine wastage was calculated as the proportion of issued doses not administered. Annual wastage rates were summarised using medians, and temporal trends were assessed using the Mann-Kendall test. Observed wastage was compared with WHO thresholds: BCG[≤]50%, MR[≤]25%, OPV[≤]10%, DPT[≤]15%, and Ugandas planning thresholds: BCG[≤]70%, MR[≤]40%, OPV[≤]15%, DPT[≤]10%. Effective Vaccine Management reports were reviewed to summarise reported reasons for wastage. Results During 2020-2025, median national wastage was 40.6% for BCG, 25.9% for MR, 10.0% for OPV, and 9.2% for DPT. OPV wastage declined from 12.8% in 2020 to 8.0% in 2025, with a significant downward trend ({tau}b=-1.00; p=0.008). OPV and DPT wastage remained largely within their respective Uganda in-country thresholds ([≤]15% and [≤]10%) for most of the study period, while BCG generally remained below the WHO threshold ([≤]50%) and MR frequently exceeded the WHO threshold ([≤]25%) but remained within Uganda's planning threshold ([≤]40%) in most years. The proportion of districts exceeding both WHO and Uganda thresholds declined for OPV from 36.3% to 5.5% (p=0.024) and for DPT from 22.6% to 1.4% (p=0.013). Wastage was consistently higher in lower-level (Health Centre II and III) facilities, compared to hospitals. Among 50 service delivery points, reported reasons included low session attendance (66%), multi-dose vial policy non-compliance (28%), and vaccine expiry (12%). Conclusion Uganda achieved reductions in OPV wastage and district-level improvements in DPT wastage, while BCG and MR remained more variable and frequently had higher wastage. Strengthening adherence to the multi-dose vial policy and improving session planning at lower-level facilities could strengthen vaccine utilisation and forecasting.

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

Trade-offs in Medical LLM Adaptation: An Empirical Study in French QA

The development of large language models (LLMs) has led to an increased focus on their adaptation to specialized domains and languages, yet the effectiveness of domain adaptation strategies remains unclear. We present a study of medical domain adaptation using French medical question-answering (QA) as a case study. We compare continual pretraining (CPT), supervised fine-tuning (SFT), and their combination across three model families, multiple sizes, and three initialization types, explicitly disentangling adaptation effects from base model choice. We evaluate both multiple-choice (MCQA) and open-ended QA (OEQA) under greedy and constrained decoding using automatic metrics and LLM-as-a-Judge evaluation. For MCQA, CPT+SFT most often achieves the best scores, but gains over SFT are small and frequently not statistically significant, making SFT a strong and cost-effective default. For OEQA, CPT consistently improves overlap-based metrics, while SFT often degrades generation quality; instruction tuning and CPT+SFT are preferred by LLM-based evaluation. Cross-lingual experiments further show effective transfer from French adaptation to English benchmarks. Overall, we provide practical guidelines for selecting adaptation strategies under computational constraints.

19.
Science (Express) 2026-05-21

Observation of quantum vortex core fractionalization and skyrmion formation in a superconductor | Science

Authors: Unknown Author

Magnetic fields can penetrate a superconductor in the form of quantum vortices, which consist of a core singularity with circulating currents. London’s quantization implies that there is one core singularity per quantum of magnetic flux in single-component superconductors. Here, we report signatures of quantum vortex core fractionalization on the potassium-terminated surface of a multiband superconductor KFe 2 As 2 . The observed splitting of single integer-flux vortices into several fractional vortices results in a disparity between the numbers of flux quanta and vortex cores. These fractional vortices often arrange in chains, which calculations show are characterized by a ℂP 2 skyrmionic topological invariant; this constitutes a different type of topological defect: the chiral skyrmion. The disparate natures of integer and fractional vortices comprising skyrmions lead to distinct spectroscopic signatures.

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

The Information-Theoretic Benefit of Shared Representations under Orthogonality Constraints

arXiv:2606.16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models. Empirically, exploiting similarity across different problems, instead of solving them individually, can significantly improve overall performance. While the generalization and sample complexity properties of multitask learning have been widely studied, the parametric complexity of joint approximation in comparison to separate approximation remains less well understood. The question is particularly relevant in modern deep learning, where models are increasingly required to satisfy structural constraints such as equivariance, conservation laws, or orthogonality. We prove lower and upper bounds on the description-length for separate and joint approximation classes, respectively, in uniform norm. We build a class of orthogonal functions by composing a shared hard feature, realized by a Rademacher-Haar wavelet series, with Sawtooth-Walsh readouts to enforce orthogonality of output coordinates. The dyadic tree structure of the Rademacher-Haar wavelet concentrates the approximation hardness in the common feature component, while the readouts act as task-specific heads. Using an information-theoretic framework, we obtain a sharp gap between the optimal approximation rates achievable by joint and separate coding. Finally, we realize this separation in a neural network model using Heaviside activations via reduction to triangle-wave approximation. Our results show that even under an orthogonality constraint joint approximation requires strictly fewer bits in compositional architectures, provided the tasks share a latent hard feature. This provides theoretical insight into the description-length-efficiency of compositional multi-output architectures and clarifies how neural networks can retain expressivity under geometric constraints.

21.
arXiv (CS.AI) 2026-06-17

Optimism Stabilizes Thompson Sampling for Adaptive Inference

arXiv:2602.06014v2 Announce Type: replace-cross Abstract: Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specific sample sizes are random and coupled with the rewards through the action-selection rule. We study adaptive inference for Thompson sampling with Gaussian randomized indices in $K$-armed stochastic bandits with independent sub-Gaussian reward noises, and identify optimism as a key mechanism for restoring stability, meaning that each arm's pull count concentrates around a deterministic scale. This stability yields asymptotically valid Wald inference despite adaptive sampling. First, we prove that variance-inflated TS is stable for any $K \ge 2$, including the challenging regime where multiple arms are optimal, with asymptotically uniform allocation over optimal arms and sharp logarithmic pull-count asymptotics for suboptimal arms. This resolves the $K$-armed extension question raised by \citet{halder2025stable}, using new winner-map and Lyapunov-drift techniques to control allocation among multiple optimal arms. Second, we analyze an alternative optimistic modification that keeps the Gaussian index variance unchanged but adds an explicit mean bonus to the index center, and establish a similar stability conclusion. In summary, suitably implemented optimism stabilizes Thompson sampling and enables asymptotically valid Wald inference in multi-armed bandits, while incurring only a mild additional regret cost.

22.
arXiv (math.PR) 2026-06-18

Evolution of Conditional Entropy for Diffusion Dynamics on Graphs

arXiv:2510.19441v2 Announce Type: replace-cross Abstract: The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their finite-time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs, and outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. In particular, we highlight that this entropic measure satisfies an information-theoretical version of the second law of thermodynamics, thereby providing a parallelism between diffusion dynamics on networks and their physical counterparts. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdös-Rényi graphs. We also obtain asymptotic results for general networks and provide bounds for the evolution of conditional entropy. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

23.
arXiv (quant-ph) 2026-06-12

A refined thermodynamic analysis of nonsecular master equations

arXiv:2606.13504v1 Announce Type: new Abstract: We present a systematic thermodynamic analysis of nonsecular master equations. We consider master equations resulting either from the partial secular and the geometric-arithmetic approximations, two approximations ensuring the positivity of the system's dynamics when some of its transition frequencies are too small to enable the full secular approximation. Both cause the system to relax towards a steady state which is not the Gibbs state of its bare Hamiltonian. Nonetheless, we build a unified, consistent thermodynamic framework for those dynamics. Starting from a microscopic expression of the second law based on system-environment correlations, we employ a systematic perturbation theory to preserve the positivity of the second law despite the approximations done on the dynamics. We show that, in spite of the weak system-bath coupling, the system-bath interaction energy participates to the energy balance, as well as the Lamb-shift. Those extra contributions give rise to work performed by the system on the bath when the former is out of equilibrium. We compare this microscopic entropy production with the definition based on the contractivity of the reduced system dynamics (Spohn inequality). We show that, unlike for secular master equations, the two entropy production rates differ because of the presence of non-vanishing stationary coherences in the energy eigenbasis. However, in the case of a single thermal bath, the difference is purely transient, and no work can be cyclically extracted from the steady-state despite its non-Gibbs form. Finally, we illustrate our results with a simple example, clarifying and completing the thermodynamic picture of Markovian dynamics in the quantum regime.

24.
arXiv (CS.AI) 2026-06-19

Zero-Inflated Gaussian Distributions Enable Parameter-Space Sparsity in Estimation-of-Distribution Algorithms

arXiv:2606.19369v1 Announce Type: cross Abstract: Estimation-of-distribution algorithms (EDAs) are a powerful class of evolutionary methods for black-box optimization, especially when little is known about the structure of the objective. Whereas classical evolutionary algorithms rely on hand-designed mutation and crossover operators, hard to devise for unknown problem structures, and a source of bias, EDAs sidestep operator design entirely: they fit a probability distribution to the best individuals and sample the next generation from it. EDAs are well established on continuous parameter spaces, but they have not previously been generalized to sparse ones, in which most coefficients of a good solution are exactly zero. Existing sparse black-box optimizers therefore reintroduce exactly what EDAs were designed to avoid: hand-crafted sparsity operators, bi-level schemes alternating between support set and active values, zeroing thresholds, and other baked-in assumptions. We close this gap by proposing multivariate zero-inflated Gaussian (ZIG) distributions as EDA sampling laws. A latent Gaussian model with separate indicator and value dimensions represents sparsity patterns, correlations among active parameters, and the interactions between the two, so sparsity patterns and active values are optimized jointly, hierarchy-free. We show that the latent parameters of this model are identifiable from observed samples, unlike in the missing-data settings where related constructions originate, and introduce practical amortized inversion-based estimators for them. The estimators accurately recover latent correlation structures, and on the Lunar Lander benchmark the resulting ZIG-EDA converges faster and reaches higher final returns than a dense Gaussian EDA, a hand-crafted sparse evolutionary algorithm, and an ad-hoc sparse EDA, while finding controllers with only a small fraction of parameters active.

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

Cross-Layer Discrete Concept Discovery for Interpreting Language Models

Interpreting language models remains challenging due to the existence of residual stream, which linearly mixes and duplicates features across adjacent layers, causing single-layer analyses to miss this cross-layer structure. Cross-layer sparse autoencoders (SAEs) address layer mixing but operate in continuous space, where concepts split across many neurons without clear boundaries. We introduce Cross-Layer Vector Quantized-Variational Autoencoder (CLVQ-VAE), a novel framework which maps representations from a lower layer to a higher layer through a discrete vector-quantization bottleneck, collapsing duplicated residual-stream features into compact, interpretable concept vectors. Our approach combines top-k temperature-based sampling with exponential moving average (EMA) codebook updates, providing controlled exploration of the discrete latent space while maintaining codebook diversity. Across both encoder- and decoder-based models on ERASER-Movie, Jigsaw, and AGNews, CLVQ-VAE outperforms clustering, single-layer vector quantized-variational autoencoder (VQ-VAE), and sparse autoencoder (SAE) baselines across three evaluation axes: removing identified concepts drops model accuracy by up to 93%, LLM judges rank our concepts first in 66.7% of comparisons, and human annotators recover model predictions from our visualizations with 78% accuracy versus 54% for clustering.