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

QK-Normed MLA: QK normalization without full key caching

Query-key (QK) normalization stabilizes attention by controlling the scale of queries and keys before the dot product, but is not immediately compatible with Multi-head Latent Attention (MLA). MLA achieves efficient decoding by caching low-dimensional latent states instead of full keys, whereas post-projection QK RMSNorm appears to require the fully projected key for every cached token. We show this apparent incompatibility is an implementation artifact, not an architectural constraint. RMSNorm decomposes into a static affine weight and a dynamic scalar RMS statistic. The static key-side weight can be absorbed into the MLA query-side projection; the dynamic key statistic reduces to one inverse-RMS scalar per token and KV group. The resulting formulation is exactly equivalent to explicit post-projection QK RMSNorm in exact arithmetic and preserves MLA's latent decode path. In our 400M runs trained for up to 100B tokens, QK-Normed MLA achieves lower training loss and better downstream accuracy than QK clipping, while H800 decode benchmarks show less than 2% latency overhead up to 256k context. These results make QK normalization a practical stabilization option for MLA models without requiring full-key caching.

02.
Nature (Science) 2026-06-17

Towards Conversational AI for Disease Management

While large language models (LLMs) have shown promise in diagnostic dialogue1, their capabilities for effective management reasoning—including disease progression, therapeutic response, and safe medication prescription—remain under-explored. We advance the previously demonstrated diagnostic capabilities of the Articulate Medical Intelligence Explorer (AMIE)1−3 through a new LLM-based agentic system optimized for multi-visit clinical management and dialogue. To ground its reasoning in authoritative clinical knowledge, AMIE leverages Gemini’s long-context capabilities4, combining in-context retrieval with structured reasoning to align its output with up-to-date clinical practice guidelines and drug formularies. In a randomized, blinded virtual Objective Structured Clinical Examination (OSCE) study, AMIE was compared to 21 primary care physicians (PCPs) across 100 multi-visit case scenarios designed to reflect UK NICE Guidance and BMJ Best Practice guidelines. AMIE was non-inferior to PCPs in management reasoning as assessed by specialists and scored better in both preciseness of treatments and investigations, and in its alignment with and grounding in clinical guidelines. To benchmark medication reasoning, we developed RxQA, a multiple-choice question benchmark derived from two national drug formularies (US, UK) and validated by board-certified pharmacists. Though AMIE and PCPs both benefited from the ability to access external drug information, AMIE outperformed PCPs on higher difficulty questions. While further research would be needed before real-world translation, AMIE’s strong performance across evaluations marks a significant step towards conversational AI as a tool in disease management.

03.
arXiv (quant-ph) 2026-06-11

Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics

arXiv:2411.03180v2 Announce Type: replace Abstract: Recently, there has been growing interest in simulating time-dependent Hamiltonians using quantum algorithms, driven by diverse applications, such as quantum adiabatic computing. While techniques for simulating time-independent Hamiltonian dynamics are well-established, time-dependent Hamiltonian dynamics is less explored and it is unclear how to systematically organize existing methods and to find new methods. Sambe-Howland's continuous clock elegantly transforms time-dependent Hamiltonian dynamics into time-independent Hamiltonian dynamics, which means that by taking different discretizations, existing methods for time-independent Hamiltonian dynamics can be exploited for time-dependent dynamics. In this work, we systemically investigate how Sambe-Howland's clock can serve as a unifying framework for simulating time-dependent Hamiltonian dynamics. Firstly, we demonstrate the versatility of this approach by showcasing its compatibility with analog quantum computing and digital quantum computing. Secondly, for digital quantum computers, we illustrate how this framework, combined with time-independent methods (e.g., product formulas, multi-product formulas, qDrift, and LCU-Taylor), can facilitate the development of efficient algorithms for simulating time-dependent dynamics. This framework allows us to (a) resolve the problem of finding minimum-gate time-dependent product formulas; (b) establish a unified picture of both Suzuki's and Huyghebaert and De Raedt's approaches; (c) generalize Huyghebaert and De Raedt's first and second-order formula to arbitrary orders; (d) answer an unsolved question in establishing time-dependent multi-product formulas; (e) and recover continuous qDrift on the same footing as time-independent qDrift. Thirdly, we demonstrate the efficacy of our newly developed higher-order Huyghebaert and De Raedt's algorithm through digital adiabatic simulation.

04.
arXiv (CS.CV) 2026-06-12

Skill-3D: Evolving Scene-Aware Skills for Agentic 3D Spatial Reasoning

This paper explores agentic 3D spatial understanding, i.e., MLLM agents performing 3D reasoning through tool use. Existing methods often misuse tools and exhibit biased tool preferences under 3D scenarios, leaving the agentic paradigm with only marginal gains over non-agentic strategies. We reveal that 3D spatial reasoning tasks are heterogeneous across scenes, while these agents apply a uniform tool-use strategy to all scenes rather than selecting tools according to the specific scene and task. To address this, we propose Skill-3D, a framework that learns self-evolving scene-aware skills. Specifically, Skill-3D identifies the task scene and records the agent's tool-use trajectory into a Scene Memory, where successful trajectories from similar scenes are aggregated and distilled into a reusable scene-aware skill, with failed ones attached to the skill as lessons. During training, once a similar scene recurs, the corresponding skill is injected to guide the agent, producing new trajectories whose successes and failures further refine the skill, forming a loop in which the memory and the skill library co-evolve. Experiments show that Skill-3D substantially improves tool utilization in 3D spatial reasoning (from 39% to 78% on VSI-Bench), driving the agent toward correct and sufficient tool use. For instance, it improves Gemini-3-Flash by 67% on MMSI-Bench. Furthermore, we conduct agentic post-training over skill-guided trajectories, which boosts Qwen3-VL-8B by 60% on VSI-Bench.

05.
arXiv (quant-ph) 2026-06-19

Indefinite Quantum Causality

arXiv:2606.19438v1 Announce Type: new Abstract: In recent years, operational approaches to quantum foundations have been developed as a means of understanding the core principles and distinctive features of quantum theory. Such approaches typically view physical processes as sequences of operations, with earlier operations serving as causes of later effects. However, a growing literature is emerging on the possibility of relaxing this assumption and allowing for quantum indefiniteness in the causal order. This development stems from a variety of motivations, both fundamental and applied, including exploring the role of causality in quantum theory, the interplay between quantum theory and general relativity, and higher-order quantum computing. A prominent offshoot of this development is the emergence of indefinite causal order as a feasible resource for quantum information processing. This review provides an overview of the current state of the art in the field, covering the methodology underlying indefinite quantum causality within the so-called "process matrix formalism", outlining key results and experimental implementations, and discussing recent advances.

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

Pepti-Agent: An AI Agent for Peptide Design and Optimization

Therapeutic peptides occupy a valuable design space between small molecules and biologics, but their development requires satisfying several competing constraints at once: solubility, hemolytic activity, and nonspecific surface fouling are governed by overlapping sequence features, so improving one property often degrades another. Computational design addresses this by pairing generative models with sequence-based property predictors, iteratively proposing and refining candidates. However, these components are typically wired together as monolithic scripts that are difficult to inspect, extend, or reuse, and they often refine sequences by natural-language reasoning rather than by tracking the evolving multi-property state of each candidate. We present Pepti-Agent, a closed-loop, peptide-specific framework that exposes generation, property prediction, and single-residue mutation as independently inspectable Model Context Protocol (MCP) tools. A large language model controller invokes these tools and consults live predictor output between calls, so refinement is guided by each sequence's current property profile rather than by language reasoning alone. Task-specific PeptideGPT models generate candidates, ProtBERT-based classifiers score solubility, hemolysis, and non-fouling, and two interchangeable mutation operators propose sequence edits. By recording a per-step trace of controller decisions, predictor outputs, and accepted mutations, Pepti-Agent offers a reproducible substrate for benchmarking multi-objective design strategies and for prioritizing candidates for experimental validation.

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

Early Anomaly-Onset Detection based on Wigner–Ville Distribution Slice Spectra: A Transmission-Grid Test Case

arXiv:2606.15856v1 Announce Type: cross Abstract: Operational disturbance monitoring in power networks requires decisions to be made from waveform windows as they arrive, rather than from completed records after the event. This study evaluates full-vector Wigner–Ville Distribution Slice (WVDS) spectra for sequential anomaly-onset detection in high-voltage grid-voltage waveforms. The approach keeps the bilinear midpoint interaction structure of the Wigner–Ville distribution and represents each 128-sample voltage window by a 128-dimensional slice spectrum, avoiding manually selected fault-frequency markers. WVDS is used with a baseline-normalized deviation (BND) score and is compared against the BND of Fast Fourier Transform (FFT-BND), raw-window autoencoders, FFT autoencoders, and WVDS autoencoders under the same thresholding and three-window persistence rule. A synthetic autoencoder–clustering teacher is used to select RTE fault records that start from an initially normal region and then transition to anomalous behavior. On the filtered test set, FFT-BND achieves the highest sensitivity, whereas WVDS-BND provides the lowest false-alarm operating point, reducing record-level pre-onset false alarms to 0.69%. The autoencoder comparison follows the same selectivity pattern: WVDS reconstruction decreases false alarms relative to FFT reconstruction but misses more examples. The results indicate that preserved WVD cross-term information can form a selective representation for online grid-waveform anomaly monitoring when false alarms are costly.

08.
medRxiv (Medicine) 2026-06-22

Survival differences and artemisinin resistance in severe malaria among HIV coinfected patients: data from Mozambique

Abstract Background Malaria remains a significant cause of morbidity and mortality, especially in sub-Saharan Africa, where rates of HIV coinfection are high. This study aimed to determine whether Plasmodium falciparum malaria treatment outcomes and rates of antimalarial resistance markers differ according to HIV serostatus in Mozambique. Methodology We conducted an observational study of non-pregnant adults, with and without HIV coinfection, admitted to the Hospital Central de Maputo for treatment of severe malaria. Plasmodium falciparum DNA was extracted from whole blood and sequenced to identify single-nucleotide polymorphisms. Statistical analyses to compare clinical outcomes and rates of nonsynonymous mutations in genes associated with drug resistance were performed in R version 4.2. Results We recruited 149 study participants aged between 18-62 years, 72 (48.3%) were female, and 59 (39.6%) were infected with HIV. Comparing clinical outcomes, we found a significant difference in anemia (hemoglobin

09.
arXiv (CS.AI) 2026-06-15

The Weight Norm Sets the Grokking Timescale: A Causal Delay Law

arXiv:2606.13753v1 Announce Type: cross Abstract: Grokking is the delayed onset of generalization in neural networks, arising long after they fit the training data. Whether the weight norm causes this delay is disputed: some studies report a critical norm at the transition, others observe grokking with no fixed norm at all. We settle this by intervening on the norm during training rather than only observing it. Under free training with weight decay, networks grok when the weight norm reaches a value Wc that varies little across seeds and learning rates (CV 1 to 2 percent) and grows with the modular base as a power law. When we instead clamp the norm to a fixed multiple rho of Wc and hold it there, the network still groks, but the delay follows T_grok proportional to exp(alpha rho). One exponent, alpha near 7.5, fits this delay across four moduli (R^2 = 0.996). Over the swept ranges the held norm moves the delay by about 19x and the learning rate by only about 2x, and holding the norm above Wc slows grokking rather than preventing it. A final LayerNorm removes the dependence by decoupling weight scale from the network function; without it the exponential law returns. This pinned-norm delay is the exponential counterpart to the logarithmic delay predicted for a freely contracting norm.

10.
arXiv (CS.LG) 2026-06-16

MIRAGE: Auditing Anti-Muslim Bias in Frontier LLMs Across Reasoning, Agentic, and Time-Coupled Conditions

arXiv:2606.16562v1 Announce Type: new Abstract: Five years after the discovery of persistent anti-Muslim bias in large language models, most evaluations remain confined to single-turn prompt completion, a setting that no longer reflects how frontier LLMs are deployed. We introduce MIRAGE (Muslim-Identity Reasoning and Agentic Generation Evaluation), a benchmark of 1{,}200 prompts spanning three deployment-realistic conditions: direct completion, chain-of-thought reasoning, and simulated agentic decision-making across content moderation, lending triage, refugee claim summarization, and hiring screens. Across six frontier models, we find that (i) chain-of-thought reasoning amplifies rather than suppresses Muslim-violence associations by 12–34\% relative to direct completion, (ii) agentic decisions exhibit a 9–22 percentage-point asymmetry between Muslim and matched non-Muslim cases on identical evidence, and (iii) bias is sharply time-coupled to retrieved news context, increasing 18–27\% under recent-conflict retrieval. Existing prompt-based mitigations transfer poorly across our three conditions, suppressing direct-completion bias while leaving agentic asymmetry largely intact. We release MIRAGE and an open evaluation harness to support targeted mitigation research.

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

A Privacy-Preserving Framework Using Remote Data Science for Inter-Institutional Student Retention Prediction

arXiv:2606.12845v1 Announce Type: cross Abstract: This study explores privacy-preserving machine learning (PPML) techniques using the PySyft platform to enable collaborative prediction of student retention between institutions. We developed a remote data science (RDS) framework with a semi-air-gapped architecture consisting of high-side and low-side servers, allowing researchers from three universities to build predictive models on sensitive student data without direct data access. Using historical data from a small private university (N=720), we evaluated three synthetic data generation approaches and validated the framework through inter-institutional collaboration. The results demonstrate consistent classification performance across institutions (Macro F1: 0.690–0.695) while maintaining strict Family Educational Rights and Privacy Act (FERPA) compliance. We also propose Data-Type-Aware Templates, a novel synthetic data method that prioritizes privacy over distributional fidelity. Our findings confirm that RDS-based PPML is technically feasible for educational settings and offers a practical alternative to federated learning for small-scale inter-institutional collaborations. The code is available at https://github.com/jtfields/NAIRR240195-Privacy-Preserving-Machine-Learning.

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

From 2D Yang-Mills to Calogero-Sutherland via a colored particle

arXiv:2606.13388v1 Announce Type: cross Abstract: We study Yang-Mills theory coupled to a particle on a cylinder, where gauge invariance and compactness reduce the dynamics to a finite dimensional quantum system. In the Abelian case, this yields a model equivalent to the Landau problem on a torus, with a degenerate ground state structure. We generalize this construction to non-Abelian gauge groups and show that, for SU(N), the system reduces to a one dimensional quantum many body problem with a singular Calogero-Sutherland-type interaction.

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

MFEN:Multi-Frequency Expert Network for Visible-Infrared Person Re-ID

Visible-infrared person re-identification (VI-ReID) is challenging due to the large modality discrepancy between visible and infrared images. We contend that this discrepancy is largely related to differing lighting conditions, including differences in light wavelength and light source type. Recently, frequency-based VI-ReID approaches have achieved notable success because frequency information can better extract identity-relevant contours and details while excluding irrelevant lighting and color. However, existing methods either do not distinguish different frequency bands or focus on only one band, which is insufficient under diverse lighting conditions. To perform comprehensive frequency domain learning, we propose a Multi-Frequency Expert Network (MFEN) that enables multi-frequency modulation and adaptively combines different bands through a mixture-of-experts design. We further introduce Random Frequency Augmentation (RFA) and Frequency Auxiliary Optimization (FAO) to better train MFEN. The three modules are complementary and jointly capture critical frequency-domain details for robust representation learning. Extensive experiments on three VI-ReID datasets demonstrate the effectiveness of our approach.

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

Coping in Crisis: Computational Modeling of Coping Styles in Digital Crisis Discourse During the 2023 Turkiye Earthquake

How do people cope when disaster strikes and can we detect it at scale, in real time, from what they write? This study addresses that question using over one million Turkish-language tweets posted in the aftermath of the February 6, 2023 earthquake in Turkiye, which unfolded in a deeply polarized political context just months before a national election. Drawing on Lazarus and Folkman's (1984) coping theory, we develop a multi-label BERTurk classifier to detect three coping styles (problem-focused, emotion-focused, and meaning-making) across four theoretically motivated crisis phases. BERTurk achieves a macro F1 of 0.693, substantially outperforming a zero-shot mDeBERTa baseline (macro F1 = 0.324). Applied to the full corpus, the classifier reveals a clear temporal trajectory: problem-focused coping dominates the urgency phase and declines sharply, emotion-focused coping rises and stabilizes, and meaning-making increases monotonically. Anger correlates most strongly with meaning-making (Spearman r = 0.387), suggesting it functions as a mobilizing force toward blame attribution rather than practical action. These findings demonstrate that coping theory can be reliably operationalized in real-world digital crisis data and that doing so can help humanitarian organizations tailor their responses to where a population actually is.

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

When to use what Schatten-$p$ norm in deep learning?

arXiv:2606.15268v1 Announce Type: new Abstract: Schatten-$\infty$ based optimizers such as Muon have shown promising empirical performance, but there remains seemingly conflicting observations regarding whether they are beneficial. We resolve this conflict by showing that the conclusion is regime dependent. Even when the objective is smooth in the Schatten-$\infty$ geometry, smaller Schatten-$p$ geometries can be optimal, specifically in the low-dimensional regime, which we show includes Chinchilla scaling. This conclusion follows from a new noise-robust acceleration result for the SODA framework for $p>2$. The same analysis explains why Muon-like methods do not require warmup, why they naturally favor large batches, and yields a batch size scaling rule for arbitrary $p$.

16.
arXiv (math.PR) 2026-06-16

Universality in the target arrival statistics of non-conservative search processes

arXiv:2606.16025v1 Announce Type: cross Abstract: Stochastic search processes in which searchers are continuously introduced to and removed from a target search domain are fundamental to a wide class of physical and artificial systems. The theory of such non-conservative search processes is, however, much less developed than for search processes with a fixed number of particles. Here we exploit a natural mapping between non-conservative stochastic search and queueing theory to derive the full time-dependent distribution of target arrivals under minimal assumptions on the underlying search process. Remarkably, we find that the steady-state inter-arrival time distribution is exactly exponential, regardless of the details of the search process, showing a robust universality that emerges directly from the queueing framework. Thus, counterintuitively, the arrival statistics of a non-conservative search process are much simpler than sequential search-and-capture processes involving a fixed number of searchers. This has major implications for target resource accumulation, where the delivery of resources is counter-balanced by their downstream consumption.

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

Decoding Insect Song: A Multitask Semisupervised Orthoptera Bioacoustic Classifier

arXiv:2606.13236v1 Announce Type: cross Abstract: Passive acoustic monitoring holds great promise for ecological inference, yet existing automated tools are typically narrowly trained and non-transferable. We address these limitations with PULSE, a semi-supervised, multi-task framework for Orthoptera bioacoustics, combining weakly-supervised species classification, self-supervised learning on unlabelled field audio, and knowledge distillation from a general-purpose bioacoustic model. Our domain-adapted specialist model outperforms a state-of-the-art general model across all metrics (macro F1: 0.21 vs. 0.07; AUC: 0.74 vs. 0.45; AP: 0.32 vs. 0.19), with active learning further raising F1 to 0.34 and AUC to 0.84. Beyond classification, the learned embeddings encode ecologically meaningful structure, exposed through an interactive visualisation tool for ecological discovery.

18.
arXiv (quant-ph) 2026-06-16

Cosmological Pseudo-Entropy

arXiv:2606.15227v1 Announce Type: cross Abstract: We study pseudo entropy $\mathcal{S}$, a recent generalization of entanglement entropy, for scalar cosmological perturbations in de Sitter space with sound speed $0.024 \leq c_s \leq 1$, and in expanding and contracting FLRW backgrounds with varying equation-of-state parameter $w$. In de Sitter space, $\mathrm{Re}(\mathcal{S})$ grows after horizon exit while $c_s$ controls its onset and saturates at late times. A similar saturation occurs in expanding-accelerating and contracting-decelerating backgrounds. In contrast, expanding-decelerating and contracting-accelerating backgrounds show large early-time $\mathrm{Re}(\mathcal{S})$ followed by oscillations after horizon re-entry. This happens because while the squeezing freezes, the squeezing angle doesn't. Unlike entanglement entropy, pseudo entropy possesses an imaginary part, $\mathrm{Im}(\mathcal{S})$, as well, which can encode the relative phase. $\mathrm{Im}(\mathcal{S})$ decays to zero in de Sitter and expanding-accelerating cases, but forms dense sub-Hubble oscillation bands in expanding-decelerating and contracting-accelerating backgrounds. Compared with entanglement entropy, Krylov complexity, and Nielsen circuit complexity, pseudo entropy captures otherwise hidden phase information; in the unsaturated regime, its slope is $\sqrt{2}$ times that of Nielsen complexity. Unlike circuit complexity, whose saturation bound is $w$-independent, pseudo entropy is sensitive to $w$ during the transition regime, making it a finer information theoretic diagnostic of cosmological dynamics.

19.
arXiv (math.PR) 2026-06-11

On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation

arXiv:2508.05032v3 Announce Type: replace Abstract: We study spatio-temporal increments of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions. We identify the exact local and uniform spatio-temporal moduli of continuity for the sample functions of the solutions. These moduli of continuity results imply the existence of random points in space-time at which spatio-temporal oscillations are exceptionally large. We also establish small-ball probability estimates and Chung-type laws of the iterated logarithm for spatio-temporal increments. Our method yields extension of some of these results to the open KPZ equation on the unit interval with inhomogeneous Neumann boundary conditions. Our key ingredients include new strong local non-determinism results for linear stochastic heat equation under various types of boundary conditions, and detailed estimates for the errors in linearization of spatio-temporal increments of the solution to the nonlinear equation.

20.
arXiv (CS.LG) 2026-06-15

MOSIC: Model-Agnostic Optimal Subgroup Identification with Multi-Constraint for Improved Reliability

arXiv:2504.20908v3 Announce Type: replace Abstract: Current subgroup identification methods typically follow a two-step approach: first estimate conditional average treatment effects and then apply thresholding or rule-based procedures to define subgroups. While intuitive, this decoupled approach fails to incorporate key constraints essential for real-world clinical decision-making, such as subgroup size and propensity overlap. These constraints operate on fundamentally different axes than CATE estimation and are not naturally accommodated within existing frameworks, thereby limiting the practical applicability of these methods. We propose a unified optimization framework that directly solves the primal constrained optimization problem to identify optimal subgroups. Our key innovation is a reformulation of the constrained primal problem as an unconstrained differentiable min-max objective, solved via a gradient descent-ascent algorithm. We theoretically establish that our solution converges to a feasible and locally optimal solution. Unlike threshold-based CATE methods that apply constraints as post-hoc filters, our approach enforces them directly during optimization. The framework is model-agnostic, compatible with a wide range of CATE estimators, and extensible to additional constraints like cost limits or fairness criteria. Extensive experiments on synthetic and real-world datasets demonstrate its effectiveness in identifying high-benefit subgroups while maintaining better satisfaction of constraints.

21.
arXiv (CS.CV) 2026-06-12

GAE: Unleashing Physical Potential of VLM with Generalizable Action Expert

Vision-language models demonstrate strong reasoning and planning abilities, yet grounding these predictions into precise robot actions remains a central challenge. Existing Vision-Language-Action methods typically entangle reasoning and action generation, leading to limited generalization. We propose Generalizable Action Expert (GAE), a task-agnostic model that converts sparse geometric plans into dense robot actions. Our approach introduces a sparse geometric interface: the VLM predicts sparse 3D waypoints representing high-level intention, while GAE maps these waypoints together with real-time point cloud observations to continuous action trajectories. GAE is pretrained on a large-scale pointcloud-trajectory dataset comprising 150k trajectories from both simulation and real-world robots. To further improve efficiency and generalization, we introduce an Action Pre-training, Pointcloud Fine-tuning (APPF) scheme that decouples learning action dynamics from geometry grounding. After pretraining, GAE is frozen and reused across downstream tasks, requiring only lightweight fine-tuning of the VLM to produce the sparse interface. Experiments show that our method achieves strong performance and generalization across diverse visual domains, camera viewpoints, and natural language instructions.

22.
Nature (Science) 2026-06-17

How the zebrafish brain weaves recent experiences into future decisions

作者: 未知作者

Animals often use recent experience to guide future choices. Whole-brain imaging in larval zebrafish (Danio rerio) reveals a dedicated neural circuit that governs history-biased decisions: the thalamus maintains the most recent event as a stable pattern of neuronal activity, and the brainstem integrates recent experiences into a continuous signal that biases future action. Whole-brain calcium imaging in the zebrafish reveals how information about events in the recent past drives future behaviour.

23.
arXiv (CS.LG) 2026-06-16

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

arXiv:2606.16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm, by a fixed-size neural network using the Elementary Universal Activation Function ($\mathrm{EUAF}$). To extend this result to $W^{s,\infty}((a,b)^d)$ for $s\in\mathbb{N}$, we introduce a smooth activation $\mathrm{DUAF}_{\infty}$ from the family of Differentiable Universal Activation Functions ($\mathrm{DUAF}_n$). We prove that any function in $W^{s,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy in the $W^{s-1,\infty}$-norm by a fixed-size $\mathrm{DUAF}_{\infty}$-activated network. We further construct sigmoidal variants $\widetilde{\mathrm{DUAF}}_n$ and show that, for every $1\leq s\leq n$, fixed-size $\widetilde{\mathrm{DUAF}}_n$-activated networks still approximate any $f\in W^{s,\infty}((a,b)^d)$ with arbitrary accuracy in the $W^{s-1,\infty}$-norm. In all these results, the width and depth bounds are computed explicitly, and the proposed activations are elementary.

24.
arXiv (math.PR) 2026-06-19

Model-independent upper bounds for the prices of Bermudan options with convex payoffs

arXiv:2503.13328v3 Announce Type: replace-cross Abstract: Suppose $\mu$ and $\nu$ are probability measures on $\mathbb{R}$ satisfying $\mu \leq_{cx} \nu$. Let $a$ and $b$ be convex functions on $\mathbb{R}$ with $a \geq b \geq 0$. We are interested in finding $$\sup_{\mathbf{M}} \sup_{\tau} \mathbb{E}^{\mathbf{M}} \left[ a(X) I_{ \{ \tau = 1 \} } + b(Y) I_{ \{ \tau = 2 \} } \right] $$ where the first supremum is taken over consistent models $\mathbf{M}$ (i.e., filtered probability spaces $(\Omega, \mathbf{F}, \mathbb{F}, \mathbb{P})$ such that $Z=(z,Z_1,Z_2)=(\int_{\mathbb{R}} x \mu(dx) = \int_{\mathbb{R}} y \nu(dy), X, Y)$ is a $(\mathbb{F},\mathbb{P})$ martingale, where $X$ has law $\mu$ and $Y$ has law $\nu$ under $\mathbb{P}$) and $\tau$ in the second supremum is a $(\mathbb{F},\mathbb{P})$-stopping time taking values in $\{1,2\}$. Our contributions are first to characterise and simplify the dual problem, and second to completely solve the problem under some structural assumptions on the measures $\mu$ and $\nu$ (namely that $\mu$ and $\nu$ are absolutely continuous probability measures that satisfy the Dispersion Assumption). A key finding is that the canonical set-up in which the filtration is that generated by $Z$ is not rich enough to define an optimal model and additional randomisation is required. This holds even though the marginal laws $\mu$ and $\nu$ are atom-free. The problem has an interpretation of finding the robust, or model-free, no-arbitrage bound on the price of a Bermudan option with two possible exercise dates, given the prices of co-maturing European options.

25.
arXiv (quant-ph) 2026-06-15

Efimov Effect in Ultracold Microwave-Shielded Polar Molecules

arXiv:2602.21433v2 Announce Type: replace-cross Abstract: A quantum-mechanical description is presented for the three-body physics of shielded dipolar molecules, including a prediction of observable Efimov physics. Despite the anisotropic and long-range nature of the interaction, shielding enables a regime in which universality emerges already at the two-body level and extends to the three-body sector, where Efimov physics emerges. On the negative side of the scattering-length resonance, computed trimer binding energies display the characteristic scaling expected for Efimov resonances. Finally, the sudden approximation can be used to create trimer bound states, starting from positive energy trap states as a way to create or detect these molecular trimers. Moreover, the three-body parameter expressed in dipolar units is found to be universal.