Papers

Denoising Diffusion Probabilistic Models have emerged as powerful generative priors across domains ranging from molecular design to high-resolution image synthesis. However, standard diffusion sampling is inherently biased toward high-likelihood regions, often limiting the diversity of outputs. In many domains, a single, high-likelihood sample is insufficient. Instead, diverse portfolios of high-performing solutions are required, motivating methods that uncover a model's full expressive range. Here we show that integrating Quality-Diversity (QD) optimisation with diffusion models enables the discovery of diverse, high-performing outputs. We first propose Quality-Diversity Diffusion, a framework that adapts QD to diffusion models by directly optimising the model's latent noise and conditioning embeddings and leveraging embedding models to quantify diversity. Second, we introduce a novel h-space Spectral Mutation operator, which guides search along directions of maximal semantic sensitivity by analysing principal singular vectors of the model's input-to-activation Jacobian. We evaluate our combined approach, Spectral-Guided Quality-Diversity Diffusion, on text-to-image generation. Against 12 baselines, our method consistently achieves the lowest FID score, demonstrating an excellent balance of image quality and diversity.

We study adaptive confidence sets for mean vectors of multivariate Gaussians with identity covariance under Huber contamination when the contamination proportion is unknown. We show that an information-theoretically optimal adaptive confidence set can be constructed by simultaneously quantifying uncertainty across all one-dimensional projections. The resulting confidence set achieves the optimal diameter and reveals a substantial adaptation cost compared with the minimax estimation error. Although statistically optimal, this construction is computationally infeasible. We establish a Statistical Query (SQ) lower bound showing that achieving diameter $O(m^{-1/2})$ requires either exponentially many queries or query tolerance $d^{-\Omega(m)}$. Thus, in contrast to robust mean estimation, adaptation to the unknown contamination proportion incurs both a statistical cost and a computational barrier within the SQ framework. Finally, we give a low-degree moment-matching algorithm that constructs an adaptive confidence set using $d^{O(m)}$ samples and time. Its diameter bound contains an additional $O(m^{-1/2})$ term beyond the information-theoretic rate, matching the dependence on $m$ in the SQ lower bound. Together, these results characterize the statistical limits of adaptive robust confidence sets under Huber contamination and quantify a computational barrier within the SQ framework.

Multimodal large language models (MLLMs) are good at video understanding and code generation, but it remains unclear whether they can recover the physical laws underlying videos, a capability essential for converting videos into executable simulations and for providing structured physical supervision in robotics. Captioning motion video does not imply that a model has inferred its governing dynamics, estimated quantitative parameters, or can regenerate the observed scene from code. Existing video-physics benchmarks evaluate plausibility, property estimation, or future-state prediction, but offer limited insight into whether models can translate visual dynamics into runnable simulation code. We introduce PhySimCode, a benchmark for physics video-to-code generation: given only a raw video, a model must infer the relevant physics, recover parameter values, and generate runnable Python that reproduces the input video. The dataset contains 160.6K procedurally generated samples spanning 162 physics phenomena across analytic SciPy simulations and PyBullet-rendered rigid-body, articulated, fluid, and contact-rich scenes; each sample bundles the simulation code, physical parameters, rendered video, and a structured chain-of-thought covering observations, laws, ODEs, numerical methods, and validation checks. We evaluate ten state-of-the-art closed- and open-source MLLMs along physical-law correctness, simulation equivalence, code executability, and parameter recovery. Models reliably state physics laws (4.27-4.93/5) yet score only 1.51-2.47/5 on inferring them from video, and the best system (Claude Sonnet 4.6) recovers just 7.7% of ground-truth parameters within $\pm 20\%$, exposing a substantial video-to-simulation gap. The 2,430-video evaluation set is available at https://huggingface.co/datasets/SourajaKundu123/PhySimCode and the evaluation code at https://github.com/SourajaKundu/PhySimCode

Cross-model KV cache sharing reduces prefill computation by allowing a receiver model to reuse prefix KV states generated by a related sender model. Existing methods optimize such reuse for latency and generation quality, but its safety implications remain unclear. In this work, we systematically evaluate this issue across diverse sender-receiver pairs and reuse configurations. We refer to deviations from the receiver's native safety behavior as safety incompatibility. Our study shows that both the direction and magnitude of safety incompatibility depend on the model pair and reuse configuration, with value reuse causing substantially larger deviations than key reuse across all evaluated pairs. Furthermore, we propose VReparo, a technique that learns per-layer and per-KV-head affine maps offline to align reused sender value tensors with their receiver-native counterparts before decoding. Across two model pairs under full KV reuse and the state-of-the-art selective reuse setting, VReparo reduces the average HarmBench attack success rate (ASR) from 57.28% to 39.21% and the average StrongREJECT score from 0.4215 to 0.2163 upon our benchmarks, while retaining an average Time to First Token (TTFT) reduction of 85.62%.

We prove mixing local limit theorems for dynamical systems in the superdiffusive regime where there is convergence to a multivariate stable law (including the nonstandard domain of the central limit theorem). We apply our results to d-dimensional observables for intermittent maps and solenoids, as well as intermittent semiflows and flows.

We observed comet 2P/Encke with the Cooled Mid-Infrared Camera and Spectrometer (COMICS) on the Subaru telescope on UT 2003 November 12.3, when the comet was at heliocentric and geocentric distances of 1.09 and 0.27 au, respectively. Imaging observations of the comet with narrow-band filters centered at 8.8, 10.5, 11.7, 12.4, 18.8, and 24.5 $\mu$m and low-resolution spectroscopic observations in the N-band (8-13 $\mu$m, $R\sim250$) of the comet were performed. The observed spatial profiles of the comet were consistent with those of a standard star (FWHM $\sim$ 0.3” at 10.5 $\mu$m, close to the diffraction-limited image size), indicating that the observed spectrum was dominated by thermal emission from the cometary nucleus. The semi-axial ratio ($a$/$b$) of the nucleus of 2P/Encke is estimated as 2.26$^{+0.33}_{-0.21}$ based on the isothermal, prolate ellipsoid model. The photometric data with the correction for rotational phases, can be explained by a blackbody temperature of $328\pm7$ K, consistent with the nucleus surface temperature empirically estimated at 1.09 au from the Sun (327 K). This blackbody approximation for the nucleus leads to $a = 3.6^{+0.5}_{-0.3}$ km and $b = 1.6^{+0.2}_{-0.2}$ km by assuming an emissivity of unity. The observed low-resolution N-band spectrum showed an overall smooth continuum with no prominent excess emission feature at $\sim$10 $\mu$m due to fine silicate grains in the cometary coma. The relative emissivity spectrum of the nucleus showed a negative feature at $\sim$9.5 $\mu$m, as seen in the mid-infrared nucleus spectrum of 460P/PanSTARRS [T. Ootsubo, et al. (2021), Icarus, 363, 114425].

We construct a smooth autonomous divergence-free vector field on $\mathbb{T}^3$ whose flow is exponentially mixing with respect to Lebesgue measure. This answers an open question about smooth autonomous exponential mixing in three dimensions. Starting from an exponentially mixing Anosov suspension flow, we perform surgery near four periodic orbits and show that the resulting manifold is diffeomorphic to $\mathbb{T}^3$. The resulting vector field has exactly sixteen hyperbolic equilibria. We also prove a general transfer theorem that preserves exponential mixing under certain singular changes of coordinates.

We establish sharp weighted Rogers–Shephard inequalities for Rényi differential entropy. For independent copies $X,X'$ of a log-concave random vector in $\R^n$, we prove $h_p(aX-bX')\le h_p(X)+n\log(a+b)$ for all $a,b>0$ and $1\le p\le\infty$, where orders $1$ and $\infty$ correspond to Shannon entropy and min-entropy, respectively. The Shannon case settles the entropic Rogers–Shephard conjecture of Madiman and Kontoyiannis and its higher-dimensional formulation. For $1\le p<\infty$, equality holds precisely for invertible affine images of random vectors with independent exponential coordinates. At $p=\infty$, the larger equality class is characterized by possibly extended-valued convex potentials that are positively homogeneous of degree one. For every $0<p<1$, uniform laws on sufficiently high-dimensional simplices violate the unweighted bound. Thus $p=1$ is the critical order for this bound to hold in every dimension. The proof combines weighted convex intersections with an exponential lift to a log-affine probability density. At the Shannon endpoint, this lift yields an exact deficit decomposition with a conditional mutual information term for an additive channel with asymmetric Laplace noise.

Linear attention promises the efficiency needed for long-context language modelling, yet its fixed-size recurrent state must simultaneously support ongoing computation and preserve information from an ever-growing history. This coupling has reinforced a prevailing view that the state's memory capacity defines the model's long-context capability. We challenge this presumed ceiling: recurrent computation need not bear the full burden of long-term storage. We introduce NoteBank, a sparse episodic memory that archives selected text before future queries are known, uses the backbone's native features for writing and addressing, and reads retrieved evidence through its native forward computation via replay. This training-free, plug-and-play interface requires no external embedding model, separately trained retriever, or separate neural reader. At one million tokens, it raises Gated DeltaNet's mean accuracy across six RULER retrieval tasks from 1.7% to 70.3%, with no observed significant retrieval degradation from 4K to 1M tokens. This recovery adds $\leqslant$0.025% to analytical FLOPs, with persistent context storage approximately 1/2,600 that of a Transformer's full MHA KV cache at matched width, depth, and precision. Experiments extend from three 1.3B recurrent backbones to Mamba-2-8B and post-trained Qwen3.5-9B, demonstrating gains on LongBench v1/v2 and MemoryAgentBench. Together, these results show that sparse evidence storage and native replay can substantially expand the long-context capability of pretrained linear attention models while retaining the efficiency of recurrent computation.

Healthcare agents must transform longitudinal clinical evidence into reliable actions through heterogeneous tools and stateful workflows, conditions under which model-centric systems may lose context, misuse tools, fail to verify consequential transitions, or cross authorization boundaries. Existing medical-agent benchmarks primarily emphasize terminal task outcomes, making it difficult to determine whether execution failures arise from the agent model, the runtime harness, or their interaction. We present the Medical Harness Protocol, an outcome-preserving framework that independently evaluates seven healthcare-specific process dimensions: Care Action Fulfillment, Clinical Resource Competence, Patient-Evidence Alignment, Clinical Workflow Continuity, Clinical Auditability, Closed-Loop Verification, and Clinical Conduct Boundaries. A normalized intervention trace further tracks whether runtime support is available, activated, delivered, adopted by the agent, and propagated into subsequent behavior. We instantiate the protocol as MedHarnessBench, comprising 342 executable tasks across FHIR/EHR operations, healthcare-administration interfaces, and multimodal clinical tools. Across more than 16,000 controlled task executions, MedHarness yields broad improvements in terminal task success, intermediate subtask completion, and healthcare-specific process quality. We further evaluate MedHarness against multiple general-purpose harnesses and use controlled single-fault perturbations to verify the sensitivity and discrimination of the seven-dimensional evaluation. These results demonstrate that healthcare-specific runtime support can substantially improve both task completion and execution quality, while revealing failures that terminal outcomes alone cannot capture. Code and resources are available at https://github.com/Tomry1114/Awesome-Agent-Harness-for-Healthcare.

We present a unified Bayesian analysis of Higgs-portal, neutron-decay, and axion-like-particle (ALP)-mediated dark matter in neutron stars within the single-fluid approximation. Using a common relativistic mean-field description of hadronic matter, we combine finite-nucleus and heavy-ion collision data, chiral effective field theory, NICER measurements of four pulsars, and GW170817. The individual dark-sector parameters remain weakly determined, while model-dependent shifts in nuclear skewness reveal the sensitivity of the inferred hadronic equation of state to the assumed dark-matter mechanism. The three scenarios yield substantially overlapping mass-radius and tidal-deformability predictions, with median maximum masses near $2.1\,M_\odot$. For $1.4\,M_\odot$ stars, the Higgs-portal model predicts higher $f$-mode frequencies and shorter damping times than the neutron-decay and ALP models, although their credible regions overlap. Comparison with three consistently reanalysed two-fluid models gives the largest Bayesian evidence to neutron decay: under the adopted priors, its Bayes factors relative to the Higgs-portal and two-fluid alternatives are approximately $24$-$37$, but only $2.2$ relative to ALP. This ranking concerns complete dark-matter models and does not establish a general preference for either fluid description or evidence for a dark component itself. Improved nuclear constraints and future gravitational-wave asteroseismology could provide complementary information to disentangle the hadronic and dark-sector contributions.

Many questions about large textual corpora concern patterns that unfold over time, such as a political group whose stance on a topic drifts from support to criticism over several years of debates. We present TL;QR (Too Long; Query with logical temporal Reasoning), a declarative query language and open-source engine for finding such temporal discursive patterns. In TL;QR, a single query combines natural-language predicates, whose truth is judged by a Large Language Model (LLM), with regular expressions and the operators of a temporal logic. The LLM answers only local questions about individual text passages; a symbolic engine then aggregates these judgments over time and links every match to the recorded passages and predicate decisions behind it. With this division of labor, the temporal and relational reasoning stays exact and auditable even over long time horizons. In addition, when a query includes a regular-expression pre-filter, only a small fraction of the corpus ever reaches the LLM. On a suite of controlled synthetic benchmarks with temporally and semantically complex patterns, TL;QR is substantially more accurate than LLM-only baselines. In a case study on ten years of European Parliament debates (442,593 multilingual speeches), TL;QR identifies candidate shifts in the political groups' stances on the GDPR privacy regulation.

Do genomic foundation models (FMs) provide predictive information beyond simple sequence composition? We evaluate frozen representations from five DNA FMs against normalized k-mer frequencies across 57 genomic classification datasets and two exploratory gene-expression regression tasks. Simple k-mer features remain competitive with most models, whereas NTv3 shows a consistent advantage; the ranking is robust to globally fixed and multi-scale k-mer baselines and alternative downstream probes. To test incremental predictive utility directly, we compare global 6-mer features with their concatenation with each FM embedding under a matched Random Forest protocol. NTv3 improves 46 of 57 datasets (mean $\Delta$MCC = +0.072), while Caduceus provides smaller gains and the other models do not improve mean MCC. We separately decompose embeddings into a component linearly predictable from 6-mer frequencies and a ridge residual, finding that linear recoverability does not reliably indicate downstream utility. Exact 6-mer-preserving shuffles further reveal task-relevant sequence-order sensitivity, most pronounced for NTv3, although order sensitivity alone does not guarantee predictive improvements. Our results establish compositional features as essential controls and offer complementary diagnostics for evaluating the added value of frozen genomic representations, without making claims about fine-tuning capacity.

Long-term memory for assistants needs a gate that decides when a new utterance retires an old stored claim. Benchmark labels for this step mark a pair as changed or not, so they cannot tell a gate that acts on established change from one that acts on a hint. We write a task contract that separates the two (SUPERSEDED vs. NEEDS-CONFIRMATION vs. COMPATIBLE), label 500 test pairs built from STALE (change pairs plus same-user controls) with three LLM annotators and two human adjudicators (one author and a second annotator; provenance reported), and evaluate Jev, a typed "System One" decision model, under pre-registered hypotheses. Of the 179 test pairs STALE marks as changed, 72 meet the contract's bar for an established change. Jev never retired a claim on 141 same-conversation non-changes. Its failure is premature retirement: the binary gate retires 39.2% of claims whose change is only suggested. A three-way decision cuts this to 15.5% at a 15.3-point detection cost, which misses our pre-registered 10-point budget, and it lands on the binary gate's own threshold frontier; these verdicts hold under three readings of the gold labels. On a held-out vault scored against a second annotator's labels, a cascade that escalated uncertain cases to a reasoning model and looked best on development data was indistinguishable from simply raising the threshold (premature retirement 26.8% vs. 6.5% on dev). Part of the gap comes from the gold labels: relative to that annotator's reading, LLM-majority gold shares most of its errors with a same-family escalation model, and an identity for binary labels says how much such shared errors hide. The rest is small-sample selection on development data. For builders this means a binary score should not be wired to delete: route suggested changes to pending evidence, and do not trust a cascade selected on development data of this size.

Linear attention and recurrent models compress past tokens into a fixed-size state that is updated at every step. However, storing these states in high precision incurs substantial memory and bandwidth costs at large batch sizes, motivating low-bit state quantization. Unlike weights and key–value caches, a recurrent state is requantized after every update, so its quantization errors accumulate across steps. Our analysis shows that these errors are highly coherent across steps, so reducing per-step errors alone is insufficient. This coherence arises mainly from small updates that are lost in rounding. To preserve these updates, we intervene both before and at rounding. Before rounding, we propose Low-Rank Bypass (LRB), which accumulates small updates in a compact low-rank buffer and periodically merges its sufficiently large elements into the state. At rounding, we observe that a state element can even move opposite to its update, and such reversals prove particularly harmful. Therefore, we propose Bounded Directional Rounding (BDR), which rounds reversed elements toward their updates without additional storage. Although BDR enlarges the rounding error, it improves the model, suggesting that the direction of an update matters more than its rounding error at a single step. Across Gated DeltaNet, GLA, Mamba2, and RetNet, our training-free method substantially outperforms INT4, while reducing state memory by up to 5.3$\times$ and speeding up decoding by up to 1.9$\times$ relative to FP32 states.

Coding agents based on frozen language models can improve their performance by refining the external context they rely on, without updating model weights. We study recursive self-improvement through behavioral specifications: natural-language code documentation that describes the behavior of program entities and guides agents in generating correct code. We formulate a self-improvement loop in which an agent generates code from its current specifications, evaluates it with execution-verified tests, and refines the specifications based on observed failures. The improved specifications then guide subsequent generation, progressively improving the agent's understanding of the codebase. However, recursive refinement is challenging because program entities are interdependent. Improving the specification of one entity can inadvertently degrade the correctness of others, a phenomenon we call output coupling. This creates a whack-a-mole effect in which local improvements cause regressions elsewhere, preventing consistent progress. We introduce SpecForge, a multi-frontier tree search framework that addresses this challenge with three mechanisms: (i) Pareto-guided state selection preserves complementary specification states and prevents premature commitment; (ii) dependency-constrained entity selection prioritizes callee-before-caller refinement; and (iii) error-diversified expansion explores multiple refinements using different subsets of test failures. On DevEval+, SpecForge achieves the best performance across five backbone models, including a 94.9% solve rate with Claude-4.5-Sonnet and a 5.7-percentage-point average improvement over the strongest baseline. The improved specifications also make the agent better at tasks outside the loop: they transfer to cross-language translation and to new-feature implementation, where they outperform the benchmark-provided requirement documents.

A central desideratum in model editing is generalization to complex tasks, which prior work formalizes under a direct generalization paradigm: treating and evaluating LLM behavior as an input-output mapping and expecting a factual update to alter outputs on reasoning tasks. Yet despite substantial empirical effort, the field consensus remains that such generalization is highly challenging and elusive. However, when we deploy the latest models in an in-the-wild chatbot-user setting, we surprisingly find that even classical editing methods exhibit remarkably fluent generalization behavior. This motivates us to revisit the obstacles to generalization and the limitations of the prevailing paradigm. We find that direct generalization is fundamentally constrained both theoretically and practically: theoretically, it suffers from an identifiability issue; and practically, existing approaches attempting to circumvent this are further hindered by the ambiguity of their constructed biases and by vulnerability to being overridden by other factors such as optimization dynamics. We instead identify compositional generalization, empowered by the increasingly strong reasoning and composition abilities of modern LLMs, as a theoretically grounded and empirically validated alternative. We validate this phenomenon across multiple models and editing methods, showing that such generalization behavior is widespread. Overall, we argue that generalizable model editing could be more than direct generalization, and call for a paradigm shift toward more generalizable and practically deployable knowledge update techniques.

We count the integral solutions of $x_1^2+x_2^2-x_3^2=D$ weighted by $\Phi(x_3/M)$, for $M$ smaller than $\sqrt D$. Such solutions correspond to binary quadratic forms of discriminant $D$, and the count becomes a sum, over the geodesics of discriminant $D$, of a function of their distance to the point $i$. We evaluate it by the spectral theory of automorphic forms. Throughout, $\theta=7/64$. For square $D=n^2$ the geodesics run from cusp to cusp, and Hecke theory reduces them to the single geodesic from $0$ to $\infty$. For every $n$ and both parities of $x_3$, we obtain an asymptotic formula with error $O(n^{1+\theta+\varepsilon}M^{-1/2})$, using the Kim-Sarnak bound and the large sieve of Deshouillers and Iwaniec (and the theta group for the parity of $x_3$). It is non-trivial for $M\ge n^{71/96+\varepsilon}$. This improves the range $n^{5/6+\varepsilon}$ of the elementary method, and confirms the corrected main term of the author's earlier work. For non-square $D=f^2D_0$ the geodesics are closed. A Hecke relation for their traces reduces everything to the fundamental discriminant $D_0$. We obtain an error $O(D^{\varepsilon}f^{1+\theta}D_0^{2/3}M^{-1/2})$, using the formulas of Duke-Imamoglu-Toth and Baruch-Mao together with the cubic moment bound of Young and of Andersen-Wu. For $D\equiv 5 \bmod 8$ this counts all solutions, and the range $M\ge D^{1/2-1/1332}$ of Friedlander and Iwaniec improves to $M\ge D^{4/9+\varepsilon}$. This paper was written in collaboration with Claude (Opus 5.5, High), an AI model developed by Anthropic.

India's Eighth Schedule recognises 22 languages, yet parallel data is uneven across them, and many language pairs, especially among lower-resource languages such as Bodo, Dogri, Santali and Kashmiri, lack direct bitext. We present BharatSetu 22-Indic 1M, a row-aligned table of 984,764 English sentences, each paired with machine translations into all 22 scheduled languages (21,664,808 Indic cells), generated with the sarvamai/sarvam-translate model family. Because every Indic cell in a row translates the same English sentence, any two columns form a translation pair: 462 directed Indic-to-Indic pairs, or 506 including English, without direct bitext. We call these pivot-derived pairs and propose a confidence layer that lets users choose how strictly each pair is connected. The corpus is machine-generated and not human-verified; quality is expected to vary by language, domain and sentence style, and pivot-derived pairs can inherit errors from both sides. We therefore release BharatSetu as a machine layer and propose a human-correction layer keyed to the same row identifiers, so that each corrected column upgrades every pair that uses it, together with an evaluation protocol. We report no translation-quality results.

Large-scale distributed training increasingly makes collective communication bandwidth-bound. In modern GPU clusters, communication libraries such as NCCL implement collectives including AllReduce over heterogeneous interconnects such as NVLink, InfiniBand, and Ethernet, making efficient use of available network bandwidth a central systems challenge. ForestColl showed that collective communication on such fabrics can be formulated using fractional tree packing; its scalable polynomial-time construction is developed for AllGather, with AllReduce obtained by composing AllGather and ReduceScatter. We present DualColl, which targets bandwidth-bound AllReduce directly. Under the tree-based AllReduce model, DualColl applies a Garg–Könemann-style multiplicative-weights algorithm and, for any $0<\epsilon<1$, computes a feasible schedule whose throughput is at least $(1-\epsilon)^2$ of the optimal AllReduce throughput. Its key component is an exact minimum-cost collective-tree oracle that projects physical-link dual prices onto a logical graph of participating ranks, reducing each iteration to shortest-path computations followed by a minimum spanning tree. We further extend the framework to local equal-next-hop packet-sprayed routing and to networks without explicit per-tree bandwidth control. For the latter, we introduce a tree-coupled max-min bandwidth-sharing model and show that tree duplication approximates an explicit fractional allocation with a provable accuracy-complexity tradeoff. Finally, we extend the fractional-packing framework to additional collective operations and multiple concurrent collective groups.

Reanalyzing the multi-wavelength data of GRB 240825A, we identify two distinct prompt-emission episodes, i.e. an early, spectrally soft plateau and a subsequent bright, spectrally hard gamma-ray pulse. We show that this signature is consistent with a two-stage central engine model, in which the early soft plateau is powered by the dipolar spin-down radiation of a transient proto-magnetar, while the later hard pulse arises from a relativistic jet launched by fallback accretion onto the nascent black hole via the Blandford-Znajek mechanism. Adopting simulation-motivated initial black hole (BH) masses ($M_{\rm BH,0}$) and spins ($a_0$), our fits to the second episode yield total masses supplied to the post-collapse disk of $M_{\rm fb}=0.45$–$0.96 M_\odot$, fallback radii of $r_{\rm fb}=16.9$–$17.6 r_g$, and characteristic fallback timescales of $t_{\rm fb}=0.13$–$0.25$ s. The corresponding maximum inner accretion rates range from $0.18$ to $0.70 M_\odot \mathrm{s}^{-1}$, which is sensitive to $a_0$. Joint spectral fits with optical-X-ray afterglow data reveal a coupled temporal evolution of dust extinction and equivalent hydrogen column density. Incorporating this extinction evolution, an external forward-reverse shock model in a wind-like medium can account for the radio-to-GeV band afterglow data. Although ambient dust and the bright host galaxy may obscure any associated supernova, late-time optical reddening remains compatible with a supernova contribution. Applying the empirical relation between the prompt spectral peak energy and the SN peak bolometric magnitude gives an illustrative estimate of $M_{\rm bol,peak}=-19.46\pm0.35$ mag for a putative associated SN. These results support a two-stage evolution of the central engine and variable dusty environment of GRB 240825A, which provides insights into the nature of its progenitor.

Respiratory auscultation provides a low-cost means of assessing pulmonary function, yet transient crackles and sustained wheezes can be difficult to recognize in noisy clinical recordings. Conventional deep learning classifiers often operate as black boxes, offering limited insight into the temporal acoustic evidence supporting their predictions. We present RespFocus, a weakly supervised framework that uses multiple instance learning (MIL) to learn inspectable temporal evidence from cycle-level labels and integrate it into classification. We also introduce PedResp2026, a multicenter pediatric respiratory sound cohort collected in routine clinical environments with adjudicated cycle-level annotations. In classification experiments, RespFocus achieves four-class Scores of 69.55% on public ICBHI 2017 and 72.91% on PedResp2026. Evidence diagnostics and matched temporal interventions support the functional contribution of the learned evidence to model predictions. Together, these findings highlight RespFocus's potential as a tool for automated respiratory sound diagnosis.

We introduce the problem of permutation burst error-correction, motivated by applications in molecular data storage with nanopore sequencing read platforms. A permutation burst of length $k$ is an error that affects a substring of length $k$ of a string of length $n$ by permuting its entries. Permutation burst errors can be corrected using classical burst error-correcting codes, such as Fire and Reed-Solomon codes. Here, we study how to reduce the redundancy of these classical codes by taking into account that the burst error preserves the weight of the substring. In addition, we further restrict our model to handle cyclic permutation bursts only, which are of independent practical and mathematical interest. Our main results include proving/establishing the following: a) for $k=o(\sqrt{n}),$ the redundancy of any permutation burst error correcting code is at least $\log n-k+\log \binom{2k-2}{k-2}+o(1).$ This result follows from McDiarmid's concentration bound; b) for $k \geq 9$ and $k=o\left(\sqrt{\frac{n}{\log n}}\right)$, the redundancy of any cyclic permutation burst error correcting code is at least $\log n +\log (k(k-1)-56)-\log\,80+o(1).$ c) the asymptotic redundancy upper bounds for the two types of substring errors that are twice the lower bound; d) constructions for both permutation burst and cyclic permutation burst errors that involve Varshamov-Tenegoltz type constraints or represent generalizations and extensions of Fire and other codes. In particular, we exhibit polynomially encodable and decodable codes that can correct cyclic bursts of length $\leq k$ using $\log n + k + 49\log k + O(\log \log k)$ redundant bits.

Let \(\alpha, \beta \in \mathbb{T} = \mathbb{R}/\mathbb{Z}\), and let \((\xi_n)_{n \ge 1}\) be independent random variables taking the values \(\alpha\) and \(\beta\) with equal probability. We study the random walk \[X_n = \xi_1 + \cdots + \xi_n \pmod 1\] and present a deterministic Diophantine condition on \((\alpha, \beta)\) that implies almost sure Poisson pair correlation. To the best of our knowledge, this is the first result providing explicit examples in this framework where the increment measure is purely discrete. The classical Fourier contraction method fails in this setting; a different approach is required. Our proof uses the parabolic geometry of returns to \(1\) and an exact covariance formula for overlapping blocks.

Generative modeling for tabular data has advanced to the point where models can synthesize realistic records, recover missing values, and generate samples conditioned on class labels or observed attributes. Despite recent advances, existing approaches either require table-specific training or restrict in-context learning to single-cell prediction. In this work, we formulate these tabular generative tasks as a single problem: modeling the joint conditional distribution of an arbitrary set of target cells given the observed cells of an unseen table. To this end, we turn to diffusion, whose denoising objective is defined jointly over all target cells rather than one cell at a time. Under the pretraining distribution, this objective is minimized by the posterior predictive distribution over the target set. Building on this, we propose TabMosaic, a unified in-context diffusion model for generating mixed-type target cells in unseen, potentially incomplete tables without table-specific training. We further show that its pretraining objective bounds the conditional negative log-likelihood and the divergence from the posterior predictive for arbitrary target sets, extending the Bayesian account of in-context learning from a single-value prediction to joint multi-cell generation. Across 48 real-world tables, TabMosaic ranks first on all evaluated generative tasks against 20 baseline approaches

We construct closed symplectic 4-manifolds admitting the structure of hyperbolic $\pi$-orbifold, addressing LeBrun's conjecture. Our simplest example has Euler characteristic $304$, is tessellated by $64$ copies of the right-angled hyperbolic $120$-cell and admits a four-fold branched covering over a product of two surfaces of genus $4$.

We study admissible entire subsolutions and radial boundary blow-up solutions of $S_k^{\frac1k}[\Delta uI-D^2u]=f(u)+g(u)|Du|^q$ for $1\leq k<n$, continuing our study of the determinant case $k=n$ in Part I. Under structural assumptions on the continuous, non-decreasing coefficients $f$ and $g$, we establish necessary and sufficient conditions for the existence of entire subsolutions when $q<2$. Our results cover the non-Lipschitz case $0<q<1$ with a possibly vanishing zero-order term, the gradient-singular case $q<0$, and sign-changing gradient coefficients. We also characterize finite-radius blow-up of radial solutions and derive two-sided estimates for the blow-up radius, as well as pointwise upper bounds for their profiles in terms of inverse Keller–Osserman functions.

We present DRanker (Disney+ Ranker), a transformer-based multitask ranking model serving personalized recommendations on the Disney+ homepage. We describe the encoder-only architecture over enriched engagement-history sequences paired with a lightweight causal debiasing mechanism, and the inference stack that enables transformer-based ranking at scale. Through iterative development, we systematically evaluated more complex alternatives and found that simpler designs consistently outperformed them on offline metrics, qualitative behavioral evaluation, and in production. Deployed globally, DRanker drives over 1% lift in our key engagement metric and 0.5% lift in daily active users across all experiences powered by the ranker. We share practical lessons on data engineering, debiasing, and architectural choices that shaped our ranking system at scale.

A gap exists in connecting biological evolution within the framework of statistical mechanics. It has been hoped that statistical mechanics would provide us with a general predictive principle for the emergence of novelty and complexity. However, the emergence of novel functional features initiated by stochastic processes remains difficult to describe, because these processes commonly arise outside near-equilibrium or linear-response regimes. To understand how environmental influences generate diverse, open-ended, complex objects by driving physical systems to specific regions of phase space over long spatial and temporal scales, a new approach to non-equilibrium thermodynamics is necessary. Here, we present the coupling of assembly theory (AT) with statistical mechanics as a framework that works within the laws of thermodynamics, but can contextualise the processes of novelty, complexity, and evolution within these laws. We map construction processes from physical space to assembly space (AS) and introduce the concept of an assembler, a machine that constructs objects contingent on previous states and is represented by bitwise operations. Using this approach, we apply principles from stochastic thermodynamics with AT to define selection within large combinatorial spaces1 and estimate the work required to create novel and complex objects. This approach allows us to represent complex processes, such as selection, within large combinatorial spaces as a set of rules for a memory-feedback loop followed by the assembler. This framework concretely defines the relationships between thermodynamics and information theory by introducing a novel aspect of physics that uses history and causal contingency to influence the probabilistic time evolution of complex systems.

Let $q=2^n$ with $n=2m+1$ for an integer $m\ge1$, and let ${\mathbb F}_q$ be the finite field with $q$ elements. Let $W_n(x)=x^{2^m+3}$ be the Welch function on ${\mathbb F}_q$. For $1\le k\le n$ and $b\in{\mathbb F}_q$, denote by $N_{n,k}(b)$ the number of $k$-dimensional ${\mathbb F}_2$-subspaces $E$ of $\mathbb F}_q$ such that \[ \sum_{x\in E}W_n(x)=b. \] In this paper, we determine $N_{n,k}(b)$ for all $k$. The only nontrivial case is $k=3$, for which the answer is given in terms of a binary Kloosterman sum. As a consequence, we prove a recent conjecture of Hou and Zhao on the third-order sum-freedom of the Welch function.