Papers

A transformer language model performs a bounded amount of computation per token, and recent work by Vishal Sikka, former CEO of Infosys, argues that this bound limits which tasks a model can carry out or verify (arXiv:2507.07505). We ask how much of the budget beneath that ceiling is spent on work the model has already done. Serving is stateless across requests: a model that answers a second question about a document recomputes the document's attention state from the first token. On seven real-world datasets, 98.7% of prompt tokens were text the model had already read. We present Galahad, a memory layer for vLLM, SGLang and llama.cpp that makes this reading a one-time cost. Taliesin saves the model's key-value (KV) state for a block of text and loads it on the next request that contains the same bytes, instead of recomputing it. Blaise keeps the documents themselves and passes the model only the section a question needs. On a recall test with 100 facts hidden in a 97,000-token corpus (Gemma 4 31B), Taliesin alone let the model attend to the whole corpus and answered 98 of 100 on llama.cpp at 3.0 s and 572 J per question, against 10 of 100, 9.3 s and 2,754 J for the same model without Galahad, which could hold only the last 12,000 tokens. With Blaise added, the model read about 668 tokens per question and answered 100 of 100 on all three runtimes at 0.59-0.64 s and 200-213 J; a tuned RAGFlow pipeline answered 77. Storing the corpus is a one-time cost of about 100 s and 28 kJ, whose energy is recovered after 13 questions. Restored state is bit-identical: all 262,144 output logits matched after restart, rehydration and hot-load. Galahad worked with all 30 models we tested under vLLM, and it fails closed: any load that does not pass its checks is recomputed. Together these results move LLM serving from stateless to stateful inference.

Asynchronous SGD is a popular algorithm for distributed learning where each client's gradient update is applied on arrival. This leads to a speed-up, but also an increased vulnerability to attacks, as fast clients can dominate the total update. We introduce Throttle, a Byzantine-robust generalization of asynchronous SGD where the key idea is to exponentially down-weight updates from faster clients by a factor $q$. Both asynchronous SGD ($q=1$) and synchronous Byzantine-robust SGD ($q\to\infty$) correspond to specific settings of Throttle. We provide a theoretical analysis of the convergence rate and validate the robustness to attacks both theoretically and empirically. Remarkably, our experiments show that this down-weighting mechanism can also improve performance over standard asynchronous SGD even in the non-Byzantine setting.

We study the global dynamics of the generalized Boussinesq equation near standing solitary waves. For even-odd perturbations, Maulen [J. Math. Pures Appl. 177 (2023)] constructed an asymptotically stable center-stable manifold M near the solitary wave Q. We complete this local description by proving that any sufficiently small even-odd perturbation of Q lying outside M either scatters in the energy space as t -> +infinity or blows up in finite time. The proof relies on two main ingredients. First, we classify even-odd solutions with energy below the ground-state energy by identifying two invariant regions, associated with scattering and blow-up, respectively. Second, we establish a one-pass theorem in one dimension: a non-scattering solution cannot re-enter a suitably chosen neighborhood of the solitary wave once it has left that neighborhood. Consequently, the solution remains confined to one of the two invariant regions. Together with the classification above, this yields a dichotomy between scattering and blow-up outside M.

We develop a general second-order asymptotic framework for estimators constructed from invariant probability measures of data-dependent Markov processes. The framework yields a universal bias correction for smooth functionals, computed from the same invariant measure used to construct the estimator, without the resampling and repeated estimation involved in bias-correction methods such as the bootstrap and jackknife. The statistical input is represented by a random one-form, allowing differentials of log-likelihoods and general random criteria, as well as estimating functions, to be treated in a common framework. Under local regularity and localization conditions, we derive second-order stochastic expansions for averages with respect to these invariant measures and for decision rules defined through general loss functions. The expansions separate the contributions of the statistical input, temperature, drift, and loss, using precontrast geometry and an O-derivative induced by the loss. The framework includes maximum likelihood and posterior-based estimators and recovers existing bias-reduction methods based on the choice of prior or adjustments to estimating equations. In the likelihood setting, for the Jeffreys posterior $\mu_n$ and its Fisher–Rao Fréchet mean $\widehat z_n$, the corrected estimator $2\gamma(\widehat z_n)-\mu_n(\gamma)$ has frequentist bias $o(a_n^2)$ for every fixed smooth functional $\gamma$, where $a_n$ denotes the estimation rate. For coordinate squared loss, the theory yields a diffusion determined only by the likelihood and Fisher information. The mean of its invariant probability measure estimates the parameter with bias $o(a_n^2)$. This construction remains available even when no bias-reducing prior exists. Numerical results in the gamma shape–scale model illustrate this bias reduction.

Blended data acquired via simultaneous-source seismic exploration conventionally require post-acquisition deblending, which typically relies on the coherence differences introduced by firing time delays (time dithering). To reduce the dependency of the deblending process on these time dithers, a novel joint constraint based on the synchrosqueezed transform and the Radon transform is proposed, operating directly in the common-shot gather (CSG) domain. Specifically, by exploiting the differences in propagation directions of the blended signals within CSGs, the synchrosqueezed transform is first employed for an initial iterative separation to extract individual sources directly from the continuous records. Once the majority of the valid signals are separated, the Radon transform is subsequently applied in further iterations to suppress the residual blending interference, thereby preventing amplitude damage to the effective signals. Compared to conventional non-CSG deblending methods, this approach bypasses the reliance on time-delay coherence differences, thus enabling real-time quality monitoring of individual sources during field acquisition. Furthermore, compared to other existing CSG-based separation techniques, the proposed joint-constraint iterative framework demonstrates superior performance when handling complex data. Applications on both synthetic and field blended datasets demonstrate that high-fidelity data separation can be successfully achieved independently of the time-dithering constraints. Finally, because the proposed method operates completely independently across different CSG slices, it is highly amenable to parallel computing, facilitating the efficient processing of massive datasets within a short timeframe.

Collocation methods based on Birkhoff interpolation at Gaussian-type points are well-conditioned for one-dimensional initial and boundary value problems [Wang et al., SIAM J. Sci. Comput. 36 (2014)], but the underlying construction does not extend directly to multiple dimensions. We address the long-standing ill-conditioning of multidimensional collocation methods for second-order elliptic-type problems. The key observation is that the second-order differentiation matrix and its inverse, the pseudospectral integration matrix (PSIM) constructed from Birkhoff interpolation at Legendre-Gauss-Lobatto points, are both similar to symmetric negative definite matrices. This enables stable diagonalisation of the dense, non-symmetric and ill-conditioned differentiation and integration matrices, even for thousands of collocation points, and leads to efficient multidimensional Birkhoff preconditioners. For variable-coefficient problems, the coefficients are incorporated directly into the diagonalisation and preconditioner construction, which is essential for highly anisotropic, high-contrast, oscillatory and degenerate elliptic operators. We provide spectral analysis and extensive two- and three-dimensional numerical experiments, demonstrating substantial reductions in condition numbers and nearly polynomial-degree-independent GMRES convergence while retaining high-order accuracy. The resulting Birkhoff-collocation schemes make multidimensional spectral collocation methods practical for challenging elliptic problems.

LLM agents increasingly rely on reusable Skills for complex, multi-step tasks, creating a critical supply-chain attack surface where poisoned Skill content steers agent decision loops under benign requests. Existing skill poisoning attacks either colocate actuation with its contextual pretext or distribute actuation across multiple Skills, but do not explicitly separate the rationale for execution from the operation itself. In this work, we reveal that untrusted agent decisions fundamentally depend on two conceptually distinct Risk-Realization Factors (RRFs): an actuation factor (specifying what concrete operation is performed) and a pretext factor (providing the situational rationale for why the agent must perform it). Guided by this abstraction, we propose a coordination-based attack paradigm: decoupling pretext from actuation. Rather than fragmenting the malicious actuation, we preserve it as an intact operation within a downstream Steering Skill, while delegating the pretext factor to an upstream Grounding Skill that subtly alters persistent environment artifacts through routine utility operations. The intact actuation thus hides in plain sight, appearing completely legitimate and task-driven only when evaluated against the fabricated pretext. Building on this formulation, we develop an automated framework that discovers authentic execution dependencies, synthesizes coordinated pretext-actuation skill pairs, and iteratively refines poisoned skill instructions via runtime closed-loop feedback. Extensive evaluations across single-session and persistent cross-lifecycle scenarios demonstrate that decoupled skill poisoning achieves high attack success, exposing a critical blind spot in isolated Skill security audits. Our automated framework code is available at https://github.com/Wenxin-buaa/CoordPoison.git.

We study preference-based bandits with general reward function classes, where a learner sequentially selects pairs of arms and observes binary preference feedback governed by the Bradley–Terry model. This setting naturally arises in applications such as recommender systems, tournament ranking, and learning from human feedback, where relative preferences are easier to elicit than absolute rewards. The observation model inherits the logistic bandit challenge of handling the problem-dependent constant $\kappa$, which accounts for the non-linearity of the link function and can grow arbitrarily large. Moreover, prior work has predominantly focused on linear or kernelized reward models, precluding the use of richer function classes. To address these limitations, we consider general reward function classes and introduce the locally sensitive eluder dimension, a novel complexity measure tailored to the logistic structure of preference feedback that yields fine-grained regret guarantees without unfavorable dependence on $\kappa$. Building on this notion, we propose GINOP (Generic INformative OPtimism), an algorithm that constructs log-loss confidence sets and jointly selects arm pairs to balance optimism and informative exploration. We establish a first-order regret bound that, in contrast with what previous results suggest, demonstrates that learning with preference feedback is as statistically efficient as learning from direct reward observation. Finally, we corroborate our theoretical findings with empirical evaluations against competitive baselines.

As model sizes continue to scale, distributed training has become inevitable. Automatic parallelization techniques can derive efficient training parallelism strategies at low cost while achieving superior performance. The difficulty of this problem is jointly determined by the complexity of the model and the underlying compute cluster. Meanwhile, mixture-of-experts (MoE) models are increasingly emerging as the dominant architecture and the rapid evolution of accelerator hardware has made cluster heterogeneity commonplace, posing substantial challenges to automatic parallelization. However, existing approaches typically target either MoE architectures or heterogeneous clusters, failing to generalize to scenarios where both challenges coexist. To this end, we present HAPMoE, a heterogeneity-aware automatic parallelism planner for MoE training. HAPMoE builds a lightweight MoE-aware cost model and efficiently searches a six-dimensional parallel space, producing parallel plans directly deployable on Megatron-LM. Experiments show that HAPMoE improves end-to-end training throughput by up to 3.2$\times$ over baselines across heterogeneous clusters. Its non-uniform pipeline partitioning yields an additional up to 78% gains, and its pruning-enhanced dynamic programming algorithm completes the search within 1 minute, demonstrating high efficiency and practical value in complex hardware environments.

We study multidimensional resource scheduling. Each job $i$ has a $d$-dimensional resource-demand vector $v_i$ and a processing time $s_i$. The scheduler assigns a start time to each job, subject to the constraint that, at every time, the total demand of the jobs being processed does not exceed $1$ in any resource dimension. The objective is to minimize the makespan. We focus on the regime in which every individual resource demand is small. We ask whether the favorable small-vector phenomenon known for multidimensional vector packing, which corresponds to the special case of unit processing times, extends to jobs with heterogeneous processing times. The key difficulty is that arbitrary processing times create temporal interactions across multiple duration scales: a long job may overlap many shorter jobs, while feasibility must be maintained throughout every job's execution interval. We prove that the small-vector phenomenon persists in this temporal setting. For any $0<\epsilon<1/4$, after normalizing the maximum processing time to $1$, if every coordinate of every demand vector is at most $O(\epsilon^2/\log(d/\epsilon))$, we give a randomized offline algorithm that produces a schedule with expected makespan at most $ (1+6\epsilon)\mathrm{OPT}+3$. Thus, sufficiently small resource demands admit asymptotically near-optimal schedules in arbitrary dimension, despite heterogeneous processing times. We also obtain constant competitive ratios in the online setting. Let $T$ denote the ratio between the maximum and minimum processing times. If every coordinate is at most $O(1/(\log d\log T))$, we give a randomized $O(1)$-competitive algorithm, with a competitive ratio independent of both $d$ and $T$. We further derandomize our approach, obtaining a deterministic $O(1)$-competitive algorithm under a comparable smallness assumption.

Non-equilibrium systems challenge the standard definitions of phases and phase transitions from equilibrium statistical physics. For example, in active fluids continuous energy injection at the microscale drives the system intrinsically out of equilibrium. This process gives rise to collective turbulent-like flows whose onset remains poorly defined. Here we show that the onset corresponds to an activity-driven phase transition, marked by the emergence of a system-spanning critical backbone of vorticity nodal lines. Combining two independent experiments, microtubule kinesin active nematics and dense suspensions of swimming bacteria, with large-scale simulations of active nematics and fluctuating nematohydrodynamics, we show that this transition occurs at a critical activity threshold. Below this threshold, vorticity structures are fragmented and vortex centres form only finite, mechanically floppy networks. Above this threshold, the nodal lines of the vorticity field percolate and the vortex centres form a rigid, system-spanning cluster. The geometric transition is characterised by the emergence of critical percolation statistics for the vorticity nodal lines, while the mechanical transition reflects the emergence of a vortex configuration that shows rigidity percolation statistics for vortex centres. We show that both transitions are absent in equilibrium systems that obey detailed balance, demonstrating that the transition is intrinsically non-equilibrium. These results establish an experimentally accessible definition of fully developed active turbulence, linking microscopic activity to macroscopic geometry, and mechanics of living systems.

Let $G$ be the graph on the positive integers in which distinct vertices are adjacent if they differ by one or their quotient in one order is prime. We prove that $6\leq\operatorname{diam}(G)\leq7$ and $4\leq\operatorname{rad}(G)\leq5$. Under Dickson's conjecture for two linear forms, we prove that $\operatorname{diam}(G)=6$ and $\operatorname{rad}(G)=4$.

Large language models (LLMs) offer strong reasoning capabilities but are often costly to access through commercial APIs, while small language models (SLMs) are easier to deploy locally yet remain weaker in reasoning. This capability-deployment gap has motivated LLM-SLM collaboration, which aims to improve SLM reasoning using LLM capabilities while preserving the deployment advantages of SLMs. Existing approaches mainly follow two paradigms. Knowledge distillation uses LLM-generated answers and reasoning trajectories to train SLMs offline, but requires parameter updates and additional training. Alternatively, online collaboration routes difficult problems to an LLM or leverages LLM-generated guidance and corrections when an SLM encounters difficulties. Although effective, online collaboration requires repeated LLM access. Moreover, the guidance produced for a particular problem is discarded after inference and cannot benefit subsequent problems involving similar reasoning states. In the paper, we focus on a more constrained setting in which the LLM is accessed only offline, the SLM parameters remain fixed, and online inference is performed solely by the SLM. To this end, we propose Reusable Latent Correction (RLC), which converts one-off natural-language guidance from a black-box LLM into persistent corrective experiences in the hidden space of an SLM. RLC stores these experiences in an external bank and retrieves them according to the SLM's current reasoning state, enabling the SLM to reuse LLM-derived corrections during inference without any online LLM calls. Experiments across multiple reasoning benchmarks and SLM scales show that RLC consistently improves SLM reasoning without parameter updates or online LLM calls. Code is available at https://github.com/ZBH031/reusable-latent-correction.

We construct the first known fault-tolerant scheme for injecting states into quantum error-correcting codes with constant space and time overhead. That is, we construct a family of constant-rate quantum error-correcting codes for which a set of bare physical qubits can be injected, i.e. fault-tolerantly encoded, into a code block. Similarly, a code state can be ejected, i.e. fault-tolerantly decoded, back into bare physical qubits. We show that these injection and ejection procedures succeed under circuit-level locally stochastic noise, while incurring just a small constant probability of corrupting each qubit, which is unavoidable for bare physical qubits. We also show how to perform fault-tolerant error correction and code-state preparation under locally stochastic noise. All of our gadgets can be implemented with constant quantum circuit depth (i.e. are single-shot), and with a number of physical qubits growing linearly with the number of logical qubits, assuming the ability to run polynomial-sized noiseless classical circuits on the side. We construct our quantum codes by taking a high-dimensional hypergraph product of classical LDPC codes, which in turn are a simplified version of Spielman's linear-time encodable codes (STOC'95). As our resulting product codes are only resilient to physical errors occurring with non-uniform probabilities across qubits, we then show how to concatenate with inner codes of various sizes to obtain fault-tolerance against uniform noise.

Speech transcripts used as long-term memory must preserve both words and stable speaker identities. Existing meeting-transcription metrics either ignore speakers or remap anonymous speakers independently in each recording, so they cannot measure whether the same person retains one identity across meetings. We evaluate persistent speaker attribution with Speaker Identified cpWER (SI-cpWER), which scores a corpus under one global speaker-ID assignment. The benchmark covers five commercial diarize-then-identify cascades, two open academic baselines, and ThyVoice on the full 129-meeting CHiME-8 NOTSOFAR evaluation set in clean and noiseaugmented form, plus CHiME-6. ThyVoice is our end-to-end reference system; it repairs overlap and gates the evidence used to create and update voiceprints. Requiring persistent identity changes the commercial ranking: ThyVoice records lower SI-cpWER than every evaluated commercial cascade in all three conditions and the lowest mean in the full panel, 47.13 versus 54.75 for the next system. Complementary lexical, diarization, per-recording attribution, and speaker-clustering diagnostics characterize upstream error surfaces in the final attributed record. These results show why persistent attribution must be evaluated directly in systems that reuse conversations across time.

Diffusion caching accelerates generation by replacing transformer computation with cached or predicted features at selected denoising steps. We introduce the Golden Path Hypothesis (GPH): under fixed inference conditions, prompt-independent cache schedules can achieve final-output quality comparable to the best prompt-specific schedules across prompts. We investigate the GPH across ten caching methods, four image and video models, and three cache ratios. Prompt-adaptive methods repeatedly select a small number of schedules, and reusing their most frequent schedules on new prompts closely matches the quality of prompt-specific choices. Exhaustive evaluation of 1.4 million schedules on four examples further identifies prompt-independent schedules that remain competitive on unseen prompts. To explain this transfer, we analyze denoising trajectories and the accumulation of caching errors. Latent-state trajectories exhibit similar structures across datasets and seeds, while an exact error decomposition shows that accumulated effects of earlier errors predict final latent-state error better than local approximation errors. This motivates searching for end-to-end schedules using final-output quality. With only a small set of examples, the resulting golden paths transfer across prompts and datasets, and can be tuned to the desired quality objective, including reconstruction fidelity or perceptual similarity.

Intrinsic motivation plays a central role in adaptive and goal-directed behavior by conferring agents reward-independent objectives and biases useful to act in noisy and uncertain environments. Active Inference addresses the problem of acting in a partially observable environment through a principled framework for belief updating and action selection. A key component of Active Inference is the specification of prior preferences, which shapes behavior by encoding desirable future outcomes. An intrinsic motivation approach called the Maximum Occupancy Principle (MOP) proposes that agents act so as to maximize occupancy over future paths of states and actions, with no preferences or epistemic targets. Despite its simple formulation, MOP gives rise to rich and adaptive behaviors that combine exploratory variability with goal-directed dynamics. In this work, we extend MOP to partially observable environments and introduce a Bellman reformulation of the Expected Free Energy for Active Inference, both incorporating belief-based inference over hidden states as part of the agent state. The Bellman formulation enables tractable offline computation via value iteration over the full belief-state space. We compare the resulting behaviors in a set of minimal experimental settings with uncertain food sources. We find that MOP agents switch between goal-directed (food seeking) behavior and exploration between different food sources, depending on their energy available and their belief state. In contrast, Active Inference agents mostly inhabit regions around a single food source, a strategy having both high pragmatic and epistemic value. We finally compare with Empowerment, which is shown to be qualitatively similar to Active Inference.

Does a language model merely predict tokens, or does it understand what it says? We make this question measurable by defining "understanding" through the lens of no-arbitrage. A model understands a vocabulary to a certain degree if a computationally bounded trader cannot extract guaranteed profit by betting against the model's probabilities on logically related claims (a "Dutch book"). We establish three theoretical results: first, because full logical coherence is computationally intractable, understanding is inherently graded, not absolute. Second, we prove that the exact optimum of standard next-token prediction is inherently incoherent across different question formats; the flaw lies in the training objective, not the architecture. Third, we show that uncertainty accumulates predictably along reasoning chains, making unjustified overconfidence an arbitrage opportunity in itself. To address this, we introduce Arbitr, a training framework where an adversarial trader penalizes the model for logical inconsistencies, paired with a calibration anchor to prevent uninformative collapse. Across five pre-registered experiments on Qwen2.5 and Phi-3.5 models, we demonstrate that standard models are highly exploitable across different phrasings. Arbitr reduces this exploitability by orders of magnitude without sacrificing task accuracy, and the effect successfully transfers to unseen logical patterns and new model families. Crucially, we uncover a scaling illusion: at 7B parameters, near-zero measured incoherence often coincides with extreme, unjustified confidence. We conclude that while Arbitr enforces rigorous logical consistency, coherence is a necessary condition for knowledge, but not a sufficient one

Electrolyte formulation design requires balancing multiple physicochemical properties, yet existing models often focus on a limited subset. Learning each property in isolation can overlook transferable chemical information, whereas indiscriminate sharing can introduce cross-property interference. Our directed transfer analysis shows that jointly learning two property prediction tasks can improve or degrade prediction relative to separate training, with asymmetric transfer effects between the tasks. We propose ElectrolyteFM, a unified multi-property prediction model which can more accurately predict multiple properties of each electrolyte by effectively identifying and utilizing property-specific features and knowledge shared across properties. More specifically, ElectrolyteFM learns property-specific representations independently and captures cross-property knowledge through a separately trained expert pool. A router selects relevant shared information for each formulation and target property, and property-specific residual adapters convert this information into corrections to the corresponding representation for prediction. Experiments on Electrolyte12 show that ElectrolyteFM reduces normalized mean absolute error averaged across 12 electrolyte properties by 14.8% relative to the strongest electrolyte-specific baseline. On an independent sodium-electrolyte dataset unseen during training, it reduces conductivity mean absolute error by 6.7% relative to the best-performing baseline.

Matching problems are ubiquitous in data science as they enable the alignment of structured objects and distributions. While existing solvers are often tailored to specific matching formulations, we unify a broad class of such problems within a common mathematical and optimization framework based on duality theory. Theoretically, we demonstrate that matching objectives decomposable as a difference of convex (DC) functions can be recast as implicit registration problems. This connection links matching to another well-studied class of objectives and yields a dual formulation amenable to natural optimization strategies. We then apply these findings to quadratic matching (QM) problems, which admit DC decompositions and for which we provide extensive convergence guarantees. Our framework applies to Gromov-Wasserstein (GW), as well as its unbalanced formulation and several variants, which are increasingly popular QM problems. Numerically, we implement our algorithms at scale for various data modalities such as graphs, point clouds, meshes, and word embeddings. Finally, our modular approach allows us to explore new formulations such as fracture matching, broadening the scope of problems that can be addressed within this framework..

Knowledge distillation transfers knowledge by encouraging a student to match a teacher's predicted class probabilities. These probabilities express not only confidence in the correct class, but also relations among incorrect alternatives. Yet closer imitation does not necessarily yield a better student. A student may already distinguish the correct class more sharply than its teacher, so further imitation can require giving back discrimination it has acquired. Our main result is an exact separation between full imitation and conditional learning. When the correct class's score advantage over each alternative must be preserved, full teacher-to-student KL minimization is blocked exactly when the student assigns no more probability than the teacher to every incorrect class. Crucially, the teacher's relative probabilities among incorrect classes remain fully learnable. We characterize the exact price of this transfer: a minimum increase in correct-class log-odds that compensates for the largest conditional-probability mismatch. Label fitting and conditional matching can therefore be completed even as full teacher KL diverges. This separation motivates task-preserving knowledge distillation (TPKD), which keeps the label gradient intact and minimally corrects the conditional gradient so that its output update preserves the label step's gains against every incorrect alternative. The corrected conditional direction retains more than half of the original first-order conditional descent at the same step size, with a tight bound. For a fixed positive conditional target and sufficiently small constant output steps, label and conditional errors vanish together. Experiments trace this learning from exact head updates to ordinary network training. TPKD reaches 88.05% accuracy on CIFAR-100 and 93.81% on CLINC150, improving over standard distillation by 0.47 and 0.35 percentage points across three seeds.

Self-supervised pre-training of time series models is currently dominated by next-token prediction and reconstruction objectives. In continuous-valued domains, these paradigms often waste model capacity on high-frequency, point-wise noise at the expense of learning invariant structure. While invariance-based self-distillation has proven highly effective in computer vision, its application to temporal data remains largely underexplored. Effectively adapting such methods to time series requires carefully designed augmentations: spatial operations like cropping can shift the timing of repeating cycles or distort the signal, while basic jittering may provide limited variation. We introduce Wavelet-based self-distillation for time series (WinoTS), an invariance-based pre-training paradigm designed specifically for temporal signals. At its core, WinoTS leverages time-frequency augmentations to construct multi-scale structural views without distorting underlying signal dynamics. Across extensive evaluations, WinoTS outperforms state-of-the-art baselines in long-term forecasting, cross-domain zero-shot transfer, and unsupervised anomaly detection. Notably, linear probing on frozen WinoTS representations frequently surpasses fully supervised models trained from scratch. Systematic ablations demonstrate that WinoTS is a flexible, architecture-agnostic framework yielding gains across time series backbones, and establish that time-frequency transformations provide a principled alternative to vision-style spatial augmentations.

Understanding the fundamental mechanisms of learning is essential for designing systems with strong generalization. Recent studies have shown that increasing the number of training domains, or enlarging the distribution shift among them, improves generalization when each domain contains sufficiently many data samples. However, the conditions under which the data samples can be considered sufficient remain unexplored. In this work, we fill this gap by establishing criteria for per-domain sample requirements based on the presented learning bounds. These criteria not only reveal an inverse linear scaling law between the number of training domains and the number of samples required per domain, but also explain the fundamental rationale behind the assumption of data sufficiency, thereby providing theoretical guidance for assessing the adequacy of existing datasets and constructing datasets. This differs from classical learning theory, as the number of samples required is highly dependent on the number of training domains. Additionally, we prove the close relationship between in-domain learning and out-of-domain generalization through the presented generalization bounds, and lastly discuss some key arguments.

Video virtual try-on has attracted increasing attention due to its broad potential in digital fashion and intelligent e-commerce. However, existing methods primarily focus on low-resolution settings and still face substantial challenges when extended to high-resolution scenarios. These limitations can be attributed to two main factors: (1) the insufficient utilization of rich garment reference information, and (2) the lack of explicit positional modeling between garment and video representations during cross-modal interaction, which weakens fine-grained local correspondence. To address these issues, we propose TexTailor, a high-fidelity video virtual try-on framework built upon a pretrained video Diffusion Transformer. Specifically, we introduce a timestep-adaptive modulation mechanism to dynamically adjust garment visual representations throughout denoising. We further develop a frame-aligned positional encoding strategy to strengthen garment-to-video correspondence, together with a multi-source injection design that reduces interference among heterogeneous conditions. Extensive experiments on multiple video virtual try-on benchmarks, including the high-resolution Eevee dataset, demonstrate that TexTailor achieves competitive performance in garment detail preservation, temporal consistency, and overall video quality.

Test-time scaling has recently emerged as a powerful approach for improving LLM reasoning by allocating additional computation during inference, substantially enhancing accuracy on challenging tasks such as mathematics and coding. To accelerate the exploration of reasoning paths, recent studies proposed speculative execution. However, we show that supporting speculative execution poses two unique challenges for LLM serving systems: (1) an explosion in the search space of candidate paths and (2) frequent, fine-grained verification tasks for candidates. To address these challenges, this paper proposes SpecScale, a serving system for efficient speculative execution. We introduce three techniques to reconcile the trade-off between latency and computational overhead: (1) early pruning of low-quality candidate paths, (2) deduplicating computation across redundant candidate paths, and (3) deferring fine-grained verification tasks. We evaluate SpecScale on challenging reasoning benchmarks, including MATH and Olympiad. Our results show that SpecScale significantly outperforms both non-speculative and recent speculative approaches, delivering substantial improvements in throughput and latency while preserving answer quality.

Autonomous AI agents can turn authors' goals into interactive narratives by independently organizing and carrying out generation and revision. As agents generate and revise extensive content, authors struggle to grasp its overall structure, local details, and relationships, complicating continued guidance. We present NarrativeSteward, an authoring environment that organizes outlines, worldbuilding, and narrative graphs as linked artifacts for agent implementation and author guidance. Agent dialogue and project-wide structural review help authors understand the evolving work and guide local and cross-layer revisions, while change records and execution verification help authors assess the resulting work. Technical tests validated the system's change records, recovery mechanisms, and execution diagnostics. In a 12-participant within-subject study, NarrativeSteward supported easier formulation of revision requests and inspection of changes, and greater perceived understanding of changes and story structure, than general-purpose agents. Qualitative findings show how reviewing the work and feedback helps authors develop requirements and guide subsequent delegation. We open-source NarrativeSteward at https://github.com/Tencent/NarrativeSteward.

For the three-qubit Shifts unextendible product basis (UPB), the minimum product-state expectation value $\lambda_{\mathrm{Shifts}}=1-3\sqrt6/8$ of the UPB projector is known, and four attaining product states were exhibited previously. We determine the complete equality set over all complex product states and prove that it consists of exactly eight product rays: two rays invariant under cyclic permutation of the three qubits and two cyclic orbits of size three. The proof combines exact phase analysis, a Gröbner-basis classification of all 28 finite real stationary points, and a complete treatment of the projective boundaries. Crucially, the eight contact rays span the full three-qubit Hilbert space, whereas the four previously known rays do not. The complete equality classification therefore establishes that the associated projector witness satisfies the spanning criterion and is optimal in the sense that no nonzero positive semidefinite operator can be subtracted while preserving block positivity. As a corollary, for the white-noise family $\rho(p)=(1-p)\rho_{\mathrm{Shifts}}+p\mathbb I/8$, where $\rho_{\mathrm{Shifts}}$ is the complementary-projector Shifts state, the same witness detects entanglement for $p<2-3\sqrt6/4\approx16.29\%$.

Accurate oscillator strengths for doubly and triply ionised heavy elements are required for quantitative spectroscopy of hot subdwarfs, but available data remain sparse. We present new radiative data for As III, Se III, Hf IV and Tl IV, calculated with the pseudo-relativistic Hartree-Fock (HFR) method including core-polarization effects and semi-empirical adjustment of radial parameters to experimental energy levels. Independent multiconfiguration Dirac-Hartree-Fock (MCDHF) computations were also performed for As III, Hf IV and Tl IV, while published MCDHF data were adopted for Se III to assess the reliability of the HFR oscillator strengths. The largest discrepancies between the two approaches are mainly associated with weak transitions, strong cancellation effects, or significant gauge disagreement. For strong transitions satisfying the adopted reliability criteria, we found a good agreement between the oscillator strengths obtained by both methods. The new data have already been applied to the spectra of the heavy-metal hot subdwarfs LS IV-14$^\circ$116 and EC 22536-5304, enabling abundance determinations for As, Se, Hf, and Tl and providing additional lines for future spectroscopic studies.

Naff's planarity estimate is a crucial tool for analysing singularities of quadratically pinched mean curvature flows in high codimension, showing that high-curvature regions become asymptotically codimension one. Naff established the estimate throughout the full Andrews–Baker pinching range in dimensions at least $7$, while in dimensions $5$ and $6$ a stronger pinching assumption was required. We close this remaining gap, proving the planarity estimate in dimensions $5$ and $6$ throughout the full Andrews–Baker range. The key new ingredient is a sharp Kato-type inequality relating the twisting of the principal normal to the gradient of the second fundamental form.

Long-context inference with Large Language Models (LLMs) is bottlenecked by the linearly growing memory of the key-value (KV) cache. Existing compression methods reduce the cache through token eviction or approximation, but degrade sharply at aggressive compression budgets. We propose PatchKV, a training-free framework that compensates KV cache compression methods by carrying part of the context in the model's weights. PatchKV pairs an off-the-shelf compressed KV cache with a context-specific weight patch, which is computed once at context-loading time and served for downstream queries for the context. The weight patch is derived in closed form via ridge regression, by aligning the block-wise activations of context-derived reference query tokens under the full cache and the compressed cache. Once merged into the model, the patch leaves the forward graph and per-query inference cost unchanged in the single-context, multi-query setting. Across long-context QA (SCBench with up to 170K tokens, SQuAD, NIAH) and math (GSM8K) benchmarks on three model architectures, PatchKV consistently improves cache compression methods, suggesting an alternative direction to compensate them at aggressive budgets.