Papers

Emerging long-horizon agentic tasks require repeated model calls, worsening the inference cost of already-costly language models. While narrow agentic tasks suggest potential for aggressive model pruning without performance drop, empirical results show existing methods proposed for question answering tasks severely degrade task performance when applied to agentic models. We trace this failure to two decisions: what to prune and how to recover. For pruning, one-shot importance estimates fail to track how the pruned model adapts. For recovery, offline distillation covers only teacher prefixes, while full-trajectory on-policy distillation causes student errors to compound across turns. In this work, we propose Trajectory-Anchored Pruning (TAP), the first structural pruning framework for reinforcement learning (RL)-trained agents. TAP couples structural pruning with efficient on-policy recovery, anchoring interactions to teacher trajectories while allowing the student to generate each reasoning-action response. A frozen dense teacher supervises the student's response prefixes, addressing within-response training-inference mismatch while preventing student-induced deviations from propagating across training turns. Instead of one-shot pruning, TAP re-scores channels using gradients of the recovery objective on the recovered student, connecting iterative channel selection to the evolving policy. With 60% of FFN channels removed, TAP retains 99.2% and 88.0% of the dense 7B agents' task success rates on ALFWorld and WebShop, respectively, while reducing GPU time per successful task by approximately 22% and 17%. These results demonstrate effective structural compression of long-horizon agents under a limited recovery budget.

In a thermally occupied multimode trapped ensemble, mode-dependent detunings can strongly suppress Ramsey contrast even when the underlying dynamics remains coherent. We develop a weak-axis-resolved Hamiltonian theory in which collective mode spins experience longitudinal detunings and overlap-dependent exchange interactions. Without exchange, the distribution of detunings across thermally occupied modes produces coherent phase mixing and an algebraically decaying Ramsey-contrast envelope in the many-mode continuum regime. At the mean-field level, exchange generates a self-consistent restoring field that reduces phase dispersion and restores collective contrast. The crossover is governed by the competition between the collective exchange scale and the thermally induced detuning spread: when the late-time contrast is expressed in terms of their ratio, results at different temperatures collapse onto a common trend, and the crossover coupling follows the predicted inverse-square thermal scaling, with a numerical exponent of 2.06. Weak irreversible pure dephasing limits, but does not eliminate, this recovery, demonstrating that exchange refocuses coherent inhomogeneous phase mixing but cannot reverse irreversible phase noise.

Häggkvist and Thomason proved that every $n$-vertex oriented graph with minimum semidegree at least $(\frac{5}{12}+o(1))n$ contains every orientation of a Hamilton cycle. Using Szemerédi's regularity lemma, Kelly later improved this to the asymptotically sharp bound $(\frac{3}{8}+o(1))n$. Taylor subsequently generalized Kelly's theorem by proving that every sufficiently large robust outexpander with linear minimum semidegree contains every orientation of a Hamilton cycle. We revisit Häggkvist and Thomason's proof and show that it can be modified to give a regularity-free proof of Taylor's theorem (and thus Kelly's theorem). Building on this, we also give regularity-free proofs of related results on Hamilton-connectivity and linkage in robust outexpanders. As applications of these results, we are able to replace the use of the regularity lemma in known results on arbitrary orientations of Hamilton cycles in $n$-vertex digraphs with minimum semidegree at least $\frac{n}{2}$ and in $n$-vertex digraphs with minimum total degree at least $(1+o(1))n$. The first step is to show that, in an $n$-vertex robust outexpander with linear minimum semidegree, two uniformly chosen disjoint sets of logarithmic size satisfy Hall's condition with high probability. The second is to show that robust expansion is inherited by uniformly chosen linear sized sets. In both cases, we use the graph-container methods of Kleitman–Winston and Sapozhenko to reduce the possible obstructions to a small enough family to permit a union bound.

Layout-to-Image generation has made substantial progress in spatial and object-level control. However, existing methods still struggle with complex scenes containing many overlapping and interacting objects. We argue that training data is a particular bottleneck: existing datasets lack examples with dense, complex object interactions. To address this gap, we introduce OverLay++, a large-scale Layout-to-Image dataset with structurally complex scenes. OverLay++ contains approximately 500K images with an average of 6.6 objects per image, exceeding existing datasets by 1.67 times in annotation density. Beyond annotation density, OverLay++ provides rich semantic detail with object captions over six times longer than in current datasets. Our dataset generation pipeline is simple and produces dense, overlapping object annotations with rich per-object captions. Across multiple benchmarks, state-of-the-art Layout-to-Image methods trained on the OverLay++ dataset show consistent improvement and faster convergence, demonstrating the importance of dense, overlap-aware, and caption-rich supervision for controllable image generation.

Multivariate ordinal data along with covariates are commonly collected in problems ranging from alignment of language models with human preferences, as well as in recommender systems. For example, data sets such as MovieLens contain several movies rated on a scale 1–5 by human users, along with their demographic information such as age or gender. Similarly, data sets such as HelpSteer collect human feedback on several attributes such as "helpfulness" or "verbosity" of LLM response on an ordinal scale, with covariates depending on the LLM prompt–response pairs. Unfortunately, the standard approaches for modeling these data (a) look at the attributes individually rather than jointly, and (b) often convert the data into pairwise or list-wise win–loss comparisons for fitting models such as Bradley–Terry and Plackett–Luce. Both of these lead to a coarsening of what is actually observed, which we address via a joint covariate-dependent consecutive ratio Markov random field model. We also show pairwise or listwise comparison models are obtained under restrictions of our joint model, and that joint modeling improves comparisons. We also develop a maximum likelihood inference procedure even in the presence of an intractable normalizer.

Induction-heated microrobots face a fundamental thermal management challenge: the alternating magnetic fields required for localized hyperthermia simultaneously generate parasitic ohmic heating within the actuation coils. Conventional cooling approaches can fail because conductive cooling structures placed near the coil can couple to the time-varying field, generating additional electromagnetic losses. This paper addresses this architectural limitation by evaluating two liquid-cooling frameworks designed to isolate the electromagnetic workspace: an indirect configuration utilizing an external copper water block, and a direct architecture routing coolant internally through a hollow helical coil. Evaluated over a 100~s window with multi-point thermocouple telemetry, the indirect water-block configuration failed due to secondary inductive coupling with the block itself, acting as an unintended susceptor that drove the block temperature to an extreme peak of 805$^{\circ}$C. In contrast, the direct internal cooling architecture successfully extracted ohmic losses at the source, sustaining a localized ablation tip temperature of 63.4$^{\circ}$C while strictly restricting surrounding fluid and boundary surfaces below defined thresholds of 33.9$^{\circ}$C and 37.6$^{\circ}$C, respectively. These results establish coil-level fluidic integration as a key design principle for thermally isolated microrobot actuation and provide a hardware foundation for future spatially controlled hyperthermia.

Reliable robotic disassembly requires part-level representations that distinguish genuine component geometry from scanning and reconstruction artifacts. In point clouds of hard disk drives (HDDs), structured ghost artifacts can resemble valid components locally while remaining inconsistent with the overall geometry, allowing erroneous measurements to receive plausible semantic labels. This creates an engineering information problem: semantic prediction confidence alone does not establish whether the underlying geometry is reliable. We propose GUARD, a geometric uncertainty-aware framework that performs point filtering and segmentation within a single forward pass by modeling the reliability of learned geometric representations. GUARD combines a multi-scale geometric transformer with a multi-bandwidth random Fourier feature Gaussian Process to estimate per-point geometric uncertainty, complemented by predictive entropy to suppress unreliable measurements while preserving informative structures. Evaluation on 2,745 real HDD point clouds shows that GUARD improves PointNet++ segmentation mean intersection over union from 0.7739 to 0.8318. Additional experiments on ShapeNetPart and ScanNet examine robustness across corruption types, point-cloud domains, and segmentation backbones. On manually annotated ScanNet samples, geometric uncertainty achieves a corrupted-point detection F1 score of 0.7931, compared with 0.2212 for predictive entropy. The results demonstrate the value of distinguishing geometric reliability from semantic confidence and reveal a tradeoff between artifact suppression and preservation of informative structures. GUARD contributes a reliability-aware approach to interpreting imperfect 3D measurements for component identification and subsequent robotic handling. Project website: https://001-wang.github.io/GUARD_Point_denoiser/.

Biventricular repair is favored for children with complex double-outlet right ventricle (DORV) to eliminate the long-term morbidity of single ventricle physiology. However, creating a baffle that maintains adequate cross-sectional area while limiting incursion on the tricuspid valve apparatus is challenging in a distorted, arrested heart. Three-dimensional (3D) models have aided baffle design with anatomic visualization but analytic approaches, including computational fluid dynamic (CFD) simulation support, have not yet been incorporated into clinical workflows. We present the preoperative, prospective construction of a DORV repair baffle guided by a semi-automated area-preserving algorithm and CFD analysis.

In this paper, we propose a unifying framework to analyze layered networked epidemic processes where the population, represented either as a networked SIS or SIR model, is coupled with an infrastructure network. We propose novel local metrics that enable the analysis of the epidemic spreading locally (node-level) and the prediction of the network-wide spreading under some sufficient conditions. Inspired by the bilayer nature of our model, we partition the layered network between intra- and inter-layer interactions. We identify conditions at the layer level which allow the characterization of the network-level basic reproduction number in terms of the physical structure of the layered network. Then, we leverage the local metrics to propose an optimization framework for epidemic mitigation based on a fundamental notion: the network-wide spreading can be quantified by the aggregation of the local (node-level) epidemic burden. We provide guarantees that the local metric-based optimization can be solved as a geometric program. We illustrate our theoretical results via numerical examples and evaluate the performance of the local metrics and the optimization framework they enable versus other existing epidemic mitigation approaches based on network-level metrics.

Comb inequalities are important cutting planes for the symmetric travelling salesman problem, yet the complexity of their exact separation has remained a longstanding question in polyhedral combinatorics. We present a reduction from 3-SAT proving that deciding whether a comb inequality is violated is NP-complete and that the corresponding separation problem is NP-hard. This result holds even when the input vector belongs to the subtour elimination polytope, every edge value is zero, one half or one and the support graph is nonplanar with maximum degree four. The reduction constructs a graph in which six-vertex ladder gadgets encode Boolean relations and cubic graphs enforce consistency among occurrences of each logical variable. For a propositional logic formula with $v$ variables and $m$ clauses, the constructed graph has $40v+70m+30$ vertices and a linear number of positive edges. The reduction also proves hardness when every permitted tooth has two or four vertices with half of the tooth in the handle. We discuss consequences for approximating the maximum comb violation, optimization over the comb relaxation and explain why hardness of separation does not automatically transfer to larger inequality families.

When we interact with large language models (LLMs), are we having a conversation? They are designed to invite us to treat them as intelligent interlocutors who remember, act, and make commitments. But appearances deceive. We introduce the artifactual stance, a framework that reconceives human-AI interaction as artifact-mediated exchanges of candidate texts. LLM outputs are candidate texts optimized for utility, not utterances bearing meaning or force. LLMs are sophisticated text generators, not speakers. Between sessions, nothing runs; between turns, no one remembers. What persists is a configuration and a transcript. The "conversation" is a user's solo performance, interpretive labour disguised by interface and artifact design. This shift dissolves recent philosophical puzzles. Questions about what 'I' and 'you' refer to in AI exchanges, about whether systems can lie or be held to promises, about the identity of our supposed interlocutors all rest on a false presupposition. There is no speaker behind the screen, hence no one to refer to, no one to hold responsible. What feels like dialogue with someone is interaction with an artifact that generates text at unprecedented scale and fit. By abandoning the conversational framing, we see these systems for what they are: immensely sophisticated artifacts that afford varied uses. The philosophical questions that matter are about the normative underpinnings of design, adoption, authorization, and human practices of use.

Multi-label topic assignment for user-generated content (UGC) – including product reviews and buyer-seller conversations – poses unique scalability challenges in large-scale e-commerce due to informal language, extreme label sparsity, and rapidly evolving taxonomies. While utilizing Large Language Models (LLMs) as labeling oracles to distill ground-truth data has emerged as an industry standard to bypass prohibitive manual annotation costs, determining the optimal, low-latency architecture for the resulting student models remains an open challenge. To address this, we conduct a comprehensive evaluation across Small Language Model (SLM) parameter scales (1B, 4B, and 8B) and architectural paradigms (causal generative versus bidirectional discriminative). Comparing generative text-to-label classifiers against discriminative baselines (DeBERTa-V3 and ModernBERT), our analysis reveals a crucial data-dependent trade-off: while discriminative models outperform ultra-lightweight generative models on structured product reviews, even the smallest 1B generative model surpasses discriminative baselines on complex, multi-turn conversational data. Furthermore, generative models maintain robust performance under massive label-set expansion (up to 112 topics) and severe long-tail distributions, whereas discriminative baselines suffer a 35% drop in Macro-F1 at scale. Finally, we detail the successful production deployment of these optimized models across both product review and conversational domains, demonstrating strict latency compliance and tangible business impact at a global marketplace scale.

Geometric heat pumping is the transfer of energy between reservoirs at equal temperature where the heat exchanged in an adiabatic cycle depends only on the driving contour in parameter space. We implement this mechanism on a superconducting quantum processor using a collision model, where a driven qubit interacts repeatedly with two ancilla qubits that are prepared in thermal states and emulate the reservoirs. Energy measurements before and after each interaction provide a calorimetric record of the heat exchanged with each reservoir. By reversing the driving contour, we extract a heat contribution associated with pumping. Its dependence on the period and on the contour follows exact simulations of the collision model, without adjustable parameters, and approaches in the slow-driving regime the geometric limit of the corresponding Lindblad dynamics.

Recent research has revealed that accessibility in virtual collaboration is not only a technical problem but also depends on allyship: the informal, interpersonal practices through which people support others' accessibility needs. Yet little research has examined how artificial intelligence (AI) might support allyship in collaborative accessibility contexts. To address this gap, we conducted a study where 18 participants (10 disabled, 8 non-disabled) reflected on four allyship scenarios with novel AI tools. Participants valued AI designs that they anticipated could help teammates express, interpret, and coordinate around access needs by reducing repeated disclosure and making allyship more actionable. At the same time, participants raised concerns when AI acted without consent, misrepresented users' intentions, or displaced the interpersonal work of allyship. Based on our findings, we introduce allyship-support tools as a class of accessibility technologies, offer design guidelines, and discuss AI in particular as a means of supporting allyship.

Artificial intelligence (AI) workloads are creating large, power-electronic loads whose effects on power systems depend on location, temporal variability, controllability, and interactions with other loads and resources. Annual electricity consumption alone cannot capture these effects. This review examines how AI data centers affect power systems stability, renewable-energy integration, and low-carbon planning by tracing the power-delivery chain from accelerators and workloads through rack converters, uninterruptible power supplies (UPS), storage, and microgrids to the transmission point of interconnection. Reported oscillatory events and multi-gigawatt load transfers highlight how facility responses can amplify disturbances, while programmable workloads and controllable power converters offer opportunities for demand flexibility. Challenges and mitigation strategies are organized across device, rack, facility, and power systems levels, spanning millisecond-to-year timescales. A bandwidth-matching framework relates disturbances to the response capabilities of mitigation resources. The review distinguishes computational energy efficiency from power systems and sustainability outcomes: lower energy consumption per token does not necessarily reduce peak demand, electrical disturbances, or carbon emissions. It examines how coordinated workload scheduling, grid-interactive UPS systems, storage, high-voltage DC distribution, and flexible interconnection can support reliability, efficiency, and decarbonization. Key research needs include dynamic load models, high-bandwidth telemetry, carbon-and grid-aware scheduling, and mechanisms for valuing flexible computational demand.

Sparse GNN training reduces computation, but deciding which edges to keep can be costly. Reusing one sparse graph is cheap, but locks training to a fixed topology, while varying it across epochs can require repeated sampling or recomputation. We introduce EDiS (Edge-Disjoint Subgraph sparsification framework), which separates one-time structural extraction from per-epoch graph composition. EDiS decomposes the graph once into cacheable edge-disjoint subgraphs, then recombines them into graphs with edge-budget constraints across epochs and retention ratios without re-extracting structure. Our default construction uses feature-based scores and successive maximum score covering forests, while the same composition mechanism also supports alternative edge selection rules. We provide a combinatorial analysis of the per-epoch sampler, the composition step that draws a training graph from the cached decomposition. We show that, under the default covering-forest selector, the stored decomposition deterministically preserves high-score cut edges, and we derive a selector-agnostic conditional bound on high-score cut survival in composed training graphs. Across 19 homophilic, heterophilic, and large-scale node classification benchmarks against 17 baselines under the same edge budget, EDiS achieves the highest mean benchmark score (accuracy/ROC-AUC) and the lowest average rank and gap-to-best among ranked methods. Ablations show the clearest benefits of structural decomposition and epoch variation at tight edge budgets.

LLMs are released at a rapid pace, raising a natural question: how do two independently trained models relate, both in which layers correspond and in how features transform between them? We study this by learning an activation alignment, a map from a source model's layerwise activations to a target's. Our method, MATCHA, factors this map into a layer map, whose output is an explicit target-by-source matrix that can be extracted and inspected, and a layer-shared feature map between hidden spaces. Most of prior work fixes the layer correspondence in advance, pairing layers at roughly the same relative depth; in contrast, we learn both factors jointly from prompts. Across 42 pairs of seven models spanning three different families, MATCHA reconstructs the target's activations more faithfully and improves retrieval-based metrics substantially, w.r.t. previous approaches. The recovered maps are broadly monotone in depth but, in contrast with most previous approaches, are consistently many-to-many: each target layer draws on a band of source layers. Our alignments also enable transfer of activation-space interventions, allowing steering vectors and probes developed for one model to transfer to another.

Objective: We investigate whether accounting for epistemic uncertainty can improve the reliability of automated defect detection in medical device manufacturing. Methods: We consider a machine learning framework that operates on heterogeneous manufacturing and device-report data represented with Knowledge Graphs. To mitigate errors arising from uncertainty in the decision model, we analyze a principled rejection strategy to abstain from predictions whose estimated epistemic uncertainty exceeds a specified threshold. We evaluate the approach using standard synthetic benchmarks and real-world medical device report data. Results: The theoretical results establish the validity of the method characterizing the regimes under which it is expected to be effective. Empirically, the rejection strategy enables explicit control of coverage, that is, the proportion of samples for which the model issues predictions, while improving performance on the retained samples. On 266,170 real-world FDA MAUDE device reports, a 10% abstention rate reduces classification error by 48%, and more aggressive rejection (approximately 70% coverage) yields near-perfect accuracy on the retained samples. On standard synthetic manufacturing benchmarks, abstaining on 9% of the decisions, our approach reduces the risk up to 63% compared with the standard no-abstention approach. Conclusions: Abstaining from predictions with high epistemic uncertainty can provide a practical tool for controlling the reliability of machine learning-based defect detection, especially in high-stakes medical device manufacturing applications. Significance: Uncertainty-aware defect detection may support safer and more reliable quality assurance in medical device manufacturing by identifying cases that require additional inspection rather than issuing potentially harmful predictions.

We develop a geometry-based capacity theory for exact-key retrieval in compressed finite-feature Hebbian associative memory. For random or approximately isotropic values, retrieval interference separates into finite-feature noise, which decreases with feature dimension, and structural interference, which is determined by squared kernel overlap among stored keys and persists in the infinite-feature limit. This yields a fit-free prediction of retrieval quality, reveals a geometry-dependent capacity ceiling, and predicts the feature budget required for a target retrieval quality. When stored values are correlated, we show that retrieval depends jointly on the key kernel and value Gram matrix, and derive finite-feature approximations that account for this interaction. We validate the theory on synthetic, visual, and medical-image representations. Overall, the framework links representation geometry directly to memory capacity and distinguishes when performance can be improved by increasing the feature budget and when the representation itself must be changed. Across these settings, the predicted retrieval curves closely match empirical behavior and correctly identify changes in the preferred memory design.

Human videos provide rich motion targets for humanoid learning, yet visually plausible references can still produce persistent failures under physics-based execution. These failures reveal where training supervision should change. We present MimicX, a policy-in-the-loop framework that uses execution feedback to refine video-driven humanoid motion tracking. Starting from reconstructed and retargeted motion, MimicX localizes difficult transitions and affected body regions, then jointly adapts tracking objectives and the reset curriculum for policy continuation. Repeated rollout verification selects execution-priority improvements subject to tracking guards. Across four core video tasks, MimicX consistently improves tracking accuracy and Robust Execution Horizon relative to the Fixed Reference baseline. Task-averaged results show a 25.7% reduction in body-tracking error and a 255.6% increase in execution horizon. Additional video, motion-reference, and collision-scene studies evaluate the method beyond the core tasks, while MimicX-HLoop accelerates feedback through heterogeneous execution. Overall, MimicX turns policy failure into actionable supervision for deciding what to refine and which refinement to retain.

Predicting transcriptional responses to genetic perturbations is central to understanding gene function. Existing predictors primarily rely on transcriptomic measurements, although chromatin accessibility provides complementary information about the cellular context in which perturbations act. Using this information requires linking chromatin context to specific perturbations and accounting for baseline differences between independently sampled control and perturbed populations. We propose ChromaPert, a chromatin-informed framework for predicting state-dependent perturbation responses. ChromaPert combines molecular and DNA-informed locus priors with paired control RNA–ATAC features to jointly represent target identity and measured cellular context. Its Chromatin-Guided Response Router (CGRR) builds a source bank of control-derived expression offsets and retrieves relevant sources using perturbation/locus or control-ATAC similarity. These offsets account for baseline differences, while conditional transport flow learns the remaining response. Across three unseen-target and held-out-state settings on K562 CAT-ATAC and Perturb-Multiome, ChromaPert achieves the highest all-gene response correlation among evaluated methods. When transferring known perturbations to held-out states, it improves correlation by 23.2% across all genes and 46.2% for the twenty most responsive genes over the strongest respective baselines. Correct RNA–ATAC pairing improves recovery of chromatin-associated response slopes over shuffled pairing, while cross-state predictions retain state-specific responses to the same perturbation.

The search for a common view of justice and fairness has challenged human collective activity, as our diverging judgments are unavoidably shaped by the self-interests of social position, personal benefit, cultural inheritance, and historical circumstance. John Rawls famously attempted to overcome this limitation through popularizing a philosophical tradition known by the phrase "the original position" - a thought experiment by which people select principles of justice without knowing the identities or advantages they will possess. Critics, however, have long questioned whether people can meaningfully suspend their social identities and suppress morally relevant forms of lived experience. Artificial intelligence engaged to calculate algorithmic and agentic fairness introduces a novel possibility. LLMs have no singular class, race, gender, nationality, or biography, yet their parameters encode linguistic representations of a vast range of human identities and moral traditions. Perhaps the ethical judgments of LLMs could approximate an integrative original position - a "view from everywhere" generated not by excluding social identities but by computationally incorporating their diversity.It is unlikely that humankind will "hand over the keys" to computational systems by simply delegating complete agentic control of distributive and procedural collective processes. But AI may play a role, perhaps a positive one, interacting with individual and collective human judgment as we often confront increasingly polarized views on what is fair and just. We present data comparing human, base model, and frontier/fine-tuned model judgments about classic moral dilemmas while systematically varying identity relationships and Rawlsian constraints on identity. We conclude by speculating whether, if advanced AI systems provide humans with thoughtful advice, humans would actually be likely to accept it.

Continuous cardiac monitoring outside clinical settings requires signals that are both informative and practical to collect during daily life. Electrocardiography (ECG) provides rich information about cardiac rhythm and waveform morphology, while wearable photoplethysmography (PPG) is easier to acquire continuously but is only an indirect cardiovascular measurement and is highly sensitive to motion. We present BeatFlow-ECG, a conditional rectified-flow model for reconstructing single-channel ECG from synchronized PPG and inertial measurements. BeatFlow-ECG models reconstruction as conditional transport from noise to ECG using a convolutional encoder-decoder with a transformer bottleneck and explicit flow-time conditioning. Motion information is incorporated through IMU-derived conditioning features, motion-dependent loss weighting, and an easy-to-hard training curriculum. We evaluate the model under leave-one-subject-out protocols on PPG-DaLiA and WESAD. BeatFlow-ECG achieves the best results among the evaluated deterministic, adversarial, and diffusion-based baselines across all reported waveform and beat-timing metrics, with Pearson correlations of 0.983 and 0.986 and R-peak F1 scores of 0.946 and 0.955, respectively. Compared with Conditional DDPM-1D, L1 error decreases from 0.085 to 0.062 on PPG-DaLiA and from 0.074 to 0.055 on WESAD. Additional analyses on PPG-DaLiA show higher correlation in fixed R-peak-relative waveform regions and lower reconstruction error across low-, medium-, and high-motion subsets.

The large KV-cache size of modern LLMs creates a barrier to efficient deployment. Recent work has explored replacing attention layers' RoPE positional embeddings with alternative decay-based mechanisms, which can then be used to prune KV-cache during inference. However, these decay functions have limited expressivity, and in practice devolve into sliding-window-like eviction patterns. In this work, we propose a unifying framework for complementary and novel decay mechanisms, capturing complex key statistics and interactions while preserving expressive RoPE embeddings and Softmax attention. The resulting Universal Attention is a highly expressive and end-to-end trainable architecture, whose composite decay mechanism acts as a natural, $\textit{adaptive}$ pruning criterion, removing tokens that contribute least to attention computation. Experimentally, Universal Attention achieves state-of-the-art $10\times$ compression on natural language and synthetic task data, while $\textit{improving}$ downstream performance compared to both state-of-the-art baselines and unpruned oracles. It further demonstrates superior long-context generalization with unprecedented $25\times$ compression at length 16k.

For the online combinatorial allocation problem with subadditive valuations, Correa and Cristi (STOC 2023) proved the existence of a $6$-competitive online algorithm, improving on the previous best $O(\log\!\log m)$-competitive online algorithm due to Dütting, Kesselheim, and Lucier (FOCS 2020), where $m$ is the number of items. However, Correa and Cristi's result is existential, and it was left open whether a constant competitive ratio is attainable via an efficient online algorithm that uses a polynomial number of demand oracle queries. In this work, we answer this affirmatively, giving an expected-polynomial-time $(6 + \epsilon)$-competitive online algorithm for any constant $\epsilon > 0$. Our techniques also recover, in the offline setting, the $(2 + \epsilon)$-approximation result of Feige (STOC, 2006). Finally, when the buyers' valuations are drawn from identical distributions, we exploit symmetry to obtain an improved $(60/11+\epsilon)$-competitive algorithm. Starting with the natural configuration LP relaxation for the problem, our main technical contribution is a recursive Bundle Score Generator (BSG) that resolves item conflicts by assigning correlated scores to the items requested by each buyer. Unlike the Random Score Generator whose existence is shown by Correa and Cristi, our BSG is efficiently computable in expected polynomial time. Moreover, it satisfies a stochastic dominance property that is sufficient to recover both Feige's offline result and Correa and Cristi's online result.

We investigate the cosmological dynamics of the nonlinear $\sigma$-model in a locally rotational symmetric Bianchi V background geometry. We employ the $SU(2)$ and the $SL(2,\mathbb{R})$ internal symmetries, for which the kinetic metric of the multi-scalar fields is a space of constant curvature. We assume an inhomogeneous ansatz for the scalar fields, such that the $\sigma$-model, which allows the existence of nontrivial solutions in the Bianchi V geometry. For an exponential potential, we perform a detailed analysis of the phase space, we determine the stationary points, and we study their stability properties. The scalar field inhomogeneities prevent both the slow-roll and hyperbolic inflationary epochs. The existence of a cosmological constant is required to describe cosmic acceleration.

Building a world model requires a state representation useful for planning and decision-making—potentially over tasks unknown at training time. In the context of financial markets, planning and decision-making may require a model to reason about market-wide conditions, asset-specific expected returns, liquidity, volatility, and cross-asset relationships. Yet financial representation learning has largely been evaluated on individual predictive tasks, oftentimes on a single time period using comparatively narrow datasets. We address this through three primary contributions. First, we introduce Market-1T, a dataset containing nearly one trillion observations across U.S. equities from 2008 to 2025 at 1 Hz resolution. Second, we develop and implement a rigorous evaluation protocol. Third, we conduct a systematic large-scale study of financial representation learning, comparing 18 encoder-training strategies across nearly two decades of market regimes. We evaluate learned representations both by their predictive utility on common finance tasks and through probes of latent structure. We find that encoders with similar predictive performance can organize market state very differently. Collectively, we establish a foundation for training and evaluating financial market representations in support of world models such as DINO-WM, V-JEPA 2, and LeWM.

The motion of a particle in a finite-depth confining potential, such as that of an electromagnetically trapped atom or ion, is approximately harmonic at low energy and softens as the escape energy is approached. When the particle is driven by a stochastic force, the heating and escape times depend sensitively on the noise power spectrum. We study escape times of particles in softening potentials driven by power-law colored noise. We identify two nested conditions for weak noise: the particle must execute many oscillations before escape, and noise forces must be small relative to forces exerted by the trap so as not to tilt the potential appreciably. In this regime, we derive expressions for the mean escape time using stochastic averaging techniques and compare them with Monte Carlo simulations of the full equations of motion. We also examine the crossover to regimes where these conditions are not met and large quasi-static forces give rise to additional escape mechanisms. Applying these results to an experimental measurement of lifetimes in a microfabricated ion trap, we find that spectral color alone cannot account for the rapid escape rates observed, whereas quasi-static barrier tilting by a stray field of plausible magnitude could. These results are relevant to the heating and escape of trapped atoms due to noisy force fields, as well as to other nonlinear oscillators subject to colored noise.

Let $P_h$ be a semiclassical pseudodifferential operator on a closed Riemannian manifold $(M,g)$, with principal symbol $p$. We consider perturbations $P_h+h^\alpha Q$, with $0<\alpha\le 1$, where $Q$ is a semiclassical pseudodifferential operator whose symbol oscillates at scale $h^\beta$, with $2\beta <\alpha$. Assuming that the classical dynamics of the unperturbed system on a regular energy surface $p^{-1}(E)$ is hyperbolic, we prove a Gutzwiller trace formula for the perturbed operator that holds up to times of order $|\log h|$. This formula relates the distribution of energy levels of the quantum system near the energy $E$ to the periodic orbits of its classical counterpart. The perturbation $h^\alpha Q$ affects only the phases appearing in the trace formula.

We study the problem of learning transition kernels for time-homogeneous jump-diffusion processes using conditional diffusion models, with the goal of generating new sample paths from training data consisting of N independent trajectories observed on a high-frequency discrete time grid. On the theoretical side, we establish non-asymptotic bounds for the conditional score estimation error and for the KL divergence between the laws of the true and generated discretely observed paths. On the numerical side, we first evaluate our method on synthetic data to assess the theoretical findings and benchmark its performance against the approach of Gao et al. (2025). We then apply our method to real-world data and investigate its performance on a probabilistic forecasting task.