Papers

Generative foundation models are attracting interest for their ability to produce desired outputs from demonstrations given at inference time, without updating parameters. However, since a few demonstrations cannot uniquely identify the intended task, the challenge is how to learn and sample from an output distribution that reflects this task uncertainty. In this work, we theoretically analyze how a Diffusion Transformer (DiT), pretrained across diverse tasks, learns and generates predictive distributions for a new query from demonstrations. We first show that the natural target to generate from finite demonstrations is not an output derived from estimating a single task, but rather a predictive distribution that captures the task uncertainty remaining after observing the demonstrations. We then prove that a DiT can learn this predictive distribution through score estimation, using attention to aggregate information from demonstrations and diffusion to generate samples. Owing to this property, with sufficient pretraining resources and diffusion sampling steps, the resulting DiT achieves the minimax optimal rate over a Hölder class of test-time tasks. These results imply that DiT acts as a statistically grounded in-context generator capable of generating distributions adapted to new tasks while retaining the uncertainty inherent in finite demonstrations.

This paper tackles visible challenges in deep ensemble learning, where deep neural networks serve as ensemble members: training and storage burdens, and robustness of cautious (set-valued) predictions targeting multiple utilities, which may involve reward-sensitivity. To mitigate the training and storage burdens, we propose to employ compact ensembles, such as Bayesian Neural Networks and Convolutional Neural Networks with the Monte-Carlo dropout prediction option, to produce probabilistic predictions. For each query instance, these probabilistic predictions are then used to define a representative distribution optimizing some statistical distance. The representative distribution is then employed to define the Bayes-optimal prediction (BOP) of any utility. To address the potential unrobustness of singleton prediction making, we propose a family of set-utilities satisfying some desirable properties and whose set-valued BOPs can be found efficiently. Empirical evidence is then given to illustrate the potential (dis)advantages of the proposed ensemble learning framework.

Learning robot policies directly on physical systems remains difficult because data collection is costly and policy exploration can be unsafe. We introduce Visual and Motor Policies from Sampling-Based Planning (VAMPS), a framework that uses Model Predictive Path Integral (MPPI) control to train reusable policies without human demonstrations. VAMPS supports two training modes. For one-step proprioceptive policies, it operates iteratively in simulation: the policy warm-starts MPPI, and the refined trajectories provide new supervision as the policy changes. A learned terminal value improves short-horizon planning, while an Implicit Q-Learning (IQL) critic guides the policy update. Iterative refinement outperforms training once on frozen MPPI data, and we transfer the learned locomotion policy to a Unitree Go2. For visuomotor policies, VAMPS operates directly from real-robot data. MPPI uses task-specific state estimates to plan and execute trajectories while recording RGB and sensor observations on a Flexiv Rizon 10S. Action Chunking with Transformers predicts action chunks, reducing the effective prediction horizon, and is trained offline on this fixed dataset. We demonstrate visuomotor pick-and-place and force-aware whiteboard erasing. In the latter task, the policy additionally observes the measured $6$-D wrench and desired normal force. These results show that VAMPS can learn policies either in simulation followed by hardware transfer or directly from autonomously collected real-robot data.

Time series often contain recurring structural patterns, and efficiently mining such patterns into compact representations is essential for scalable analysis of long sequences. Cartesian tree (CT) equivalence provides a well-established structural abstraction that preserves hierarchical order structure while discarding exact values and fine-grained ordinal variations. By grouping multiple ordinal patterns into a shared structural form, CT equivalence offers a principled way to compress recurring temporal structure. However, mining frequent CT-equivalent patterns at scale remains computationally expensive. A naive pairwise approach repeatedly constructs and counts CT representations over subsequences, requiring $O(n^4)$ time for a sequence of length $n$, which severely limits its applicability to long sequences. We propose a new Cartesian pattern mining algorithm based on a Cartesian suffix tree that compactly organizes CT-equivalent subsequences and reuses shared structural information. Our method reduces exhaustive CT-pattern occurrence collection from $O(n^4)$ to $O(n^2)$ time, and we formally prove the correctness and complexity bounds. We further show that this computational gain translates into effective compact representations. Across diverse time-series datasets, a small set of mined CT patterns preserves meaningful clustering structure, and comparisons with finer-grained order-preserving representations show that CT equivalence reduces redundant ordinal distinctions under limited feature budgets. Our implementation is available at https://github.com/hyundong98/CT-Miner .

Large language models (LLMs) are typically pretrained in high precision but increasingly deployed with low-precision post-training quantization (PTQ). Recent studies have shown that using weight averaging during pretraining can improve PTQ performance compared with learning-rate decay, suggesting that it might provide a simple way to improve the pretraining-to-quantization transition. But the mechanism behind weight averaging remains insufficiently explained. This leads to inconsistent and fragile performance gains, thereby preventing practitioners from applying such a technique confidently. As a response, we formulate weight averaging as a trade-off between retaining training progress and improving robustness under perturbation. We further derive a continuous family of averaging kernels that unifies conventional strategies and achieves the Pareto frontier between the two competing goals. Critically, a theoretical framework for performing weight averaging under PTQ is developed. It can be shown that coarser quantization is more susceptible to perturbations, whereas finer quantization could be less affected. Thus, our results could provide unified theoretical guidance for performing weight averaging under different PTQ conditions. Experiments validate both the predicted behavior and the proposed averaging strategy. Code is available at https://github.com/MOFA-LAB/weight-averaging-for-ptq.

Consider a sample of size $N$ from a two-layer hierarchical Pitman–Yor model, and let $\xi(N)$ denote the random number of clusters generated at the first layer of the hierarchy. We study moderate deviation principles for partition statistics evaluated at the random sample size $\xi(N)$. In particular, we establish moderate deviation principles for the total number of clusters $K_{\xi(N)}$ and for the frequency count $M_{l,\xi(N)}$, the number of upper-level clusters represented by exactly $l$ first-level clusters. Our analysis combines fixed-sample-size small-tilt asymptotics with a moderate deviation principle for the random index $\xi(N)$. A uniform small-tilt argument, together with exponentially weighted tail estimates, allows us to pass from deterministic sample sizes to the hierarchical random-index setting. We obtain explicit deviation speeds and good rate functions on a family of intermediate scales between the typical growth order $N^{\alpha_1\alpha_2}$ and the linear scale $N$. The resulting rate functions exhibit a common power-law structure governed by the product $\alpha_1\alpha_2$, revealing a multiplicative effect of the two levels of the hierarchy.

Approximate Message Passing (AMP) algorithms are attractive as they are computationally efficient and simultaneously admit a precise characterization in terms of the low-dimensional "state-evolution" recursion. In this work, we establish quantitative universality for AMP with centered rank-one sensing matrices $Z_i=(x_ix_i^\top-I_d)/\sqrt d$, where $x_i$ are independent standard Gaussian vectors. These matrices arise in quadratic regression and learning quadratic neural networks. Their normalized vectorizations have isotropic covariance in dimension $p=d(d+1)/2$, but strongly dependent coordinates. For linear observations with Gaussian noise and prescribed smooth, bounded spectral denoisers, we compare rank-one sensing with a covariance-matched isotropic Gaussian ensemble. At a fixed iteration horizon, with $n\leq Cp$ and uniform bounds on the normalized signal energy, initialization, coefficients, and first four denoiser derivatives, normalized signal overlaps, cross-time overlaps, and smooth linear spectral statistics differ by $O(d^{-1/2})$ in every fixed $L^m$. This yields universality of the normalized mean-squared error, fixed spectral moments, and empirical spectral distributions. Whenever the Gaussian observables admit a joint state-evolution limit, the same predictions hold under rank-one sensing. The proof uses columnwise Lindeberg replacement, leave-one-out analysis, smooth spectral expansions, and high-moment concentration. For prescribed smooth spectral denoisers, the result establishes the AMP universality conjectured by Maillard et al. (arXiv:2408.03733).

The corpus callosum (CC) is a major white-matter structure and a well-established marker of brain aging, but most studies quantify it using scalar summaries that discard its boundary geometry. We present a Riemannian shape-space framework \cite{fletcher2013geodesic-regression} for analyzing age-related morphological change in the midsagittal CC, applied to the OASIS-1 cohort. Each contour is represented by $128$ landmarks and embedded into Kendall shape space, where translation, rotation, and scale are removed. We derive a multivariate geodesic regression with exact Riemannian gradients and use the fitted age-velocity field to localize age-related deformation to five anatomical sub-regions. In the cognitively normal cohort ($n = 252$), geodesic regression outperforms the Euclidean linear benchmark ($R^2 = 0.1355$ vs.\ $0.1216$). Regional energy is anterior-dominant: the Genu carries $46.1\%$ and the Anterior Body $23.3\%$ of total age-related shape change, together accounting for $\sim 69\%$ despite comprising only $\sim 41\%$ of landmarks. Signed projections confirm the ordering (Genu $r = 0.562$; Anterior Body $r = 0.507$). In contrast, age explains less than $0.5\%$ of shape variance in Alzheimer's disease ($n = 88$), indicating that the disease disrupts the healthy aging trajectory. A tangent-space classifier achieves an age-group AUC of $0.791$ from the 2D contour alone, exceeding a recent volumetric benchmark ($0.67$).

In the field of deep learning, has seen significant advancements; however, shadow removal remains a persistent challenge owing to the variable sizes and colors of shadows influenced by lighting conditions. This study proposes a novel shadow feature refinement network (SFR-Net), which leverages supervised learning, feature refinement loss, and knowledge distillation to enhance shadow removal performance. A dedicated post-processing algorithm is further introduced to restore natural color consistency in the generated shadow-free images. We evaluated our method on two public datasets: the adjusted image shadow triplet dataset (ISTD+) and the shadow removal dataset (SRD), which demonstrate strong generalization capabilities under diverse conditions. On ISTD+, our model achieved a root mean square error (RMSE) of 3.4627 and structural similarity index measure (SSIM) of 0.9382 across the entire image. On SRD, it recorded an RMSE of 4.3781 and an SSIM of 0.9341. These comprehensive results show that our approach performs competitively across both shadow and non-shadow regions while setting a promising direction for robust and perceptually natural shadow removal. Code is available at https://github.com/DongHyun99/SFRNet.

Partnered human-humanoid interaction couples locomotion with continuous physical contact. A humanoid needs to coordinate with a person's motion while responding to interaction forces and maintaining stable and natural movement. We present CoDance, a framework for learning reactive and compliant human-humanoid interaction from video. We study partnered dancing as a challenging instantiation, where a humanoid coordinates its footsteps with a moving partner and maintains continuous two-hand contact. Given a single video of two human dancers, CoDance retargets their motions into a robot reference and a moving partner. We introduce a multi-link compliance augmentation that transforms the kinematic demonstration into force-aware training data by adapting the robot reference under structured forces at both hands. Policies trained on this data follow the observed partner while preserving the demonstrated locomotion style and responding compliantly to physical interaction. In simulation, the policies adapt their footsteps to changes in the partner and reproduce approximately 80% of the wrist displacement encoded by the augmented demonstrations. On a physical humanoid, CoDance enables sustained two-hand dancing with a human partner including repeated transitions between forward and backward motions.

Large language model watermarking embeds detectable statistical signals during decoding, but the resulting changes to token probabilities can degrade generation quality. This trade-off is particularly important for code, where small changes in token selection can break syntax or alter program behavior. Existing code watermarking methods mitigate this risk through entropy-based insertion or syntax-aware token selection, but they do not directly construct the watermark over the set of continuations admitted by the current grammar state. We propose Grammar-Guided Code Watermarking with Green Temperature (GTCW), which integrates grammar-constrained decoding with probability-aware watermarking. At each decoding step, GTCW restricts the candidate set to grammar-admissible tokens and partitions this support into keyed green and red subsets. At eligible high-entropy positions, green temperature reweights the green tokens according to the model's relative preferences, strengthening the watermark signal while retaining the grammar constraint. Across five models and five benchmarks spanning four programming languages, GTCW achieves a mean AUROC of 73.61%, compared with 67.83% for the strongest baseline, while maintaining a mean Pass@1 of 59.18% versus 59.58% for unwatermarked generation. Our implementation is available at https://github.com/hyundong98/GTCW .

Test-time compute can improve mathematical reasoning, but can short-budget runs predict how mathematical reasoning scales with additional compute? We introduce a Discovery–Execution (DE) framework that predicts the aggregate held-out scaling curves through a convolution of strategy discovery and conditional execution. From independent short-budget attempts and oracle-sketch-conditioned runs, the framework estimates cumulative success along held-out reasoning trajectories under alternate compute allocations. We evaluate four models on 35 fresh Olympiad problems and non-geometry problems from IMO-ProofBench Advanced. Under the DE framework, near-saturated execution predicts geometric scaling, as observed for the GPT models. For Claude Opus 4.8, incorporating measured execution substantially improves held-out forecasts over geometric extrapolation across one- and two-arm allocations. As a secondary application, regularized DE (R-DE) decisions to continue or restart yield lower average regret than the best model-specific retrospective policy. Together, these results show that measuring conditional execution provides information about longer reasoning that short-budget success rates do not always capture.

We apply the renormalization group method to examine the interplay between the charge density-wave and superconductivity phases in two quasi-one-dimensional tight-binding electronic bands coupled by the electron-phonon interaction. The electronic and phonon energy scales are embedded in a two-cutoff scaling scheme at finite temperature for the renormalization group flow equations of intra- and inter-band phonon-mediated interactions between electrons. At the one-loop level different regimes of renormalization are derived covering both the adiabatic and antiadiabatic domains for small and large phonon frequencies. Finite temperature phase diagrams as a function of nesting frustration of the electron spectrum are thus obtained. The possibilities for superimposed charge density-wave and superconducting ordered states are given. The emergence of domes of superconductivity resulting from quantum critical reinforcement of Cooper pairing by charge density-wave order fluctuations is found. The impact of the multiband character of the electronic structure on the ordering temperature of superconductivity, quantum criticality, and isotope effect is discussed.

Let $\mu$ be a doubling Radon measure in $\mathbb R^d$ with support $X$. We prove a local and quantitative form of the Bennewitz–Lewis theorem in this setting: if a Radon measure $\nu$ satisfies the Bennewitz–Lewis condition on a bounded relatively open set $V\subset X$ with a small enough constant, then $\nu|_V\ll\mu|_V$ and its density satisfies a reverse Hölder inequality on every compact subset $K\subset V$. Along the way we develop the dyadic toolkit these arguments run on — triple cubes defined through neighbours, the basis $\mathcal{D}\cup3\mathcal{D}$, and a Whitney decomposition — and we collect the Muckenhoupt-type classes of weights over that basis. The same machinery yields a local Gehring lemma for enlarged balls: both theorems are deduced from a single bootstrapping lemma, stated once for $p=1$ and $p>1$.

AI agents increasingly rely on tools exposed through the Model Context Protocol (MCP) to complete user tasks. Hundreds of thousands of MCP servers are listed across marketplaces, yet they are organized only by coarse, marketplace-specific server categories. This makes it difficult for agents and users to identify tools for a given operation, find functional alternatives, and assess how those alternatives differ. We present MCPacific, the largest tool-level, cross-marketplace map of the MCP ecosystem. MCPacific collects 368,754 MCP server listings corresponding to 124,267 unique servers across 17 marketplaces, statically extracts 1,328,233 tool specifications from these servers in seven languages, and organizes them into a hierarchical functional taxonomy of 58,915 capabilities. We construct the taxonomy through an iterative LLM-driven design-test-refine process and map the full corpus to it using calibrated embedding routing. Our study reveals that MCP extends well beyond developer tooling, with 85% of tools serving other domains. Functional alternatives are widespread but unevenly distributed: 98.5% of tools have at least one alternative, yet nearly a quarter of capabilities are supported by only one tool. Functionally comparable tools also differ in security alerts, code complexity, and project maintenance, with complexity differing by more than 2.5x in 41% of comparable tool pairs. Finally, presenting candidate tools through the taxonomy rather than a flat list improves task completion rate across all four evaluated models, with gains of up to 12 percentage points in Pass@0.75 for crowded candidate sets.

Analog in-memory computing is a promising platform for on-device execution of large language models because it performs matrix–vector multiplications (MVMs) in memory and in parallel, reducing data movement. However, limited digital-to-analog converter precision, input noise, and finite conductance states can degrade model accuracy, while full-model retraining to address these effects can be costly. We develop an optimizer-agnostic, parameter-efficient adaptation method based on Low-Rank Adaptation (LoRA), keeping the pretrained weights stored on analog arrays fixed while training the LoRA weights to adapt to downstream tasks and hardware non-idealities. Reliable adaptation requires handling errors in both forward and backward MVMs and physical weight updates. We use input reshaping to reduce input-induced MVM errors and update accumulation to retain small updates before programming them to finite-state analog devices. Across Llama-3.2-1B-Instruct and Llama-3-8B with both Muon and AdamW, input reshaping improves analog LoRA fine-tuning under noisy MVM computation. Update accumulation separately preserves sub-threshold updates and substantially improves adaptation under finite-resolution programming, including configurations with as few as 20 conductance states. Additional experiments show consistent held-out negative log-likelihood improvements across noisy analog settings.

The PPAD-completeness of computing Nash equilibria in bimatrix games has driven extensive research into polynomial-time algorithms for $\epsilon$-approximate Nash equilibria. Determining the strongest approximation guarantee achievable in polynomial time is a fundamental question in the complexity of approximate Nash equilibria. Despite sustained efforts, breaking the $1/3$ barrier has long been regarded as a difficult open problem. In this paper, we give an affirmative answer by proposing a simple, symmetric deterministic polynomial-time algorithm that has no tunable hyperparameters and achieves an approximation guarantee of approximately $0.30954+\delta$. The main idea is to enrich the optimization framework of Tsaknakis and Spirakis with building blocks drawn from our work on strategy mixing and automated approximation analysis, yielding a new algorithmic structure that provides a conceptual explanation for the improved guarantee.

Pluggable type systems extend the basic type system of a programming language by introducing additional type hierarchies to specify more complex properties and dependencies between variables. We consider the Constant Value Checker, a pluggable type checker for Java implemented using the Checker Framework, which provides various pluggable type systems and corresponding checkers. The Constant Value Checker lets users specify restrictions on the values a primitive integer or boolean variable can hold using a set or range of constant values. However, the current implementation of the Value Checker makes use of a limited set of syntactic typing rules that, in practice, often fail to verify well-typedness of more complex code. In this paper, we introduce an extension to the Checker Framework using Satisfiability Modulo Theories (SMT) solvers to address these limitations by creating corresponding first-order logic formulas for expressions whose type checks fail with the current syntactic typing rules and determining their well-typedness based on the satisfiability of these formulas. Furthermore, we introduce new dependent types for specifying allowed values with expressions that can depend on other variables in the program.

Rossman, Servedio, and Tan proved that the polynomial hierarchy is infinite relative to a random oracle. This paper strengthens this celebrated result by considering strong separations, witnessed by immune languages. The main result of the paper shows that with respect to a random oracle the levels of the polynomial hierarchy separate with immunity. Specifically, with probability one over a random oracle $A$, for every $k\geq 1$ there is a language in $\Sigma_{k}^{P,A}$ that is immune to $\Pi_{k}^{P,A}$, and, symmetrically, a language in $\Pi_{k}^{P,A}$ that is immune to $\Sigma_{k}^{P,A}$. We thus extend classical results due to Bennett and Gill and Vereshchagin. We accomplish this by developing a "rare-or-wrong" approach to strong separations. We highlight the flexibility of the approach by strengthening other separations with respect to a random oracle from the complexity-theoretic literature.

An addition formula is a closed-form formula for reproducing kernels of orthogonal polynomials of several variables; the latter are kernels of orthogonal projection operators. We derive addition formulas for two families of orthogonal polynomials, which consist of wrapped products of classical Gegenbauer polynomials on the unit ball with either classical Jacobi polynomials on the simplex or product Laguerre polynomials, each of which is given explicitly as a multilayer of integrals of a classical orthogonal polynomial of one variable. These formulas provide a powerful tool for analysis and allow us, in particular, to reduce a substantial portion of analysis on the Fourier orthogonal expansions on the domains to that of one variable.

We develop and analyse a conforming piecewise affine finite element method for the Grad–Mercier equation, a nonlocal elliptic model for magnetic equilibria whose source depends on the global rank of a flux function. The principal difficulty is that the unique continuum equilibrium has a maximum plateau of prescribed positive area. The solution therefore samples the rank law only above the plateau mass, while perturbations that separate equal values may distribute this mass over several numerical ranks and thereby alter the non-strict rank source. We exploit the continuum well-posedness structure to replace the rank law by an equivalent clipped, nonnegative law, and replace Lebesgue measure by a mass-lumped nodal measure. Equal nodal values are assigned a common rank interval, thereby retaining the full lumped mass of each tied level. The resulting weighted rearrangement gives a strictly convex discrete energy and hence a unique finite element equilibrium. On meshes satisfying a discrete comparison principle, the discrete equilibrium is nonnegative and bounded above by a computable barrier. A Poisson-preconditioned rearrangement iteration converges on each fixed mesh and admits computable a posteriori energy and energy-norm bounds. As polygonal finite element domains converge to the physical cross-section, the discrete equilibria converge strongly in $H^1_0(\Omega)$ and uniformly on $\overline\Omega$ to the unique Grad–Mercier equilibrium. Reconstructed equilibrium sources converge weak-* in $L^{\infty}(\Omega)$ to the original nonlocal source.

We study the two-dimensional periodic resistive compressible magnetohydrodynamic equations with constant shear viscosity and magnetic diffusivity, bulk viscosity $\rho^\beta$, and pressure $\rho^\gamma$. For every $\beta>1$ and $\gamma>1$, we construct global finite-energy renormalized weak solutions from strictly positive bounded $W^{1,q}$ densities, $q>2$, and arbitrary $H^1$ velocity and magnetic data. The construction combines approximation-independent finite density moments, generalized effective-flux identities, and a joint logarithmic renormalization of the density and its entropy defect. An augmented relative energy containing the $\beta$-power density potential yields weak–strong uniqueness against positive $H^2$ strong solutions for the same full pressure range. We also establish global strong existence for a large-background family when $\gamma>\max\{5-2\beta,\beta+1\}$. Writing $m=\int\rho_0$, the density perturbation is bounded in the scaled norm $m^{(\gamma-3)/2}\|\rho_0-m\|_{H^2}$, while the fixed $H^2$ velocity and magnetic norms need not be small. For sufficiently large $m$, frequency-dependent acoustic dissipation, staged vorticity weights, and a separate initial-layer flux estimate close a simultaneous bootstrap. The admissible pressure exponents have infimum $7/3$, with the endpoint excluded. For $\beta>2$ the relevant damping rate is the minimum of the viscous and pressure-relaxation rates; keeping both rates extends the argument without an upper restriction on $\beta$. The strong theorem has no upper restriction on $\gamma$ under this scaled density hypothesis; for fixed additive density perturbations it applies in the stated lower range up to $\gamma=3$.

We study the realization problem for point schemes of skew polynomial algebras. We approach this problem combinatorially by translating it into the study of certain $3$-uniform hypergraphs, which we call point hypergraphs. We first give a homological criterion characterizing point hypergraphs. Using this criterion, we study hypergraphs obtained by deleting triangles from triangulations of connected orientable closed surfaces. Deleting exactly one triangle always gives a non-point hypergraph. When the triangulation has no separating nonfacial $3$-cycles, deleting either no triangles or at least two triangles gives a point hypergraph, and the one-triangle deletions are minimal non-point hypergraphs with respect to taking induced sub-hypergraphs. It follows that point hypergraphs cannot be characterized by finitely many forbidden induced sub-hypergraphs. Next, for each point hypergraph, we construct an affine moduli variety of skew polynomial algebras realizing it, and determine its dimension. For point hypergraphs arising from the above surface construction, we obtain an explicit dimension formula in terms of the number of vertices, the Euler characteristic, and the number of deleted triangles. Finally, we characterize point hypergraphs on six vertices in terms of a four-vertex local condition together with a single exceptional obstruction.

Frozen speech foundation models (SFMs) make downstream adaptation efficient: the backbone can stay fixed while a task learns layer fusion and a lightweight classifier. Full adversarial fine-tuning is a standard route to robustness, but generating adversarial examples and updating the backbone for every task sacrifices that efficiency. We ask whether robustness can instead be learned before future tasks are known. For a frozen backbone and linear classifier, robustness can be understood through the interaction between representation stability and decision-boundary margin. This leads directly to our design: we stabilize representations across the hidden layers, rather than only the final layer, while preserving clean representations; after clean adaptation selects the layer mixture, we keep it fixed and enlarge only the classifier margin, without downstream adversarial examples. We evaluate Wav2Vec2, HuBERT, and WavLM Large on four tasks under adaptive 30 dB attacks. Across 12 backbone-task pairs, hierarchical robustification improves robust accuracy by 46.4 pp, while margin refinement adds 4.0 pp for 1.1 pp of clean accuracy. Code and configurations are available at https://github.com/arefmousavi/hierarchical-robust-sfm.

We show that, under some mild assumptions, every quasi-pointed category C carries a canonical near-torsion theory (T,F), where T consists of the 0-supported objects, that is, those admitting a morphism to the initial object 0, and F consists of the subterminal objects. The coreflection and the reflection of an object A are then given by the projection $A \times 0 \to A$ and by the strong-epimorphic part of $A \to 1$, respectively. Using the general construction of the "largest" non-pointed torsion theory associated with a near-torsion theory, we prove that (T,F) is a (non-pointed) torsion theory in the full subcategory of those objects A for which the canonical sequence $t(A) \to A \to f(A)$ is short exact, in the sense that it is both a kernel and a cokernel diagram. This subcategory is the whole of C whenever C is sequentiable, that is, a regular protomodular and quasi-pointed category. We describe the resulting torsion theories in the category of Lie-Rinehart algebras and in the categories of crossed modules over a fixed group. We also show that (T,F) is a torsion theory in the (non-protomodular) category of monoids over a group G all of whose elements have finite order.

Rubric-based reinforcement learning (RL) provides interpretable rewards for aligning large language models (LLMs) by evaluating responses against query-specific evaluation criteria. To construct rubrics at scale, a straightforward approach to LLM-based rubric generation is to prompt an LLM to generate a rubric directly from the query. However, rubrics directly generated by LLMs are vulnerable to reward hacking, since omitted or underspecified criteria allow the policy to obtain high rubric rewards with low-quality responses. Existing LLM-based rubric generation methods improve the granularity and coverage of the generated criteria but do not proactively guard against reward hacking. To address this limitation, we propose RubricArmor, an adversarial framework that exposes and mitigates potential reward hacking at the rubric generation stage before it occurs in subsequent RL. Specifically, RubricArmor performs adversarial evolution, in which an attack step and a repair step alternate over multiple rounds. The attack step simulates the reward hacking of the policy by constructing adversarial responses that satisfy the current rubric but fail to properly complete the task. The repair step then revises the rubric to detect the response defects exposed by the attack step while preserving other valid criteria. Extensive experiments demonstrate that RubricArmor outperforms competitive rubric generation baselines and translates into more effective downstream rubric-based RL.

Code surgery measures a logical operator of a quantum LDPC code with $O(d)$ rounds of syndrome extraction. Lifted surgery amortises this cost on Abelian group-algebra codes by measuring an orbit of logical operators under a translation symmetry in one merged code. We extend it to two-block group-algebra codes over non-Abelian groups and ask whether non-commutativity lets one merged code measure more operators than any Abelian group of its symmetries. We classify the block-affine automorphisms of these codes and find that, measured against this full group, most apparent non-Abelian gains disappear. We prove that the gain is at most the index of a largest Abelian subgroup. We find codes with exact distance up to $13$ where the gain is two, including codes in which one merged code reads out every logical qubit, and codes over products of $A_4$, $S_4$ and SL(2,3) with gain three for a best logical, up to $[[336,26,12]]$. A merged-distance lemma gives a simple condition for the gadget to preserve the code distance. In circuit-level simulations with Relay-BP decoding, at the error rates we can resolve, the non-Abelian gadget is as reliable as, or more reliable than, the Abelian gadgets it replaces within statistical error, while using two to three times fewer rounds.

Sign language-text alignment remains a fundamental challenge for text-driven sign language understanding. Existing methods predominantly rely on appearance-heavy RGB representations, which entangle motion semantics with visual variations and lead to ambiguous motion-language grounding. In this paper, we reformulate sign language-text alignment in a structured kinematic space and propose a kinematics-centric framework that adopts 3D SMPL-X motion as the primary representation. By explicitly modeling the kinematic dynamics of signing in a unified motion space, our approach reduces reliance on appearance signals and yields more semantically consistent representations. To capture the compositional nature of sign language, we introduce a gloss-guided local alignment mechanism that leverages gloss temporal spans as weak supervision to decompose continuous motion into coherent segments and establish fine-grained motion-text correspondences, thereby reducing ambiguity in localizing word-level semantics in continuous signing. Furthermore, we develop a visual distillation strategy, where RGB signals serve as privileged supervision during training to provide complementary contextual cues, while being completely removed at inference time. Extensive experiments on standard benchmarks demonstrate that our method achieves state-of-the-art bidirectional retrieval performance on CSL-Daily and competitive results on PHOENIX-2014T. These results highlight the effectiveness of kinematic representations and explicit local grounding for sign language-text alignment.

Large Language Model (LLM) inference has become the dominant workload in modern AI systems, requiring serving infrastructures to maximize throughput while meeting strict latency Service-Level Objectives (SLOs). Since state-of-the-art LLMs exceed the compute and memory capacity of a single GPU, inference is commonly distributed across multiple GPUs using tensor parallelism (TP), pipeline parallelism (PP), or hybrid parallelism (HB). However, selecting the most effective parallelism strategy remains challenging due to complex interactions among computation, communication, pipeline utilization, sequence length, batch size, and model architecture. Existing approaches largely rely on empirical evaluation and provide limited analytical insight into the trade-offs among these strategies, particularly across the distinct prefill and decoding phases of inference. In this paper, we present a unified analytical framework for modeling distributed LLM inference under TP, PP, and HB. The framework decomposes end-to-end latency into computation, inter-GPU communication, and pipeline bubble overhead, and derives analytical models that capture TP collective communication, PP point-to-point communication, and pipeline utilization as functions of hardware, model, and workload characteristics. The model further characterizes the differing execution behavior of prefill and decoding, explaining why PP-oriented configurations favor compute-intensive prefill while TP-oriented configurations reduce decoding latency by eliminating pipeline bubbles. Experiments with modern LLMs on multi-GPU platforms validate the model and confirm the fundamental compute-communication trade-off across parallelism strategies. The framework provides practical guidance for parallelism selection, capacity planning, and optimization of future LLM serving systems.

Quantum hardware advances now make it practical to explore quantum approaches to scientific problems. Applied quantum computing research sits at the intersection of domain knowledge, algorithms, theoretical physics, device physics, and quantum and classical computational methods. The breadth of expertise required and the inherent project complexity challenge not only any individual researcher, but also generic AI systems. Here, we introduce the Quantum Agentic Operating System (QAOS), a structured agentic research system designed to address this challenge for quantum and computational R&D projects. QAOS is built around a nonlinear workflow graph of heterogeneous multi-agent nodes, with a controlled flow of context and computational resources. It decomposes a complex research project into sandboxed multi-agent tasks executed under constraints from the project graph, task-relevant methodologies, and necessary verification steps. We demonstrate QAOS on a quantum chemistry prototyping task, in which it is asked to set up a minimal model for a proton-transfer problem and to implement its solution using sample-based quantum diagonalization (SQD), together with classical reference methods such as FCI (exact diagonalization) and density functional theory (DFT). We compare the QAOS solution to those obtained with baseline agents (Claude Sonnet 5 with the Claude Code harness). In contrast to QAOS, the baseline agents silently ignore explicit instructions, and the runs show large variability.