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01.
arXiv (CS.CV) 2026-06-17

StereoFactory: A Unified Merging Framework for Robust Stereo Matching

Stereo matching has advanced through foundation models trained on large-scale datasets, yet this paradigm suffers from a scalability bottleneck: incorporating new data requires costly joint retraining. Model merging offers a scalable post-hoc alternative by integrating knowledge from specialized models after source checkpoints are available. However, existing merging methods typically retain all available models or rely on greedy inclusion, which can preserve harmful task-vector interference. We propose StereoFactory, a coarse-to-fine evolutionary framework for adaptive model merging. Stage~1 employs a genetic algorithm to search the combinatorial space of model subsets, determining which models should participate. Stage~2 addresses module-level knowledge specialization (different functional modules exhibit distinct preferences for knowledge sources) through CMA-ES optimization of architecture-adaptive routing over the selected task vectors, with optional module-level scaling. Experiments across two architectures and four benchmarks demonstrate that StereoFactory consistently achieves the best four-benchmark average under the same checkpoint pool, reducing the average error from 3.80 to 3.30 on NMRF and from 2.88 to 2.19 on FoundationStereo relative to the strongest controlled baseline. The post-hoc search requires only 2.7–3.7\% of the corresponding joint-retraining wall-clock time. Analysis reveals that knowledge contributions are inherently module-specific, and selected subsets can transfer across architectures with minimal degradation. Code will be publicly released upon acceptance at: https://github.com/XiandaGuo/StereoFactory.

02.
arXiv (CS.CL) 2026-06-12

How reliable are LLMs when it comes to playing dice?

We investigate the probabilistic reasoning capabilities of large language models through a controlled benchmarking study on discrete probability problems. We constructed two datasets, respectively a set of standard exercises and a set of counterintuitive exercises, designed to trigger heuristic reasoning, and evaluated 8 state-of-the-art models, each tested with and without Chain-of-Thought prompting. Models achieve an average accuracy of 0.96 on standard problems but only 0.59 on counterintuitive ones. We further provide empirical evidence of token bias: performance drops by over 20% when canonical formulations are replaced by disguised variants. Embedding misleading suggestions in the prompt reduces performance by up to 34%, with no model proving immune. Taken together, the reported findings suggest that current LLMs are not yet genuine probabilistic reasoners, despite their success in advanced mathematical problems.

03.
arXiv (quant-ph) 2026-06-12

A Quantum Algorithm for Random Number Generation

arXiv:2606.13034v1 Announce Type: new Abstract: We present a quantum algorithm for random number generation that achieves a provable quadratic speedup over classical Markov chain mixing, building on the Diaconis-Shahshahani Fourier analysis of the top-to-random card shuffle. The algorithm integrates three quantum primitives into a unified mixing circuit: the Quantum Fourier Transform (QFT), which diagonalizes the Markov transition operator; controlled phase rotations, which encode the shuffle eigenvalue spectrum; and the Grover diffusion operator, which acts as a quantum analogue of the Aldous-Diaconis strong uniform stopping time by reflecting amplitudes about their mean at each iteration. For an n-qubit register, the mixing time is O(\sqrt{n \log n}) iterations. Extending to m qudits of local dimension d reduces this to O(\sqrt{\log_d N}) iterations, where N = d^m, compared to the classical O(n \log n) bound. The qudit formulation further reduces QFT circuit depth from O(\log^2 N) to O(\log_d^2 N) gates per layer by encoding the same N-state space using m = \log_d N subsystems instead of \log_2 N qubits. We validate both variants on IBM superconducting hardware.

04.
arXiv (CS.LG) 2026-06-15

Realizing Native INT8 Compute for Diffusion Transformers on Consumer GPUs: A Fused INT8 GEMM Kernel for Ideogram 4.0

arXiv:2606.14598v1 Announce Type: new Abstract: Post-training INT8 (W8A8) quantization of diffusion transformers is widely deployed as a speed optimization, yet on consumer Ampere GPUs it is frequently slower than the FP8 and NF4 alternatives it is meant to beat. We trace this to a software artifact: the production "INT8" forward quantizes weights and activations only to immediately dequantize them back to bf16 and run a bf16 matrix multiply, never engaging the GPU's INT8 tensor cores, so the hardware's compute advantage is left entirely unrealized. We close this gap with a single fused Triton INT8 GEMM (int8xint8->int32 on Ampere tensor cores, with per-token x per-channel dequantization and bias folded into the epilogue, autotuned per GEMM shape) dropped into the Ideogram 4.0 diffusion transformer's linear layers in place of the dequantize-to-bf16 path. In the kernel, the int8xint8->int32 accumulation is bit-exact against torch._int_mm and the dequantized output matches the reference at cosine similarity 1.0 with no NaNs, running 2.8-4.2x faster than bf16 per GEMM. End to end it delivers a ~1.1x (~9-10%) speedup at 768px, and at 1024px it generates an image in 156.5 s on a single RTX 3090, faster than the single-card NF4 (164.5 s) and FP8 (172.9 s) baselines, at no measurable quality cost on these point estimates (PickScore/CLIPScore). INT8 thus goes from the slowest variant to the fastest, and 1024px becomes single-GPU feasible. The primary speed criterion (beat FP8, by ~9.5%) is comfortably met; the NF4 margin (~4.9%, single-run n=4) is within run-to-run variance we did not quantify and is best read as consistent with meeting the stretch target. We close with an honest deployment map: the win is specific to consumer Ampere, and on A100 and B200 the same kernel loses to those cards' fast native bf16/FP8 paths.

05.
arXiv (CS.CL) 2026-06-12

Getting Better at Working With You: Compiling User Corrections into Runtime Enforcement for Coding Agents

Interactive LLM agents are becoming part of daily work, but they do not reliably become easier to work with over time: a correction remembered in one session may still be violated in the next. We study this gap between preference access and preference compliance. In tasks derived from anonymized real-user friction cases, Mem0 memory still leaves 57.5% of applicable preference checks violated. We introduce Test-time Rule Acquisition and Compiled Enforcement (TRACE), a drop-in skill-layer pipeline for coding-agent runtimes that mines user corrections, rewrites them as atomic rules, and compiles them into runtime checks that must pass before an agent completes future tasks. Unlike runtime checks written ahead of time by developers, TRACE skills come from the user's own chat corrections. We evaluate TRACE with simulated user-in-the-loop experiments on ClawArena coding-agent tasks and MemoryArena-derived memory-intensive tasks. On ClawArena, TRACE reduces held-out preference violation from 100.0% to 37.6% on in-distribution tasks and from 100.0% to 2.0% on out-of-distribution tasks. On MemoryArena-derived tasks, TRACE reduces in-distribution violation from 100.0% to 60.5% while matching or exceeding the strongest memory baseline on task pass. These results suggest that compiling corrections into runtime enforcement can address a repeated-friction failure mode that memory alone does not reliably solve, reducing the need for users to restate the same correction across future sessions. Experiment code is available at https://github.com/YujunZhou/TRACE_exp, and the deployable skill is available at https://github.com/YujunZhou/tellonce.

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

libhmm: A Modern C++20 Library for Hidden Markov Models with Correct MLE Emission M-Steps

Authors:

arXiv:2605.29208v2 Announce Type: replace-cross Abstract: We describe libhmm, a C++20 library for Hidden Markov Model parameter estimation, sequence decoding, and model selection. libhmm addresses two gaps in existing software: the absence of a well-maintained, zero-dependency C++ HMM library suitable for embedding in production systems, and the widespread use of method-of-moments (MOM) approximations in the emission distribution M-step of the Baum-Welch algorithm. The library implements correct maximum likelihood estimators for sixteen scalar emission distributions, including an ECME algorithm for the location-scale Student-t distribution, Newton-Raphson maximization for Gamma, Beta, Weibull, and Negative Binomial distributions, and the von Mises distribution for circular data. All forward-backward and Viterbi calculations operate in full log-space. SIMD acceleration is provided for AVX-512, AVX2, SSE2, and ARM NEON via compile-time dispatch with scalar fallback. Version 4 adds multivariate observation support via the BasicHmm template, with three multivariate emission families (diagonal Gaussian, full-covariance Gaussian, and independent components) each with correct weighted MLE M-steps. Python bindings are available via the companion package pylibhmm. We compare libhmm against established C and C++ HMM libraries and against published R reference packages on seven real-data benchmarks, and discuss the architectural tradeoffs made in the design.

07.
arXiv (CS.CL) 2026-06-15

MASLab: A Unified and Comprehensive Codebase for LLM-based Multi-Agent Systems

LLM-based multi-agent systems (MAS) have demonstrated significant potential in enhancing single LLMs to address complex and diverse tasks in practical applications. Despite considerable advancements, the field lacks a unified codebase that consolidates existing methods, resulting in redundant re-implementation efforts, unfair comparisons, and high entry barriers for researchers. To address these challenges, we introduce MASLab, a unified, comprehensive, and research-friendly codebase for LLM-based MAS. (1) MASLab integrates over 20 established methods across multiple domains, each rigorously validated by comparing step-by-step outputs with its official implementation. (2) MASLab provides a unified environment with various benchmarks for fair comparisons among methods, ensuring consistent inputs and standardized evaluation protocols. (3) MASLab implements methods within a shared streamlined structure, lowering the barriers for understanding and extension. Building on MASLab, we conduct extensive experiments covering 10+ benchmarks and 8 models, offering researchers a clear and comprehensive view of the current landscape of MAS methods. MASLab will continue to evolve, tracking the latest developments in the field, and invite contributions from the broader open-source community.

08.
arXiv (CS.AI) 2026-06-16

Discovering Lattice Reduction Strategies via Self-Play

arXiv:2606.15301v1 Announce Type: cross Abstract: The Lenstra-Lenstra-Lovász (LLL) algorithm is a seminal contribution to computer science used for lattice basis reduction, yet its polynomial-time outputs produce bases that are far from optimal as the dimension grows. We show that deep reinforcement learning can discover strictly superior, generalizable reduction strategies by interacting with the primitive action space of LLL. We formulate lattice reduction as a single-player Markov Decision Process (MDP) and train a deep residual network using an AlphaZero-style self-play pipeline augmented with adaptive-horizon MCTS (Monte Carlo Tree Search), which couples multi-step network predictions with an entropy-gated expansion mechanism. The resulting policy, DeltaStar, is trained exclusively on small $8$-dimensional $q$-ary lattices and requires fewer primitive row operations than LLL. Crucially, it generalizes zero-shot to unseen moduli and higher dimensions up to $n=32$ without retraining.

09.
arXiv (CS.CV) 2026-06-11

LASA: A Weak Supervision Method for Open-Vocabulary Scene Sketch Semantic Segmentation

Open-vocabulary scene sketch semantic segmentation aims to assign dense semantic labels to sparse line drawings based on flexible category vocabularies specified at inference time, without relying on pixel-level annotations during training. Unlike natural images, sketches lack texture and color cues, making semantic understanding heavily dependent on stroke layout and spatial configuration, a challenge that renders single-layer vision-language features inherently unstable. Our key observation is that attention maps from different Vision Transformer layers encode complementary spatial cues: shallow layers capture global structural layouts, while deeper layers focus on local stroke intersections and object parts. This suggests that cross-layer aggregation provides a more robust structural prior than any individual layer alone. Leveraging this insight, we propose a structure-aware framework built upon Layer-wise Accumulated Structural Attention (LASA), which aggregates multi-layer attention to guide hierarchical semantic alignment under weak supervision and refine predictions during inference. Experiments on FS-COCO, SFSD, and FrISS show that LASA improves mIoU by $+3.43$, $+8.01$, and $+15.74$ over the prior weakly supervised baselines, demonstrating consistent gains in both segmentation accuracy and spatial coherence. Our source code will be made publicly available.

10.
arXiv (quant-ph) 2026-06-16

Worst-case depth hierarchy for shallow quantum circuits

arXiv:2606.16425v1 Announce Type: new Abstract: Circuit depth is a central resource in complexity theory. While bounded-depth classical circuits admit well-understood hierarchy theorems, the internal structure of constant-depth quantum computation remains comparatively unexplored. We prove an explicit depth hierarchy theorem for $\mathsf{QNC}^0$. For each $d\ge 12$, we construct a family of two-round interactive problems on which no depth-$(d-1)$ quantum circuit can achieve near-perfect success, regardless of gate set, circuit size, or ancillary qubits. In contrast, we prove that our construction admits realizations by simple bounded fan-in quantum circuits of depth larger than $d$ by a small constant factor. Moreover, all bounded fan-in classical circuits of sublogarithmic depth (in the input size) fail to achieve perfect success on these tasks for every $d$, yielding a hierarchy of problems that show unconditional quantum advantage of $\mathsf{QNC}^0$ over $\mathsf{NC}^0$. A key obstacle is the scarcity of lower bound techniques for quantum circuits. To address this, we develop methods to analyze how depth affects a circuit's ability to realize nonlocal correlations amongst its output qubits in a fine-grained manner. Our approach exploits the correspondence between constraint systems and nonlocal games, translating group-theoretic constructions into rigid operator-valued constraint systems and then into non-local games. In particular, we construct constraint systems whose unique faithful operator-valued solutions require every perfect strategy, and every near-perfect strategy to a fixed precision, to implement multi-controlled phase operations. This reduces to a nonlocal unitary-synthesis problem, yielding depth lower bounds for both shallow quantum and classical circuits. These results show that increasing depth strictly increases computational power within $\mathsf{QNC}^0$, establishing a genuinely quantum hierarchy.

11.
arXiv (CS.CL) 2026-06-17

Compositional Skill Routing for LLM Agents: Decompose, Retrieve, and Compose

Authors:

LLM agents increasingly rely on external skills – reusable tool specifications – but real-world tasks often require composing multiple skills, not just selecting one. We formalize this as the Compositional Skill Routing problem: given a complex user query and a large skill library, decompose the query into atomic sub-tasks, retrieve the appropriate skill for each sub-task, and compose an executable plan. We present SkillWeaver, a decompose-retrieve-compose framework combining an LLM task decomposer, a bi-encoder skill retriever with FAISS indexing, and a dependency-aware DAG planner. To support evaluation, we introduce CompSkillBench, a benchmark of 300 compositional queries over 2,209 real MCP server skills spanning 24 functional categories, sourced from the public MCP ecosystem. Our experiments reveal that task decomposition quality is the primary bottleneck: standard LLM decomposition reaches only 34.2% category recall at the step level. To address this, we propose Iterative Skill-Aware Decomposition (SAD), a retrieval-augmented feedback loop that iteratively aligns decomposition with available skills. SAD improves decomposition accuracy from 51.0% to 67.7% (+32.7%, Wilcoxon p < 10^-6) in a single iteration; DA-conditioned analysis confirms that correct granularity is the prerequisite for effective retrieval (CatR@1 rises from 34% to 41% when DA=1). SkillWeaver reduces context window consumption by over 99%, and transfer experiments confirm generalization (+35.6% relative DA gain even when target categories are absent from the retrieval pool).

12.
arXiv (quant-ph) 2026-06-15

Real-time pseudo entropy and modular-Hamiltonian correlations

arXiv:2606.14208v1 Announce Type: cross Abstract: Pseudo entropy is a complex-valued generalization of entanglement entropy defined from a reduced transition matrix. We study the pseudo entropy associated with a real-time transition matrix between an initial pure state and its unitary time evolution. For a subsystem $A$, we show that the short-time behavior of real-time pseudo entropy is governed by the correlation between the physical Hamiltonian $H$ and the modular Hamiltonian $K_A=-\log\rho_A$ of the initial reduced state, $ S_A(t,0)=S_A(0)-it \langle K_A(H-\langle H\rangle)\rangle + \mathcal{O}(t^2)$. For Hermitian dynamics, the initial imaginary response is controlled by the symmetrized covariance of $H$ and $K_A$ with an overall minus sign, while the initial real response is governed by their commutator. Thus the imaginary part of real-time pseudo entropy is not merely a branch artifact: it is a time-oriented modular response generated by the correlation between microscopic time evolution and subsystem coarse graining. We clarify the relation of this result to the known first law of pseudo entropy, derive an all-order expression in a Schmidt-diagonal model, recover thermal pseudo entropy as a special case, illustrate the covariance/commutator decomposition in a two-qubit model, and confirm the covariance response in transverse-field Ising-chain quenches, including a finite-size study of a modular susceptibility near the Ising critical region. We discuss how this amplitude-level oriented response can be related to ordinary entropy production, and also give a concrete $\mathcal{PT}$-symmetric toy-model illustration of the non-Hermitian extension.

13.
arXiv (CS.CV) 2026-06-18

Low-Cost Neuromorphic Fall Detection Using Synthetic Event Data and Hybrid SNNs

This work presents the development of hybrid models that integrate spiking neural networks (SNNs) with components of convolutional neural networks (CNNs) to learn from simulated event-based camera data (Dynamic Vision Sensor, DVS) generated from conventional smartphone videos. Aimed primarily at human fall detection, the approach leverages the energy efficiency and spatio-temporal processing capabilities of SNNs by converting video frames into event-based data. The proposed models are evaluated through simulations on multiple datasets, comparing their performance to that of traditional machine learning models. Results demonstrate significant gains in efficiency without sacrificing accuracy, underscoring the potential of combining SNNs and DVS technology for complex tasks in real-world environments.

14.
arXiv (CS.CV) 2026-06-18

Spatially Stratified Distillation for Heterogeneous Radar Place Recognition

Scalable, all-weather place recognition increasingly relies on heterogeneous radar place recognition to bridge diverse hardware platforms. A notable application is matching queries from cost-effective 4D automotive radars against high-fidelity reference maps built by dense spinning radars. This process is fundamentally limited by the extreme sparsity (and narrow field-of-view) of the 4D sensor, which captures only a fraction of the structural density present in the spinning radar database. Prior efforts address this issue by unifying different radar signals. That is, projecting both signals into a common representational space. Yet, they suffer performance degradation in multi-session environments. In this paper, we propose spatially-stratified distillation (SSD); a strategy that replaces standard uniform distillation with an asymmetric spatial alignment derived directly from physical radar returns. In regions where both radars exhibit overlapping returns, SSD enforces strong feature alignment. Crucially, in sparse regions where the 4D student lacks returns but the teacher contains valid structure within the shared field of view, SSD applies heavily discounted distillation weights. Extensive evaluations of the recent HeRCULES dataset demonstrate that SSD significantly outperforms prior place recognition methods, achieving state-of-the-art results on its challenging dynamic sequences.

15.
arXiv (CS.LG) 2026-06-19

A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel components

arXiv:2503.17386v2 Announce Type: replace-cross Abstract: Crashworthiness is a key performance measure in the design of safety-critical vehicle panel components such as B-pillars. Finite element (FE) simulations are widely used to evaluate crash responses but remain computationally expensive for large-scale, nonlinear impact scenarios, particularly when integrated into iterative design and optimisation processes. Although machine learning-based surrogate models have been developed for rapid crashworthiness analysis, they exhibit limitations in detailed representation of complex 3-dimensional components. Graph Neural Networks (GNNs) have emerged as a promising solution for processing data with complex structures. However, existing GNN models often lack sufficient accuracy and computational efficiency to meet industrial demands. This paper proposes Recurrent Graph U-Net (ReGUNet), a graph-based surrogate model for crashworthiness analysis of vehicle panel components. By representing FE meshes in graph form, the model naturally accommodates complex irregular structural geometries. Its hierarchical architecture improves computational efficiency and accuracy, while the introduction of recurrence enhances stability of temporal predictions over multiple time steps. A side-impact case study of hot-stamped steel B-pillars with varying geometries is used to generate training dataset. The trained model demonstrates high accuracy in predicting the dynamic deformation behaviour and crashworthiness indicators of previously unseen component designs. ReGUNet achieves over a 52% reduction in the average deformation prediction error relative to baseline methods, together with markedly improved computational efficiency. ReGUNet provides rapid and reliable crashworthiness assessments, which in turn accelerates the design cycle of vehicle panel components.

16.
arXiv (CS.AI) 2026-06-11

Intelligent Automation for Embodied Benchmark Construction: Pipelines, Embodiments, Simulators, and Trends

arXiv:2606.12207v1 Announce Type: cross Abstract: Embodied intelligence now spans navigation, household assistance, manipulation, autonomous driving, aerial agents, and multimodal large-model control. This expansion has made benchmark construction a central bottleneck for reliable evaluation. Unlike static datasets, embodied benchmarks combine task specifications, environments, robot data, demonstrations, annotations, metrics, evaluation scripts, and release policies into a single evaluation system. This survey reviews the literature through a five-stage construction pipeline: requirement and task construction, data acquisition, data cleaning and annotation, benchmark suite generation and metric definition, and evaluation execution with diagnostic feedback. For each stage, the survey analyzes the transition from manual curation to traditional automation, foundation-model assistance, and agentic closed-loop workflows. It also compares qualitative construction costs across human labor, data and asset acquisition, compute and simulation, validation and debugging, governance and maintenance, and rework risk. The main conclusion is that automation does not simply reduce benchmark cost. Instead, it often shifts cost toward validation, auditability, version control, and long-term governance. Progress in embodied evaluation will therefore depend not only on larger benchmark suites, but also on construction pipelines that are diagnosable, auditable, and responsibly refreshable.

17.
bioRxiv (Bioinfo) 2026-06-19

HTS-Oracle v2: Prospective AI-Guided Discovery and Experimental Validation of Small Molecule Modulators Across Multiple Targets

High-throughput screening (HTS) remains the cornerstone of early-phase small molecule discovery yet consistently underperforms against immunotherapy targets, yielding validated hit rates below 0.1%. Here we introduce HTS-Oracle v2, which features rigorous cross-validation that ensures honest performance estimates. HTS-Oracle v2 was trained and validated across four clinically significant immune checkpoint targets (CD28, ICOS, LAG-3, and TIGIT) achieving ROC-AUC values of 0.968, 0.969, 0.875, 0.928 respectively under rigorous cross-validation. For prospective experimental validation, HTS-Oracle v2 was applied to an 8,960-compound Enamine Protein Mimetic Library, selecting only 25 compounds per target for experimental testing using temperature-related intensity change (TRIC) technology, a 99.7% reduction in screening burden. HTS-Oracle v2 identified 4, 5, 4, and 6 validated binders from 25 prospectively selected compounds per target, corresponding to validated hit rates of 16%, 20%, 16%, and 24%, respectively. Notably, 67-80% of all experimentally confirmed hits across the full 8,960-compound library were captured within just 25 model-selected compounds per target. For CD28, this represents a 28-fold improvement over HTS-Oracle v1 (239x versus 8.4x), establishing HTS-Oracle v2 as an efficient platform for AI-guided prospective hit discovery across immunotherapy targets.

18.
arXiv (CS.AI) 2026-06-16

A comparative and critical study of EEGNet for fNIRS-driven cognitive load classification

arXiv:2606.16160v1 Announce Type: cross Abstract: Accurately classifying cognitive load from functional near-infrared spectroscopy (fNIRS) signals remains a significant challenge due to temporal variability, inter-subject differences, and sensitivity to preprocessing choices. This study provides a comprehensive evaluation of EEGNet for fNIRS-based cognitive load classification by systematically examining the effects of temporal segmentation strategies (overlapping vs. non-overlapping), window lengths (10s, 20s, 30s), feature extraction methods (Analysis of Variance (ANOVA), Principal Component Analysis (PCA), Fast Independent Component Analysis (FastICA)), learning rate configurations (fixed and adaptive), and evaluation protocols (random split vs. subject-independent (SI)). Results from random-split experiments show that overlapping segmentation, combined with smaller fixed learning rates (0.01-0.001), yields the highest accuracies, due to temporal redundancy and dense sampling of hemodynamic transitions. However, SI evaluation reveals a substantial drop in accuracy, demonstrating limited generalization to unseen participants. Under SI evaluation, non-overlapping segmentation outperformed overlapping windows, with the best accuracy of 56.11% achieved using PCA features with a 20-second window and a 0.1 learning rate. These findings indicate that eliminating temporal redundancy helps the model learn more robust and generalizable representations of cognitive load across individuals. Although adaptive learning rate strategy improved training stability, it did not surpass the performance of optimally selected fixed learning rates. The study highlights the critical role of segmentation strategy and learning rate selection in improving model generalization and identifies methodological considerations essential for developing reliable, real-time, and SI cognitive load classification systems using fNIRS.

19.
arXiv (CS.CV) 2026-06-19

Rethinking Robust Adversarial Concept Erasure in Diffusion Models

Concept erasure aims to selectively unlearning undesirable content in diffusion models (DMs) to reduce the risk of sensitive content generation. As a novel paradigm in concept erasure, most existing methods employ adversarial training to identify and suppress target concepts, thus reducing the likelihood of sensitive outputs. However, these methods often neglect the specificity of adversarial training in DMs, resulting in only partial mitigation. In this work, we investigate and quantify this specificity from the perspective of concept space, i.e., can adversarial samples truly fit the target concept space? We observe that existing methods neglect the role of conceptual semantics when generating adversarial samples, resulting in ineffective fitting of concept spaces. This oversight leads to the following issues: 1) when there are few adversarial samples, they fail to comprehensively cover the object concept; 2) conversely, they will disrupt other target concept spaces. Motivated by the analysis of these findings, we introduce S-GRACE (Semantics-Guided Robust Adversarial Concept Erasure), which grace leveraging semantic guidance within the concept space to generate adversarial samples and perform erasure training. Experiments conducted with seven state-of-the-art methods and three adversarial prompt generation strategies across various DM unlearning scenarios demonstrate that S-GRACE significantly improves erasure performance 26%, better preserves non-target concepts, and reduces training time by 90%. Our code is available at https://github.com/Qhong-522/S-GRACE.

20.
arXiv (CS.LG) 2026-06-17

Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries

arXiv:2507.11366v2 Announce Type: replace-cross Abstract: We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based methods (time-average convergence) or contraction-map-based methods (last-iterate convergence). We propose a new method based on Hamiltonian dynamics in physics and prove that it can characterize the set of NE in a finite (linear) number of iterations of alternating gradient descent in the unbounded setting, modulo degeneracy, a first in online optimization. Unlike standard methods for computing NE, our proposed approach can be parallelized and works with arbitrary learning rates, both firsts in algorithmic game theory. Experimentally, we support our results by showing our approach drastically outperforms standard methods.

21.
arXiv (math.PR) 2026-06-16

A Low-Regularity Semigroup Sewing Lemma via Quotient Structures

arXiv:2606.16164v1 Announce Type: new Abstract: We develop a low-regularity Sewing theory for the semigroup coboundary $\hat\delta=\delta-a$ associated with a strongly continuous semigroup $S$. Unlike the ordinary low-regularity Sewing problem, the semigroup setting has an intrinsic algebraic non-uniqueness below the threshold $1$, in the sense that solutions are canonical only modulo semigroup cocycles. Accordingly, the natural target is a quotient space rather than an increment space. We identify this quotient structure and construct the corresponding semigroup Sewing map. The construction uses a frozen terminal-time transform, which rewrites semigroup defects, for each terminal time, as ordinary low-regularity Sewing problems on a frozen simplex. This reduction, however, does not by itself produce a genuine semigroup increment; the main additional step is to prove that the frozen solution classes are compatible as the terminal time varies and hence assemble into a canonical quotient class for $\hat\delta$. This yields canonical classes for $0

22.
arXiv (CS.LG) 2026-06-18

How Does the ReLU Activation Affect the Implicit Bias of Gradient Descent on High-dimensional Neural Network Regression?

arXiv:2603.04895v2 Announce Type: replace-cross Abstract: Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima. The implicit bias refers to the limiting global minimum that is attained by a common optimization algorithm, such as gradient descent (GD). In this paper, we characterize the implicit bias of GD for training a shallow ReLU model with the squared loss on high-dimensional random features. Prior work (Vardi and Shamir, 2021) showed that the implicit bias does not exist in the worst-case, or corresponds exactly to the minimum-$\ell_2$-norm interpolating solution under exactly orthogonal data (Boursier et al., 2022). Our work interpolates between these two extremes and shows that, for sufficiently high-dimensional random data, the implicit bias approximates the minimum-$\ell_2$-norm solution with high probability with a gap on the order $\Theta(\sqrt{n/||\lambda||_1})$, where $n$ is the number of training examples and $\lambda$ denotes the spectrum of the data covariance matrix. Our results are obtained through a novel primal-dual analysis that carefully tracks the evolution of predictions, data-span coefficients, as well as their interactions, and show that the ReLU activation pattern quickly stabilizes with high probability over random data.

23.
arXiv (CS.CV) 2026-06-18

Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm

This paper addresses low-rank tensor completion (LRTC) by proposing a novel nonconvex surrogate, namely the ratio of the tensor nuclear norm to the tensor Ky Fan p-k norm (TNPK), to accurately approximate the tensor tubal rank. The TNPK possesses appealing properties, including scale invariance, parameter flexibility, and the existence of closed-form solutions under specific choices of p and k. With specific parameter settings of p and k, it reduces to the ratio of the tensor nuclear norm to the tensor Ky Fan k norm (TNK) or the ratio of the tensor nuclear norm to the tensor Frobenius norm (TNF). We construct a LRTC model and, under the tensor null space property (NSP), prove that low-rank tensors are local minimizers of the proposed model. Moreover, we derive the proximal operator of the Ky Fan p-k inverse-norm and further develop an efficient alternating direction method of multipliers (ADMM) algorithm with guaranteed subsequential convergence under mild conditions. Extensive experiments on synthetic and real-world datasets validate the superior performance of our method against state-of-the-art competitors.

24.
arXiv (CS.CL) 2026-06-18

LLM Compression by Block Removal with Constrained Binary Optimization

In this paper, we formulate the compression of large language models (LLMs) by optimally deleting transformer blocks (``block removal'') as a constrained binary optimization (CBO) problem that can be mapped to a physical system (Ising glass), whose energies are a strong proxy for downstream model performance. This formulation enables an efficient ranking of a large number of candidate block-removal configurations yielding many high-quality, non-trivial solutions beyond those only removing consecutive regions. Our method performs strongly in the deep compression regime, such as for 50% compression of Llama-3.3-70B-Instruct, where we achieve an almost 23 percentage point increase on the MMLU benchmark compared to other state-of-the-art (SOTA) block-removal methods. For lighter compression, it performs on par with those methods across several benchmarks for Llama-3.1-8B-Instruct, Qwen3-14B (both before and after retraining), as well as Llama-3.3-70B-Instruct. The approach is computationally efficient and requires only forward and backward passes on a calibration dataset for a few active parameters. Additionally, we demonstrate that using good heuristic solvers for the CBO problem provides solutions that perform well on downstream tasks in negligible runtime when it is unfeasible to solve the problem exactly. The method can be readily applied to any architecture. We illustrate this generality on the recent NVIDIA-Nemotron-3-Nano-30B-A3B-FP8 model, which exhibits a highly inhomogeneous and challenging block structure, and where we outperform SOTA for AIME25 and GPQA when removing either 2 attention layers or 3 mixture-of-experts layers.

25.
arXiv (CS.CL) 2026-06-16

Learn-to-learn on Arbitrary Textual Conditioning: A Hypernetwork-Driven Meta-Gated LLM

Conventional LLMs may suffer from corpus heterogeneity and subtle condition changes. While finetuning can create the catastrophe forgetting issue, application of meta-learning on LLMs is also limited due to its complexity and scalability. In this paper, we activate the meta-signal of $\beta$ within the SwiGLU blocks, resulting in a meta-gating mechanism that adaptively adjusts the nonlinearity of FFN. A hypernetwork is employed which dynamically produces $\beta$ on textual conditions, providing meta-controllability on LLMs. By testing on different condition types such as task, domain, persona, and style, our method outperforms finetuning and meta-learning baselines, and can generalize reasonably on unseen tasks, condition types, or instructions. Our code can be found in https://github.com/AaronJi/MeGan.