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01.
arXiv (math.PR) 2026-06-18

Stable size-biasing and the positive scale-mixture order of generalized Gaussian laws

arXiv:2606.18458v1 Announce Type: new Abstract: Let $X_r\sim N_r(0,1)$ be the centered unit-scale generalized Gaussian random variable with density proportional to $\exp(-|x|^r/2)$. We prove that, for $p,q>0$, there exists a strictly positive random variable $V$, independent of $X_q$, such that $X_p\stackrel{d}{=}VX_q$ if and only if $p\le q$. Moreover, the law of $V$ is unique. For $pq$, the required Mellin quotient, viewed as the candidate characteristic function of $\log V$, is unbounded by Stirling's formula, and hence cannot be a characteristic function. The factor laws form a multiplicative cocycle, $V_{p,r}\stackrel{d}{=}V_{p,q}V_{q,r}$, for $p\le q\le r$, where the factors on the right-hand side are independent copies. Thus the Mellin quotient isolated by Dytso, Bustin, Poor and Shamai is realized constructively throughout the $p

02.
medRxiv (Medicine) 2026-06-18

Hospital staff views on the visibility, role and impact of Acute Learning Disability Liaison Services in Wales: a service evaluation

People with a learning disability experience marked health inequalities. In Wales, Acute Learning Disability Liaison Services (ALDLS) are delivered by specialised learning disability services, and all roles within them are undertaken by Learning Disability Liaison Nurses (LDLN). These services aim to enable access to, and delivery of, secondary care by supporting reasonable adjustments, facilitating communication, and coordinating care for people with learning disability during hospital encounters. However, independent evidence of the impact of ALDLS on patient care remains limited. This evaluation tries to address this evidence gap by examining hospital staff perceptions of the visibility, role, and impact of ALDLS across Welsh Health Boards, with the aim of informing service design and development and improving secondary care access and care for people with learning disability. The service evaluation used a qualitative approach involving interviews and a focus group with hospital staff across the seven Welsh Health Boards who had experience working with or interacting with ALDLS staff to care for patients with learning disability. Findings cover six key areas including i) visibility and delivery of ALDLS, ii) Barriers and challenges to effective ALDLS delivery, iii) Enablers of effective ALDLS delivery, iv) Positive impacts for patients with learning disability, v) Negative impacts and unintended consequences when the service is absent or limited, and vi) Participants recommendations for future improvements of ALDLS. To synthesise the findings, we developed an overview diagram, which illustrates how ALDLS may influence care quality in acute hospitals. The overview places the liaison service at the centre, showing how organisational enablers and barriers shape its delivery, and how its core functions support improvements in safety, timeliness, effectiveness, efficiency, equity, and patient-centred care. From the findings we have identified recommendations for practice and policy. These include that ALDLS should be recognised as a core, safety-critical component of acute hospital care for people with a learning disability, rather than an optional add-on. In practice, services should be more visibly embedded within routine pathways, with consistent site-based presence, clear referral criteria, early identification through electronic flagging and notification systems, and routine involvement in multidisciplinary planning for complex admissions and procedures. At policy level, ALDLS provision should be recognised within equality and patient safety frameworks as an essential service requiring sustained investment, national minimum configuration standards, adequate staffing, and better-integrated digital systems to support continuity, equitable access, and person-centred care.

04.
arXiv (quant-ph) 2026-06-15

Interpreting Bohm-like quantum potentials in "Computing quantum waves exactly from classical action"

arXiv:2605.20443v3 Announce Type: replace Abstract: The recent posting arXiv:2605.02621 [14], commenting on the article rspa.2025.0413 [7], argues that the proof of Lemma 3.1 in [7] is missing the spatial derivative of the density, which would lead to a Bohm-like quantum potential. This technical note shows why the propagated density is independent of space in the Feynman propagator construction of Lemma 3.1. This is done by extending the proof of Lemma 3.1 explicitly with Bohm-like quantum potential terms along the stationary action paths, and then showing that these terms are exactly zero. In [7], this property can also be verified directly on most examples (double slit, Aharonov-Bohm, potential well, harmonic oscillator, tunneling, EPR, QED), as well as in the derivations of the Pauli, Dirac, and Maxwell equations. For more general nonlinear actions, a time rescaling may be required to guarantee this space independence along stationary paths. In the hydrogen atom example, this time rescaling can be computed in closed form. In contrast to the general wave of the Madelung solution [9] Lemma 3.1 of [7] is defined first for a propagator, and a general wave is then constructed in a second step. Recall that a propagator is a specific quantum wave, which is initialized at $t=0$ with a Dirac impulse at a given initial position or momentum. In turn, a general wave is constructed in a second step by superposing a distribution of initial conditions using the propagator. This key difference is why the Bohm-like quantum potential terms disappear in the construction [7] (specifically, in the first step) while the Bohm potential in the Madelung analysis does not. This fundamental difference is also consistent with the fact that the wave construction in [7] extends naturally to relativistic contexts, while Bohmian non-locality notoriously prevents such extensions. Keywords - Response to arXiv:2605.02621, in relation to rspa.2025.0413

05.
arXiv (CS.CV) 2026-06-18

Learned Radius Estimation for UDF-Based Point Cloud Reconstruction

Surface reconstruction from point clouds is important for consumer-grade 3D capture, including AR/VR and indoor scanning. Local-patch Unsigned Distance Field (UDF) methods are lightweight and generalizable, but their accuracy depends on the support radius, traditionally fixed or selected by a one-dimensional curvature heuristic that cannot capture heterogeneous local geometry. We propose a learned per-query radius selector that predicts a continuous support radius and plugs into a frozen LoSF-UDF backbone. The selector is trained using off-grid target radii obtained by parabolic interpolation of cached UDF error curves. Experiments show improved fine-scale reconstruction accuracy.

06.
arXiv (CS.LG) 2026-06-12

Adjusted Cup-Product Neural Layer

arXiv:2606.13568v1 Announce Type: new Abstract: Many important observables in physics and geometry are cup products of cochains. The adjusted cup product neural layer has been introduced in this paper. It is a neural primitive that hard wires the cup product with an adjustment term from higher gauge theory. This creates a readout that is gauge invariant by design. Their main theoretical result shows that on a closed cycle the output relies entirely on the adjustment coefficient. Setting this coefficient to zero removes the output completely regardless of other parameters. Thus the adjustment is the only source of gauge invariant signal. They prove this observable is a nonzero quadratic form and is exactly invariant under one and two gauge transformations.

07.
arXiv (CS.CV) 2026-06-16

Context-Aware RL for Agentic and Multimodal LLMs

Large language models (LLMs) often fail when answering requires identifying a small but decisive piece of evidence within a long or complex context, such as a single line in a tool trace or a subtle detail in an image. We propose ContextRL, a context-aware reinforcement learning (RL) method that improves long-horizon reasoning and multimodal performance through an indirect auxiliary objective. Instead of supervising only the final answer, ContextRL presents the model with a query, an answer, and two highly similar contexts, and rewards it for selecting the context that supports the query–answer pair, thereby encouraging fine-grained grounding. We construct contrastive context data in two domains: for coding agents, trajectories serve as contexts, yielding 1k pairs built via condition filtering; for multimodal reasoning, images serve as contexts, yielding 7K pairs built via generative editing and similarity search. ContextRL achieves average gains of +2.2% over standard GRPO on 5 long-horizon benchmarks, and +1.8% across 12 diverse visual question answering benchmarks. To disentangle the effect of the proposed objective from that of additional data, we compare against data-augmentation baselines that repurpose the same contrastive contexts as standard query–context–answer examples. These baselines provide little to no improvement, showing that the gains arise from the proposed context-selection objective rather than from the contrastive data alone.

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

Avoiding Exponential Blow-Up in Distributive Lattice Submodular Minimization

Authors:

Submodular function minimization has gained a lot of interest in recent years. They are highly applicable in the area of Computer Vision and Machine Learning. Often such applications require to work with submodular functions defined on distributive lattice. Current best way of dealing with it is using a transformation which extrapolates the submodular function for the respective boolean lattice. It makes optimization system too inefficient due to enlargement of the working space. Quantitatively, the expanded space has additional exponential (in set size) number of elements. We propose a generic framework for dealing with distributive lattice which only works within distributive lattice. Our framework allows one to use already established submodular function minimization algorithms for boolean lattice. In our experiment, we show the huge improvement in terms of running time over tranditional methods for handling distributive lattice.

09.
arXiv (CS.AI) 2026-06-15

EvoTrainer: Co-Evolving LLM Policies and Training Harnesses for Autonomous Agentic Reinforcement Learning

arXiv:2606.03108v2 Announce Type: replace Abstract: Autonomous LLM training is often framed as recipe search, which leaves the training harness largely static. This limitation sharpens in agentic RL, where shifting bottlenecks and scalar rewards mask diverse failure modes. We introduce EvoTrainer, an autonomous training framework that co-evolves LLM policies and training-side harnesses through empirical feedback: it diagnoses rollout-level evidence, revises diagnostics, backtests interventions, and accumulates reusable skills. Evaluated on mathematical reasoning, competitive-programming code generation, and repository-level software engineering, EvoTrainer matches or exceeds the human-engineered RL references under the same data, codebase, and evaluation protocol, with the largest gain on long-horizon agentic SWE. Trajectory analyses show that retained strategies diverge across domains, evolving diagnostics prevent invalid high-scoring branches from being promoted, and reusable skills shape later search. Autonomous LLM RL should move beyond recipe search toward joint evolution of policies and the training harnesses that interpret them.

10.
arXiv (CS.LG) 2026-06-15

Lower Complexity Bounds for Nonconvex-Strongly-Convex Bilevel Optimization with First-Order Oracles

Authors:

arXiv:2511.19656v3 Announce Type: replace Abstract: Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure. In this work, we focus on the smooth nonconvex-strongly-convex setting and develop new hard instances that yield nontrivial lower bounds under deterministic and stochastic first-order oracle models. In the deterministic case, we prove that any first-order zero-respecting algorithm requires at least $\Omega(\kappa^{3/2}\epsilon^{-2})$ oracle calls to find an $\epsilon$-accurate stationary point, improving the optimal lower bounds known for single-level nonconvex optimization and for nonconvex-strongly-convex min-max problems. In the stochastic case, we show that at least $\Omega(\kappa^{5/2}\epsilon^{-4})$ stochastic oracle calls are necessary, again strengthening the best known bounds in related settings. Our results expose substantial gaps between current upper and lower bounds for bilevel optimization and suggest that even simplified regimes, such as those with quadratic lower-level objectives, warrant further investigation toward understanding the optimal complexity of bilevel optimization under standard first-order oracles.

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

The Unreasonable Effectiveness of Discrete-Time Gaussian Process Mixtures for Robot Policy Learning

arXiv:2505.03296v2 Announce Type: replace-cross Abstract: We present Mixture of Discrete-time Gaussian Processes (MiDiGap), a novel approach for flexible policy representation and imitation learning in robot manipulation. MiDiGap enables learning from as few as five demonstrations using only camera observations and generalizes across a wide range of challenging tasks. It excels at long-horizon behaviors such as making coffee, highly constrained motions such as opening doors, dynamic actions such as scooping with a spatula, and multimodal tasks such as hanging a mug. MiDiGap learns these tasks on a CPU in less than a minute and scales linearly to large datasets. We also develop a rich suite of tools for inference-time steering using evidence such as collision signals and robot kinematic constraints. This steering enables novel generalization capabilities, including obstacle avoidance and cross-embodiment policy transfer. MiDiGap achieves state-of-the-art performance on diverse few-shot manipulation benchmarks. On constrained RLBench tasks, it improves policy success by 76 percentage points and reduces trajectory cost by 67%. On multimodal tasks, it improves policy success by 48 percentage points and increases sample efficiency by a factor of 20. In cross-embodiment transfer, it more than doubles policy success. We make the code publicly available at https://midigap.cs.uni-freiburg.de.

12.
arXiv (CS.LG) 2026-06-15

Dynamic Free-Rider Detection in Federated Learning via Simulated Attack Patterns

arXiv:2604.04611v2 Announce Type: replace Abstract: Federated learning (FL) enables multiple clients to collaboratively train a global model by aggregating local updates without sharing private data. However, FL often faces the challenge of free-riders, clients who submit fake model parameters without performing actual training to obtain the global model without contributing. Chen et al. proposed a free-rider detection method based on the weight evolving frequency (WEF) of model parameters. This detection approach is a leading candidate for practical free-rider detection methods, as it requires neither a proxy dataset nor pre-training. Nevertheless, it struggles to detect ``dynamic'' free-riders who behave honestly in early rounds and later switch to free-riding, particularly under global-model-mimicking attacks such as the delta weight attack and our newly proposed adaptive WEF-camouflage attack. In this paper, we propose a novel detection method S2-WEF that simulates the WEF patterns of potential global-model-based attacks on the server side using previously broadcasted global models, and identifies clients whose submitted WEF patterns resemble the simulated ones. To handle a variety of free-rider attack strategies, S2-WEF further combines this simulation-based similarity score with a deviation score computed from mutual comparisons among submitted WEFs, and separates benign and free-rider clients by two-dimensional clustering and per-score classification. This method enables dynamic detection of clients that transition into free-riders during training without proxy datasets or pre-training. We conduct extensive experiments across three datasets and five attack types, demonstrating that S2-WEF achieves higher robustness than existing approaches.

13.
arXiv (CS.CL) 2026-06-15

MoDiCoL: A Modular Diagnostic Continual Learning Dataset for Robust Speech Recognition

Modern Automatic Speech Recognition (ASR) systems have made remarkable progress on standard benchmarks, yet performance gaps have emerged under real-world distribution shifts, caused by recording conditions, accents, speech impairments, and noise. Existing datasets and benchmarks typically isolate these factors, which overlooks their co-occurrence in real-world applications. In this paper, we argue that model robustness can be treated as a dynamic capability that continually develops, and we introduce MoDiCoL, a Modular Diagnostic Continual Learning dataset designed for controlled analysis of linguistic content, speaker characteristics, and acoustic environments. Furthermore, we propose a real-world-inspired continual learning curriculum to simulate incremental updates and study how robustness is acquired, transferred, and forgotten. We evaluate three continual learning strategies and provide detailed insights into robustness under evolving conditions.

14.
arXiv (CS.CL) 2026-06-19

ShoppingBench: A Real-World Intent-Grounded Shopping Benchmark for LLM-based Agents

Existing benchmarks in e-commerce primarily focus on basic user intents, such as finding or purchasing products. However, real-world users often pursue more complex goals, such as applying vouchers, managing budgets, and finding multi-products seller. To bridge this gap, we propose ShoppingBench, a novel end-to-end shopping benchmark designed to encompass increasingly challenging levels of grounded intent. Specifically, we propose a scalable framework to simulate user instructions based on various intents derived from sampled real-world products. To facilitate consistent and reliable evaluations, we provide a large-scale shopping sandbox that serves as an interactive simulated environment, incorporating over 2.5 million real-world products. Experimental results demonstrate that even state-of-the-art language agents (such as GPT-4.1) achieve absolute success rates under 50% on our benchmark tasks, highlighting the significant challenges posed by our ShoppingBench. In addition, we propose a trajectory distillation strategy and leverage supervised fine-tuning, along with reinforcement learning on synthetic trajectories, to distill the capabilities of a large language agent into a smaller one. As a result, our trained agent achieves competitive performance compared to GPT-4.1.

15.
arXiv (CS.LG) 2026-06-16

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

arXiv:2606.16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the variational form is implemented using a Petrov-Galerkin formulation. Dirichlet boundary conditions are imposed directly, while the source terms are computed using automatic differentiation. Computational experiments on standard two-dimensional problems demonstrate that the proposed method achieves high accuracy in both the maximum and L_2 norms. These results confirm the efficiency and robustness of the Petrov-Galerkin VPINN approach in accurately capturing the multiscale features of two-dimensional SPPs.

16.
arXiv (CS.AI) 2026-06-19

Analyzing Defensive Misdirection Against Model-Guided Automated Attacks on Agentic AI Systems

arXiv:2606.20470v1 Announce Type: cross Abstract: Agentic AI systems increasingly rely on language-model components to interpret instructions, process external data, invoke tools, and coordinate with other agents. These capabilities make prompt-injection and jailbreak attacks more consequential, especially as attackers adopt model-guided automation to scale probing, prompt refinement, and response evaluation. This work analyzes the resulting attack-defense setting through a probabilistic model of a target system, its defense mechanism, and the attacker's automated judge. Our analysis shows that conventional detect-and-block defenses can allow attacker success rate (ASR) to approach one as the query budget grows, since predictable refusals provide useful feedback to automated search. We then examine detect-and-misdirect, where detected malicious interactions receive controlled, non-operational responses designed to induce false-positive errors in the attacker's judge. This strategy reduces the positive predictive value of attacker-selected candidates and yields a bounded asymptotic ASR. We evaluate a proof-of-concept realization of this strategy through Contextual Misdirection via Progressive Engagement (CMPE), a lightweight conversational misdirection method designed to replace predictable refusal text with safe but strategically misleading responses in automated jailbreak settings. On jailbreak benchmarks, CMPE reduces estimated ASR upper bounds by up to two orders of magnitude and nearly eliminates verified attack success in end-to-end PAIR and GPTFuzz attack runs.

17.
arXiv (CS.CL) 2026-06-15

Can professional translators identify machine-generated text?

This study investigates whether professional translators without prior specialized training can reliably identify short stories generated in Italian by artificial intelligence (AI). Sixty-nine translators took part in an in-person experiment, where they assessed three anonymized short stories - two written by ChatGPT-4o and one by a human author. For each story, participants rated the likelihood of AI authorship and provided justifications for their choices. While average results were inconclusive, a statistically significant subset (16.2%) successfully distinguished the synthetic texts from the human text, suggesting that their judgements were informed by analytical skill rather than chance. However, a nearly equal number misclassified the texts in the opposite direction, often relying on subjective impressions rather than objective markers, possibly reflecting a reader preference for AI-generated texts. Low burstiness and narrative contradiction emerged as the most reliable indicators of synthetic authorship, with unexpected calques, semantic loans and syntactic transfer from English also reported. In contrast, features such as grammatical accuracy and emotional tone frequently led to misclassification. These findings raise questions about the role and scope of synthetic-text editing in professional contexts.

18.
arXiv (CS.AI) 2026-06-15

When Good Verifiers Go Bad: Self-Improving VLMs Can Regress on New Tasks

Authors:

arXiv:2606.14629v1 Announce Type: cross Abstract: Verifier-driven self-DPO is a common recipe for self-improving production visual-language models. In this setup, a frozen verifier scores candidate generations, the top- and bottom-scoring candidates form a preference example, and DPO updates the learner. The deployment-time assumption is monotone: a stronger verifier should yield a stronger student. We show that this assumption can fail because verifier quality is highly task-specific. On a four-rung open-source verifier ladder across MathVista, MMMU, and BLINK, the same verifiers that are above-threshold and improve a Qwen-3-VL-2B student on MathVista become sub-threshold on MMMU, where their task-rubric accuracy drops to 8% to 23%. In this regime, every verifier we tested silently regresses the student, producing drops of 3.4 to 10.9 percentage points below the frozen baseline while the DPO training loss continues to decrease. The regression replicates on a second student, Qwen-2.5-VL-3B. Moreover, within the failure regime, damage is confidence-inverted: the more accurate-but-still-wrong verifier causes larger regression than a near-random verifier, suggesting that progress-gated replay amplifies confidently wrong preference pairs. We give a compact mechanistic explanation via a variance theorem for progress-gated replay and its direction-mismatch failure mode. The deployment message is operational rather than purely diagnostic: before running any verifier-driven loop, teams should measure target-task rubric accuracy, rank verifiers by target-task rubric quality rather than parameter count, and treat diminishing returns in above-threshold regimes as a verifier-side compute budget cap.

19.
arXiv (CS.AI) 2026-06-11

APPO: Agentic Procedural Policy Optimization

arXiv:2606.12384v1 Announce Type: cross Abstract: Recent advances in agentic Reinforcement Learning (RL) have substantially improved the multi-turn tool-use capabilities of large language model agents. However, most existing methods assign credit over coarse heuristic units, such as tool-call boundaries or fixed workflows, making it difficult to identify which intermediate decisions influence downstream outcomes. In this work, we study agentic RL from two perspectives: where to branch and how to assign credit after branching. Our pilot analysis shows that influential decision points are broadly distributed throughout the generated sequence rather than concentrated at tool calls, while token entropy alone does not reliably reflect their impact on final outcomes. Motivated by these observations, we propose Agentic Procedural Policy Optimization (APPO), which shifts branching and credit assignment from coarse interaction units to fine-grained decision points in the sequence. APPO selects branching locations using a Branching Score that combines token uncertainty with policy-induced likelihood gains of subsequent continuations, enabling more targeted exploration while filtering out spurious high-entropy positions. It further introduces procedure-level advantage scaling to better distribute credit across branched rollouts. Experiments on 13 benchmarks show that APPO consistently improves strong agentic RL baselines by nearly 4 points, while keeping efficient tool-calls and maintaining behavior interpretability.

20.
arXiv (CS.LG) 2026-06-11

Robustness of Mixtures of Experts to Feature Noise

arXiv:2601.14792v2 Announce Type: replace Abstract: Despite their practical success, it remains unclear why Mixture of Experts (MoE) models can outperform dense networks beyond sheer parameter scaling. We study an iso-parameter regime where inputs exhibit latent modular structure but are corrupted by feature noise, a proxy for noisy internal activations. We show that sparse expert activation acts as a noise filter: compared to a dense estimator, MoEs achieve lower generalization error under feature noise, improved robustness to perturbations, and faster convergence speed. Empirical results on synthetic data and real-world language tasks corroborate the theoretical insights, demonstrating consistent robustness and efficiency gains from sparse modular computation.

21.
arXiv (quant-ph) 2026-06-16

Noise-induced shallow circuits and absence of barren plateaus

arXiv:2403.13927v3 Announce Type: replace Abstract: Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that in the task of estimating observable expectation values any noise truncates most quantum circuits to effectively logarithmic depth. We then prove that quantum circuits under any non-unital noise do not exhibit barren plateaus for cost functions composed of local observables. However, by using the effective shallowness, we also design an efficient classical algorithm to estimate observable expectation values within any constant additive accuracy, with high probability over the choice of the circuit, in any circuit architecture. Taken together, our results establish that, unless we carefully engineer quantum circuits to take advantage of the noise, noisy quantum circuits are unlikely to offer an advantage over shallow ones for algorithms that output observable expectation value estimates, such as many variational quantum machine learning proposals.

22.
arXiv (CS.AI) 2026-06-16

EChO-Agent: Evidence Chain Orchestration Agent for Audio Reasoning

arXiv:2606.15141v1 Announce Type: cross Abstract: While LALMs show promise on audio question answering, they fail to focus on question-relevant segments of audio and provide a clear, checkable reasoning process when dealing with complex audio reasoning. Reinforcement learning and tool-augmented prompting can help models better relate questions to audio but lack a reliable way to understand, integrate, and self-verify audio segments. To address this gap, we present EChO-Agent, a modular agent framework that reformulates complex audio QA as a planning, tool execution, evidence integration, and answer verification workflow. Experiments on MMAR benchmark show EChO-Agent improves both accuracy and rubric scores over baseline and ablation studies show evidence integration is the key factor.

23.
arXiv (math.PR) 2026-06-16

Small moments of the sensitivity of polynomial threshold functions

arXiv:2606.16004v1 Announce Type: new Abstract: In the first version of Chang, Slote, Volberg, and Zhang's paper [BSA_of_PTF], the authors modify a nice recursive approach due to Kane in [Correct_exponent_for_AS] where he bounded the average sensitivity of polynomial threshold functions. In [BSA_of_PTF] Kane's argument was adopted to estimate the boolean surface area of polynomial threshold function. The bridge is a combinatorial averaging lemma considering all balanced partitions. The lemma serves as a substitute for an additive property of average sensitivity. With the lemma, one can apply a Kane-type algorithm to derive a recurrence. Solving the recurrence then gives an upper bound of $e^{C_d \sqrt{\log n}}$ for the boolean surface area. In the second version of the same paper, the authors derive a polylog upper bound for BSA of PTFs. The difference is that they use a tail estimate for the sensitivity function. With the help of a polynomial restriction lemma in [poly_restriction] they sharpen the upper bound. It is noteworthy that when applying the polynomial restriction, each coordinate is put into each part independently with equal probability. As a result, a partition does not necessarily have equal-size blocks. In other words, it may not be balanced. In this note, we first investigate the effect of different partitioning. Second, we use the recursive method in the first version to derive a polylog upper bound for $\mathbb E[s(x)^{\eta}]$ where $\eta < 1/2$. It is interesting to note the phase transition that happens at $\eta=1/2$ in both versions of the proof (but in a completely different form). Section [PhaseTr-s] treats that.

24.
arXiv (CS.LG) 2026-06-15

LoMC: Localized Multidirectional Correction for Refusal Suppression in Routed Foundation Models

arXiv:2606.13709v1 Announce Type: cross Abstract: We study controlled post-training refusal suppression in routed MoE and hybrid-MoE foundation models, aiming to increase non-refusal target-response behavior while preserving general capability under a compact intervention footprint. Existing broad direction-based edits can perturb general-purpose computation, whereas support-only expert edits often lack sufficient capacity to correct heterogeneous refusal representations. To address this limitation, we introduce Localized Multidirectional Correction (LoMC), a support-gated intervention framework that follows a support-then-correction execution order: it first identifies a compact edit support, then aggregates prototype correction directions into layer-wise correction directions, and finally applies rank-one layer-wise correction only within the selected support. By using the edit support as a structural gating constraint, LoMC increases correction capacity without expanding the intervention scope. Experiments on text-only and multimodal safety benchmarks across four routed backbones show that LoMC substantially improves non-refusal target-response behavior while maintaining general capability under a compact intervention footprint.