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01.
arXiv (quant-ph) 2026-06-12

Block algebra for morphing circuits

作者:

arXiv:2606.12724v1 Announce Type: new Abstract: Morphing circuits are a new paradigm for quantum error correction that relaxes hardware requirements. We present four constructions for CNOT-based CSS morphing circuits with explicit qubit connectivity degrees. All four constructions are specified in block algebra notation, with entries in algebras generated by permutation matrices. The first three are obtained by rewriting existing surface- and color-code morphing circuits; the fourth is a new three-round construction modeled on the 6.6.6 color code. The surface-code construction recovers the morphing circuit of Ref. [ST25] for two-block group algebra codes. Numerical search then instantiates these permutation matrices using regular representations of finite groups. [ST25] M. H. Shaw and B. M. Terhal, Phys. Rev. Lett. 134(9), 090602 (2025).

02.
arXiv (CS.LG) 2026-06-24

SLEEPING-DISCO 9M: A large-scale pre-training dataset for generative music modeling

arXiv:2506.14293v4 Announce Type: replace-cross Abstract: We present Sleeping-DISCO 9M, a large-scale pre-training dataset for music and song. To the best of our knowledge, there are no open-source high-quality dataset representing popular and well-known songs for generative music modeling tasks such as text-music, music-captioning, singing-voice synthesis, melody reconstruction and cross-model retrieval. Past contributions focused on isolated and constrained factors whose core perspective was to create synthetic or re-recorded music corpus (e.g. GTSinger, M4Singer) and arbitrarily large-scale audio datasets (e.g. DISCO-10M and LAIONDISCO-12M) had been another focus for the community. Unfortunately, adoption of these datasets has been below substantial in the generative music community as these datasets fail to reflect real-world music and its flavour. Our dataset changes this narrative and provides a dataset that is constructed using actual popular music and world-renowned artists.

03.
arXiv (CS.CV) 2026-06-25

Learning Action Priors for Cross-embodiment Robot Manipulation

Most Vision-Language-Action (VLA) models build on a Vision-Language Model (VLM) backbone by attaching an action module and optimizing the full policy jointly. This design inherits strong visual and linguistic priors from the VLM, but leaves the action module to learn physical motion almost from scratch. As a result, the policy lacks an explicit motion prior, forcing early optimization to simultaneously discover temporal action dynamics and cross-modal alignment, a challenge further amplified in cross-embodiment settings. In this work, we propose to pretrain the action module with motion priors before cross-modal VLA alignment. Specifically, we introduce a two-stage training framework that equips the action module with cross-embodiment temporal motion structure before VLA training begins. In Stage~1, a lightweight flow-matching-based encoder-decoder action module efficiently learns temporal motion structure solely from unconditioned action trajectories, without processing visual or language tokens. In Stage~2, this learned prior is transferred to VLA training through decoder reuse and early-stage latent distillation, aligning visual-language features with the action embedding space while still allowing end-to-end policy refinement. In addition, the trained encoder serves as a compact history compressor, summarizing state-action histories into a single temporal context token for history-aware modeling at negligible cost. Extensive experiments across 13 diverse cross-embodiment tasks on both simulated and real-world platforms validate the effectiveness of our approach. Compared with VLA training without action priors, our model achieves faster convergence, higher success rates, and substantially stronger performance on data-scarce real-world tasks. Moreover, scaling up the action data in Stage~1 yields a more generalizable action prior that directly improves downstream VLA performance.

04.
arXiv (CS.AI) 2026-06-12

Decoding Insect Song: A Multitask Semisupervised Orthoptera Bioacoustic Classifier

arXiv:2606.13236v1 Announce Type: cross Abstract: Passive acoustic monitoring holds great promise for ecological inference, yet existing automated tools are typically narrowly trained and non-transferable. We address these limitations with PULSE, a semi-supervised, multi-task framework for Orthoptera bioacoustics, combining weakly-supervised species classification, self-supervised learning on unlabelled field audio, and knowledge distillation from a general-purpose bioacoustic model. Our domain-adapted specialist model outperforms a state-of-the-art general model across all metrics (macro F1: 0.21 vs. 0.07; AUC: 0.74 vs. 0.45; AP: 0.32 vs. 0.19), with active learning further raising F1 to 0.34 and AUC to 0.84. Beyond classification, the learned embeddings encode ecologically meaningful structure, exposed through an interactive visualisation tool for ecological discovery.

05.
arXiv (CS.CV) 2026-06-16

DySink: Dynamic Frame Sinks for Autoregressive Long Video Generation

Autoregressive long video generation often adopts bounded-memory streaming for efficiency, typically combining local windows for short-term continuity with static early-frame sinks as long-range anchors. However, this fixed allocation keeps early frames cached even when the current visual state has substantially diverged from them, while discarding potentially more relevant intermediate history. As a result, the retained long-range context may become less adaptive and bias generation toward outdated cues; in severe cases, RoPE-induced phase re-alignment can homogenize inter-head attention and cause sink collapse, where content regresses toward sink frames. We propose DySink, a retrieval-based framework that maintains a compact memory bank and selects visually relevant historical frames as dynamic frame sinks. DySink couples adaptive retrieval with a sink anomaly gate, which detects excessive inter-head consensus over retrieved context and suppresses collapse-prone context. Experiments on minute-long videos show that DySink consistently improves dynamic degree over strong baselines while also achieving higher temporal quality. The code and model weights will be released at https://github.com/yebo0216best/DySink.

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

Separable Neural Architectures as Physical World Models: from Mathematical Theory to Applications

arXiv:2606.14934v1 Announce Type: cross Abstract: This work introduces the Separable Neural Architecture (SNA), a function representational class combining neural approximation with tensor decomposition. The SNA decouples localized coordinate functions (atoms) from global interactions governed by a sparse, low-rank interaction object. This architecture possesses a compact and smooth inductive bias well-suited for solving partial differential equations (PDEs). When viewed as a Galerkin trial space under the variational SNA (VSNA) framework, the formulation satisfies classical variational guarantees under Lax-Milgram: well-posedness, quasi-optimality, convergence, and stability. In high-dimensional spatiotemporal–parametric PDEs, the VSNA mitigates the curse of dimensionality by scaling algebraically rather than exponentially. Exploiting an entirely factorized, tensor-native alternating least squares (ALS) optimization framework reduces this cost to linear in dimension. The VSNA is validated across elliptic, hyperbolic, and parabolic systems, demonstrating close alignment with predicted algebraic and spectral scaling rates. We showcase the SNA as a "solve once, query anywhere" physical world model via two engineering case studies: a 7D parametric manufacturing simulation and an experimental thermal-to-property inversion pipeline for Inconel 718. The VSNA executes a 1,000,000-query Monte Carlo sweep in 102s on a standard laptop CPU, yielding a 150,000x speedup over a full-grid finite element baseline hosted on an NVIDIA A100 GPU. It further enables real-time generative inverse-mode reconstructions under 100ms. These results demonstrate that the SNA serves as a compact mathematical substrate for continuous parameter manifolds to enable real-time inversion, optimization loops, and rapid uncertainty propagation.

07.
arXiv (math.PR) 2026-06-16

A non-asymptotic bound on the TV distance between a Wishart matrix and an appropriately scaled GOE matrix

arXiv:2606.16018v1 Announce Type: new Abstract: In this note, we prove a non-asymptotic version of a theorem by Bubeck, Ding, Eldan, and Rácz, showing that a Wishart matrix is close in total variation to an affine transformation of a GOE matrix. The proof mirrors the proof given by Bubeck et al., with some changes made to make it non-asymptotic.

08.
arXiv (CS.AI) 2026-06-17

First Proof Second Batch

arXiv:2606.18119v1 Announce Type: new Abstract: To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set of ten problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors. This document includes the problems, our methodology, and the results of our testing. We provide links to supplementary documents including the human solutions, the AI-generated solutions, and the referee reports and logs for the AI-generated solutions. The ten problems were contributed by the following mathematicians: (1) Dariusz Kaloci\'nski and Theodore A. Slaman, (2) Richard Schwartz, (3) Aleksa Milojevic and Benny Sudakov, (4) Larry Guth, (5) Oleg Butkovsky, Jonathan Mattingly, and Lorenzo Zambotti, (6) Joshua Evan Greene and Duncan McCoy, (7) Sucharit Sarkar, (8) Sam Payne and Jidong (Jayden) Wang, (9) Sylvie Corteel and John Lentfer, (10) Srivatsav Kunnawalkam Elayavalli.

09.
medRxiv (Medicine) 2026-06-15

Bidirectional associations between cannabis use, oddball performance, and P3 event-related potential

Importance: Cannabis use remains prevalent in youth despite concerns regarding its potential impact on cognitive function. Unraveling whether the association between cannabis use and cognition is partially due to preexisting differences or primarily related to use is vital to understanding underlying mechanisms. Objective: To estimate the longitudinal association between cannabis initiation and cognitive trajectories, indexed by task performance and P3 event-related potential (ERP), and to estimate whether baseline cognition is associated with cannabis initiation. Design: Data were analyzed from the ongoing longitudinal Collaborative Study on the Genetics of Alcoholism (COGA) cohort, which was followed up approximately every 2-5 years from 2004 to 2025. Setting: 6 sites across the United States. Participants: Adolescent and young adult offspring of past COGA participants and control families who reported on their cannabis use and who had Visual Oddball (VOP) performance and P3 ERP data (N=4814; 52.4% female, 68.4% white) were grouped based on the timing of cognitive data collection relative to cannabis initiation into Pre-onset (n=2,449; [&ge;]1 assessment) and Post-onset (n=998; [&ge;]3 assessments) subsamples. Main Outcomes and Measures: VOP measures include performance accuracy (%), reaction times (ms), and P3 amplitude (V) and latency (ms) during target trials. Cannabis measures included lifetime use of cannabis (i.e., ever used) and age at first use. Results: High P3 amplitude, and prolonged P3 latency and reaction time were associated with a reduced hazard of cannabis initiation (All Hazards Ratio, [H.R.s]< 0.91, p's

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

Theory of the correlated quantum Zeno effect in a monitored qubit dimer

arXiv:2503.22846v2 Announce Type: replace Abstract: We theoretically investigate the stochastic dynamics of two qubits subject to one- and two-site correlated continuous weak measurements. When measurements dominate over the local unitary evolution, the system's dynamics is constrained and part of the physical Hilbert space becomes inaccessible: a typical signature of the Quantum Zeno (QZ) effect. In this work, we show how the competition between these two measurement processes give rise to two distinct QZ regimes, we dubbed standard and correlated, characterised by a different topology of the allowed region of the physical Hilbert space being a simply and non-simply connected domain, respectively. We develop a theory based on a stochastic Gutzwiller ansatz for the wavefunction that is able to capture the structure of the phase diagram. Finally we show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.

11.
arXiv (CS.CL) 2026-06-25

Measuring Research Difficulty of Academic Papers: A Case Study in Natural Language Processing

With the rapid growth of the number of academic papers, systematically evaluating the difficulty of research and its relationship to academic impact offers important significance for research topic selection and resource allocation. However, current studies lack quantitative assessments of research difficulty and its correlation with academic impact. This paper proposes a comprehensive evaluation system for research difficulty, incorporating factors such as academic collaboration, content, and references. Taking the field of Natural Language Processing (NLP) as a case study, we extract both internal and external features from academic papers, compute multiple research difficulty indicators. We assign their weights using the entropy weight method and perform a weighted sum to obtain the research difficulty score of academic papers. This paper uses the citation frequency of academic papers to measure academic impact. To validate our approach, NLP experts assessed the difficulty of a sample of papers, and correlation analyses confirmed the reliability of our measurement. Empirical results reveal that in NLP, factors such as the number of pages, reference count, and participation of high-level institutions are significantly associated with academic impact. Moreover, we identify an inverted U-shaped relationship between research difficulty and academic impact. It suggests that moderately difficult research tends to achieve greater academic impact.

12.
arXiv (math.PR) 2026-06-25

On a remark of de Gennes concerning three-dimensional polyelectrolytes

arXiv:2604.08389v2 Announce Type: replace Abstract: This work is inspired by a remark of de Gennes about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For polyelectrolytes, the repelling potential is the Coulomb potential arising from pairs of charged particles. We show that in the continuous case of Brownian motion in three dimensions, the spread of the polymer, in particular the the radius of gyration of a polyelectrolyte of length $T$ grows linearly with $T$, up to logarithmic corrections.

13.
arXiv (CS.CV) 2026-06-16

Trusted Multi-View Deep Learning Classification of Fetal Congenital Heart Disease with Feature-level and Decision-level Fusion

Congenital heart disease (CHD) refers to the abnormal anatomical structure caused by the abnormal development of the heart and great vessels during embryonic development. Traditional diagnostics often fail to achieve high accuracy and efficiency, especially given the complexity of cardiac anatomy. This study presents a specialized multi-view deep learning framework for CHD binary classification using echocardiographic images. A large-scale CHD dataset, including five views, was used to train the model, enabling it to integrate multi-angle image data. The framework utilizes advanced feature extraction and attention mechanisms to improve diagnostic precision and reliability. An uncertainty-based decision-making component is also integrated to handle low-quality images, enhancing diagnostic outcomes. Experimental results show that this method achieves top-tier performance on our dataset and provides a robust tool for early CHD detection, underscoring its potential for clinical use. The dataset and source code will be released upon paper acceptance.

14.
arXiv (CS.CV) 2026-06-17

RAIGen: Rare Attribute Identification in Text-to-Image Generative Models

Text-to-image diffusion models achieve impressive generation quality but inherit and amplify training-data biases, skewing coverage of semantic attributes. Prior work addresses this in two ways. Closed-set approaches mitigate biases in predefined fairness categories (e.g., gender, race), assuming socially salient minority attributes are known a priori. Open-set approaches frame the task as bias identification, highlighting majority attributes that dominate outputs. Both overlook a complementary task: uncovering rare or minority features underrepresented in the data distribution (social, cultural, or stylistic) yet still encoded in model representations. We introduce RAIGen, the first framework, to our knowledge, for label-free rare-attribute discovery in diffusion models, requiring no predefined minority categories. RAIGen leverages Matryoshka Sparse Autoencoders and a novel minority metric combining neuron activation frequency with semantic distinctiveness to identify interpretable neurons whose top-activating images reveal underrepresented attributes. Experiments show RAIGen discovers attributes beyond fixed fairness categories in Stable Diffusion, scales to larger models such as SDXL, supports systematic auditing across architectures, and enables targeted amplification of rare attributes during generation. The project page is available at https://vssilpa.github.io/RAIGen_webpage/ .

15.
arXiv (CS.CL) 2026-06-11

Multi-Agent Reasoning with Adaptive Worker Allocation for Stance Detection

Stance detection requires identifying an author's position toward a target, often from short-form texts where stance is implicit, indirect, or rhetorically framed. Although large language models (LLMs) achieve strong performance on this task, single-pass prompting can be brittle when multiple interpretations are plausible. Existing aggregation strategies, such as majority voting or self-consistency, improve robustness by combining labels, but they discard the intermediate reasoning needed to resolve conflicting interpretations. We introduce a multi-agent reasoning framework with adaptive worker allocation for stance detection that shifts aggregation from label-level voting to reasoning-level synthesis. The framework employs a Manager-Worker architecture in which a Manager adaptively allocates a variable number of Worker agents based on input complexity. Each Worker analyzes the input from a distinct perspective and produces a reasoning-only explanation without emitting a stance label; the Manager then synthesizes these explanations to produce the final prediction. We evaluate the proposed framework on SemEval-2016, P-Stance, and COVID-19 Stance using Llama, Mistral, and Gemini. Results show that the framework yields the largest gains on implicit and context-dependent stance cases, achieving 86.07 Macro-F1 on COVID-19 and 82.90 on SemEval-2016, while remaining competitive on more explicit stance datasets such as P-Stance. These findings suggest that adaptive reasoning-level aggregation is most beneficial when stance cannot be reliably inferred from surface cues alone.

16.
medRxiv (Medicine) 2026-06-22

Image-based deep learning for emergency electrocardiogram classification

Automated electrocardiogram analysis has advanced largely through digital waveforms, yet many emergency-care workflows rely on ECGs available only as printed tracings, scanned reports, PDFs or mobile photographs. We developed an image-based deep learning system for emergency ECG classification and evaluated it in InCor-EMG, an expert-adjudicated dataset of 18,519 emergency ECGs spanning 12 ECG categories, with labels from 19 cardiologists. On the held-out test set, the final ConvNeXt ensemble achieved a macro F1-score of 0.807 (95% CI, 0.788-0.825), compared with 0.820 (95% CI, 0.805-0.832) for annotating cardiologists, and higher F1-scores than Mortara Veritas in most evaluated categories. Performance was associated more strongly with inter-reader agreement than with training sample size and remained informative across scanned and photographed ECGs, with supportive performance in model-enriched temporal and heterogeneous public-image evaluations. These findings support ECG image classification when digital waveforms are unavailable.

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

Plan-and-Verify Video Reward Reasoning with Spatio-Temporal Scene Graph Grounding

Reward models for text-to-video (T2V) generation guide post-training but often fail at fine-grained semantic alignment. We trace this to two structural weaknesses in existing reasoning-based reward models: they do not systematically verify every condition described in the prompt, and the visual evidence supporting each judgment remains implicit in their free-form reasoning. We propose SG-PVR, a video reward model that addresses these limitations through plan-and-verify reasoning grounded in spatio-temporal scene graphs. The verification plan decomposes the prompt into atomic claims, ensuring every requirement is checked. The spatio-temporal scene graph, encoding entities, attributes, and temporally-grounded relations, is extracted from the video and maintained as a persistent structured visual reference throughout reasoning. Each claim is verified against both the video and the scene graph, anchoring judgments in explicit visual evidence. SG-PVR achieves strong performance on semantic alignment, including fine-grained temporal semantics. As a test-time reranker, it further enhances compositional alignment in T2V generation.

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

Trusting Right Predictions for Wrong Reasons: A LIME Based Analysis of Deep Learning Interpretability in Lung Cancer Diagnosis

Lung cancer is the leading cause of cancer-related mortality, with approximately 2.5 million new cases and 1.8 million deaths annually, making reliable diagnosis a clinical priority. Although deep learning models have achieved strong performance in lung cancer classification, evaluation has largely focused on predictive accuracy, leaving their decision-making processes insufficiently examined. This study compares three architecturally distinct models: a Convolutional Neural Network (CNN), a pretrained ResNet50, and a Vision Transformer (ViT), trained on the IQ-OTH/NCCD lung cancer CT dataset. Local Interpretable Model-Agnostic Explanations (LIME) were applied to investigate model reasoning. In addition to standard performance metrics, a dual-correlation framework was introduced to measure both prediction agreement and explanation agreement across model pairs. All three models achieved strong classification performance, with ResNet50 attaining 98.61% accuracy, CNN 97.91%, and ViT 93.75%, while all achieved ROC-AUC scores of 0.99. Prediction correlations exceeded 0.99 across all model pairs, indicating highly consistent outputs. However, LIME explanation correlations remained below 0.26, revealing substantial differences in the image regions used to reach those predictions. Analysis of misclassified samples further identified a consistent spatial pattern: incorrect predictions were associated with attention outside the lung parenchyma, whereas correct predictions focused primarily within lung regions. These findings demonstrate that prediction agreement is a poor proxy for reasoning consistency, and that interpretability evaluation must be treated as an independent validation criterion alongside predictive performance in clinical AI systems.

19.
arXiv (CS.AI) 2026-06-18

Practical Anonymous Two-Party Gradient Boosting Decision Tree

arXiv:2605.26903v2 Announce Type: replace-cross Abstract: Structured data is well handled by gradient-boosted decision trees (GBDT), which are usually trained on vertically partitioned features across mutually distrustful parties. High speed and interpretability make GBDTs popular in finance and healthcare, where neural networks may fall short. Enabling secure computation for GBDTs poses unique challenges, requiring secure record alignment for comparison. Relying on private set intersection (PSI) is a de facto approach. Mistaking PSI for a safety measure actually exposes which record identifiers (IDs) are shared between the datasets. Although circuit-PSI could help, it is costly for generic uses. New ideas are needed to efficiently train in a "dark forest". Aiming to hide the IDs, we initiate the study of anonymous GBDT training on split data held by two parties. Dual circuit-PSI in our design lets the parties alternate as receiver to run pick-then-sum over local features. Via oblivious programmable pseudorandom functions, we propagate circuit-PSI outputs as shared state across runs. Avoiding universal alignment, we resolve the neglected dilemma that ID hiding incurs a cost that scales with domain size. Next, we halve the cost of ciphertext packing used to convert single-instruction multiple-data homomorphic encryption from (ring) learning with errors in prior secure GBDT (Usenix Security' 23) and related secure machine-learning computations. Comparative experiments show our protocol remains competitive with leaky approaches in efficiency. Enabling ID-hiding aggregation, our techniques can extend to other vertically partitioned analytics.

20.
arXiv (CS.CV) 2026-06-16

Navigating Distribution Shifts in Medical Image Analysis: A Survey

Medical Image Analysis (MedIA) has become indispensable in modern healthcare, enhancing clinical diagnostics and personalized treatment. Despite the remarkable advancements supported by deep learning (DL) technologies, their practical deployment faces challenges posed by distribution shifts, where models trained on specific datasets underperform on others from varying hospitals, or patient populations. To address this issue, researchers have been actively developing strategies to increase the adaptability of DL models, enabling their effective use in unfamiliar environments. This paper systematically reviews approaches that apply DL techniques to MedIA systems affected by distribution shifts. Rather than organizing existing methods by technical characteristics, we explicitly bridge real-world clinical constraints – such as limited data accessibility, strict privacy requirements, and heterogeneous collaboration protocols – with the technical paradigms able to address them. By establishing this connection between operational constraints and methodological evolution, we categorize existing works into Joint Training, Federated Learning, Fine-tuning, and Domain Generalization, each aligned with specific healthcare scenarios. Beyond this taxonomy, our empirical analysis suggests that, as domain information becomes progressively less accessible across these paradigms, performance improvements become increasingly constrained, and further uncovers a gradual shift in methodological focus from explicit distribution alignment toward uncertainty-aware modeling, ultimately pointing to the need for more deployability-aware design in real-world MedIA.

21.
arXiv (CS.LG) 2026-06-19

Probe-and-Refine Tuning of Repository Guidance for Coding Agents

arXiv:2606.20512v1 Announce Type: cross Abstract: LLM-based coding agents need higher-level operational knowledge about a repository (which files house which subsystems, how to run the test suite, which workflows have historically led to wrong fixes) that does not exist in the code itself. Engineers typically maintain \texttt{AGENTS.md} files to supply this context as instructions for coding agents, but whether they help is contested: recent studies disagree on whether LLM-generated guidance improves or harms agent performance. In this paper we show that how the guidance is produced is the decisive variable, and introduce probe-and-refine tuning: a procedure that uses synthetic bug-fix probes to iteratively diagnose and patch a repository's guidance file through single-shot LLM calls, with no agent loop or tool use during tuning. On SWE-bench Verified across four independent trials with Qwen3.5-35B-A3B at 200 steps, probe-and-refine achieves 33.0\,\% mean resolve rate vs.\ 28.3\,\% for the static knowledge base used to initialize it and 25.5\,\% for an unguided baseline ($p < 0.001$ for both probe-and-refine contrasts). The improvement comes from coverage rather than precision: refined guidance produces evaluable patches for 14.5 percentage points (pp) more instances while per-patch precision remains statistically constant ($\sim$59\,\%, $p = 0.119$), showing that improved guidance helps agents reach the correct file rather than improving the quality of the changes they make. Further, a step-budget experiment shows that guidance is what lets the agent use a larger step budget productively, and a cross-model experiment with NVIDIA-Nemotron-3-Nano-30B-A3B finds that the tuning loop degrades when the model cannot generate sufficiently diagnostic output, though per-patch precision remains constant even then.

22.
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.

23.
arXiv (quant-ph) 2026-06-12

Scalar Quantum Fields: Theory Space and its Geometry

arXiv:2606.12580v1 Announce Type: cross Abstract: Scalar fields provide perhaps the simplest playground in which to develop our understanding of quantum field theory. In this lecture, we consider what it means to write down a scalar quantum field theory and how we can give geometrical interpretations to the space of such theories: the theory space.

24.
arXiv (CS.CL) 2026-06-16

Do You Really Need a GPU to Guard Your LLM? CPU-Class Classifiers and Multi-Stage Pipelines for Safety Enforcement at Scale

Safety classifiers that screen LLM inputs for jailbreak attempts have become standard deployment components, yet almost all production systems rely on GPU-based models: fine-tuned transformers and LLM-as-a-judge pipelines. These approaches impose significant per-query latency and infrastructure cost. Very little research has asked whether CPU-based classifiers, such as support vector machines and gradient-boosted trees trained on TF-IDF features, can match their accuracy across the conditions that production deployments encounter. We evaluate five CPU classifier families, Mamba-130M as an SSM-based GPU classifier, and transformer-based GPU models (DeBERTa-v3 and Gemma-2B with LoRA) across nine jailbreak sources and three regimes: in-distribution (D1), out-of-distribution (D2), and adversarially obfuscated (D3). On D1, the best CPU classifier matches the best transformer GPU model at roughly one-fifth the deployment cost. On D2, CPU classifiers fail via confident miscalibration, producing high-confidence false negatives that bypass escalation entirely. On D3, CPU classifiers outperform transformer GPU models by more than 26 percentage points in F1. Based on these complementary failure modes, we design GuardChain, a three-stage safety pipeline (Regex -> CPU -> GPU) that routes each prompt to the cheapest stage capable of a confident decision. The CPU stage alone resolves 80\% of in-distribution prompts at near-peak accuracy, and the GPU stage recovers the out-of-distribution failures. For practitioners deploying LLM safety at scale, this work provides evidence that GPU-class infrastructure is unnecessary for the majority of traffic.

25.
arXiv (CS.CV) 2026-06-25

Efficient Remote Sensing Instance Segmentation with Linear-Time State Space Distilled Visual Foundation Models

The computational complexity of Transformers scales quadratically with the number of tokens, which significantly constrains the efficiency of vision models, particularly recent ViT-based foundation models in dense prediction tasks. Instance segmentation, a typical dense visual prediction task in the remote sensing field, faces similar challenges. In this paper, inspired by the recent advances of knowledge distillation in large language models, we introduce RS4D - a new remote sensing instance segmentation method with linear computational complexity, which addresses the inefficiency of long sequence modeling through distilled state space modeling (SSM). We propose an adaptive noise and masking knowledge distillation training method for pre-training lightweight SSM backbones, which effectively compresses knowledge from the vast self-attention space into a compact, dense linear state space. We also design a remote sensing image instance segmentation architecture based on this lightweight visual encoder, where we explore variants of three different backbones and two segmentation heads. Extensive experiments are conducted on multiple benchmark datasets, including SSDD, WHU, and NWPU. Compared to ViT-based approaches, our proposed SSM backbone achieves an 8x reduction in parameters and a 9x reduction in FLOPs while maintaining comparable or superior accuracy to both ViT- and CNN-based instance segmentation methods. The implementation codes have been publicly available at https://github.com/QinzheYang/RS4D.