arXiv:2607.17282v1 Announce Type: new
Abstract: Given a binary-labeled linearly separable dataset, and the objective is to compute the maximum-margin separating hyperplane, also known as the hard-margin Support Vector Machine (SVM) classifier. This paper investigates whether, if given an initial separating hyperplane, can it be exploited to reach this unique optimum more efficiently. We present a geometric approach that gradually improves the alignment of the hyperplane, starting from an initial separating hyperplane, while preserving separation and continuously increasing its margin until convergence to the global optimum. At each iteration, the method considers only local information, namely the current active set, and aims to re-align the hyperplane according to the optimal separating hyperplane of this reduced subset. Consequently, the original convex quadratic optimization problem is addressed through a sequence of smaller subproblems. The paper presents the algorithm in detail, together with a preliminary experimental evaluation and several theoretical findings. The results suggest that, when an initial separating hyperplane is available, the proposed method can be competitive on larger datasets and, in some cases, can outperform state-of-the-art approaches that solve the optimization problem directly.
Science Journals
arXiv:2607.17283v1 Announce Type: new
Abstract: Single-stream autoregressive decoding of large language models is bound by memory bandwidth: each generated token requires one full forward pass through the target model, and successive passes cannot be parallelized. Speculative decoding restructures this computation: a small draft model proposes $K$ tokens autoregressively, the target model scores all of them in one batched pass, and a rejection-sampling rule provably preserves the target model's output distribution. We present a from-scratch, device-agnostic (CUDA/MPS/CPU) implementation and an empirical study across five draft/target backend configurations on a consumer Apple-silicon laptop. Distribution equivalence is verified at three levels, culminating in a two-sample test over roughly 9,200 real-model tokens per method ($\chi^2 = 162.5$, dof $= 200$, $p = 0.976$) and exact greedy-sequence agreement. The best configuration reaches a measured $1.61\times$ wall-clock speedup at $K=6$, on an acceptance profile declining from 69.7% at $K=1$ to 37.8% at the optimum, while three of five configurations decelerate, either because the draft fails to out-speed a small target or because the quantized Metal backend executes "parallel" verification serially, an effect we isolate and quantify. The failures are as instructive as the successes: speculative decoding pays off only when verification is genuinely batch-parallel and the draft/target latency gap is real.
arXiv:2607.17285v1 Announce Type: new
Abstract: Mixed finite element methods based on Raviart--Thomas spaces are widely used for the numerical approximation of second--order elliptic problems in flux form. On quadrilateral meshes, however, the bilinear mapping from the reference element introduces a spatially varying Jacobian, which may violate the inclusion property $\mathrm{div}\,V_h \subset W_h$ for the standard Raviart--Thomas spaces.
In this paper we propose a simple modification of the classical Raviart--Thomas elements on quadrilateral meshes. The modification consists of adding geometrically motivated correction terms to the local basis functions in order to compensate for the geometric distortion introduced by the bilinear mapping. The resulting spaces retain the same dimension and degrees of freedom as the classical Raviart--Thomas elements while restoring the compatibility property.
We present a general framework for constructing such modified spaces and illustrate the approach by developing modified versions of the lowest order and next--to--lowest order Raviart--Thomas elements. Theoretical analysis establishes optimal approximation properties under the standard shape--regularity assumption for quadrilateral meshes. Numerical experiments on distorted meshes confirm the predicted convergence rates and show that the modified elements yield consistently improved accuracy over the classical Raviart--Thomas formulation as the geometric distortion increases.
arXiv:2607.16524v1 Announce Type: new
Abstract: Cooperative multi-agent RL systems routinely use team-averaged rewards, a feedback-attribution choice that gives each agent the team outcome regardless of its individual contribution. We ask whether this leaves a measurable signature, geometric or behavioral, on learned representations. We propose EffRank/$n$ (effective rank normalized by agent count) and $D_\text{act}$ (mean pairwise KL divergence between agents' action distributions) as low-overhead diagnostics for reward-attribution effects, then test them on competent MAPPO agents in SMACv2 \texttt{protoss\_5\_vs\_5}, where unit type is encoded in the observation. In an observation $\times$ reward-attribution comparison (unit type observed vs.\ masked; individual damage-contribution reward vs.\ shared team reward), geometry follows observation rather than reward. With unit type observed, shared and individual rewards have similar EffRank/$n$ ($0.31{\pm}0.03$ vs.\ $0.29{\pm}0.02$) and probe accuracy ($0.75{\pm}0.05$ vs.\ $0.73{\pm}0.05$, both $\gg 1/3$ chance), while $D_\text{act}$ leans higher under individual rewards ($1.23{\pm}0.06$ vs.\ $1.07{\pm}0.20$). Masking unit type cuts the above-chance probe signal by more than half, to $0.49$ in both reward arms. In short: individually rewarded agents are competent and separable by role, but on SMACv2 the observation explains the geometry and reward attribution shows up mainly in behavior. Thus geometric diagnostics must control for observed role information and test persistent roles that are not directly observed. EffRank/$n$ and $D_\text{act}$ add $<$5\% overhead.
arXiv:2607.17507v1 Announce Type: new
Abstract: Regional climate prediction presents unique challenges for time series foundation models, which typically process temporal patterns through single-pass inference. Expert climatologists, in contrast, employ multi-scale temporal analysis and iterative refinement based on systematic error diagnosis. We present RGMR (Residual-Guided Multi-Resolution Refinement), an inference-time framework that adapts pre-trained foundation models to perform structured coarse-to-fine refinement for climate forecasting without updating backbone parameters. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR is architecture-agnostic across the three TSFM backbones evaluated per site (TimesFM, TimeGPT, TabPFN) and consistently lowers test-set MSE on three South Australian sites and three additional regions outside South Australia. Applied to TimesFM, the wrapper reduces one-month-ahead SPEI MSE by up to 18.9\% across the three South Australian sites (mean reduction $\approx$18.7\%). Overall, RGMR provides a practical route for deploying frozen TSFMs in regional climate forecasting workflows.
arXiv:2607.18164v1 Announce Type: new
Abstract: Digital Twins rely on surrogate models to mirror physical systems in real time, yet these models can degrade as operating conditions evolve, a phenomenon known as concept drift. Maintaining surrogate fidelity under drift, particularly when models must also capture aleatoric uncertainty, remains an open challenge. Existing adaptive frameworks lack principled mechanisms for detecting when updates are needed, for efficiently adapting models from limited streaming data, and for certifying that updates genuinely improve predictive performance. Here we present an adaptive Digital Twin framework that integrates a Fisher score--based multivariate drift detector, Low-Rank Adaptation (LoRA) for parameter-efficient continual learning, and a Mann--Whitney $U$ test for online statistical validation. The framework monitors surrogate-model confidence via Fisher score vectors, triggers targeted fine-tuning of fewer than 1% of model parameters upon drift detection, and statistically certifies predictive improvement before deploying the updated surrogate. Applied to a stochastic linear system and a directed energy deposition additive manufacturing process as case studies, the framework successfully detects distributional shifts with short delays and restores both predictive accuracy and uncertainty quantification under abrupt and incremental drift. These results establish a statistically rigorous and computationally tractable pathway for sustaining the trustworthiness of neural-network--based Digital Twins throughout their operational life cycle.
arXiv:2607.18004v1 Announce Type: new
Abstract: Many visual reinforcement learning (RL) algorithms learn representations by matching latent distances to a behavioral distance induced by reward and transition similarity. In practice, the choice of the latent distance can strongly affect performance: using a fixed, pre-specified global norms (e.g., $\ell_p$ norms or other hand-designed metrics) may be overly restrictive to capture the behavioral distance. In contrast, unconstrained pairwise distances may admit degenerate solutions that drive the metric loss down without improving the representation. To address this gap, we introduce **PAMD: Pairwise Adaptive Mahalanobis Distance**, which parameterizes a positive-definite, pair-conditioned metric for measuring latent state similarity.
PAMD is a simple plug-in for existing bisimulation-based methods, offering a more expressive yet structured alternative to fixed, pre-specified latent distances. We empirically validate our method on visual MuJoCo continuous-control tasks, where final performance of several recent bisimulation-based RL algorithms is substantially improved when equipped with the distance we propose.
arXiv:2607.17286v1 Announce Type: new
Abstract: Issue localization, which identifies code locations requiring modification from issue descriptions, is a critical step in automated software maintenance. Existing approaches predominantly attempt to directly align issue descriptions with code elements, yet often struggle due to the inherent abstraction gap between the issue description and code implementation. Seeking alternative signals, our theoretical analysis suggests that test suites can serve as executable proxies for requirements, reducing localization uncertainty by 7.73 bits of entropy on average. A large-scale empirical study on 18 repositories validates this premise: existing tests cover 96.98\% of ground-truth files, and the two-hop pathway yields stronger semantic connectivity than direct matching in 82.4\% of cases. Despite their potential, leveraging tests for localization faces two key challenges: the semantic gap separating issue descriptions from test identifiers, and the substantial noise in execution traces from infrastructure code. To address these, we propose IssueExec, which bridges the semantic gap through domain-knowledge-enhanced test representations and filters noise via hierarchical trace analysis. Experiments on SWE-bench Lite show that IssueExec achieves state-of-the-art performance, improving function-level Recall@1 by 41.57\% over the strongest baseline. When integrated into the Agentless pipeline, IssueExec resolves 17.72\% more issues, demonstrating practical downstream benefits.
arXiv:2607.16348v1 Announce Type: new
Abstract: Machine learning-based intrusion detection systems (IDSs) often suffer from class imbalance and vulnerability to adversarial attacks, leading to degraded detection performance and reduced robustness. This study proposes a TabTransformer framework augmented by the Boundary-Seeking Generative Adversarial Network (BGAN) for flow-based intrusion detection using the CICIDS2017 dataset. BGAN serves a dual purpose by generating synthetic minority-class samples to mitigate data imbalance and producing adversarial samples to evaluate model robustness. Experimental results demonstrate that BGAN augmentation improves TabTransformer's Macro-F1 score from 82.96% to 86.50%, with the largest class-wise improvement observed for Web_Attack (F1 score: 0.29 to 0.61). Robustness evaluation shows that all non-augmented models experienced a 100% Performance Drop Rate (PDR) under adversarial testing, whereas all BGAN-augmented models achieved negative PDR values, indicating improved resilience. Furthermore, the augmented TabTransformer maintained stable and low False Triggered Rate (FTR) values (1.51%-2.92%) across all noise levels, compared with the BGAN-augmented Decision Tree, which reached 49.09% under benign perturbations. These findings demonstrate that BGAN consistently enhances both class balance and adversarial robustness, while the proposed BGAN-TabTransformer framework provides an effective and adaptive intrusion detection solution for adversarial network environments.
arXiv:2607.17287v1 Announce Type: new
Abstract: The suffix array ($\SA$) and inverse suffix array ($\ISA$) are fundamental data structures in string algorithms. Given a text of length $n$ over an integer alphabet of size $\sigma$, explicitly storing these structures requires $\Theta(n\log n)$ bits, motivating compressed representations that approach the information-theoretic minimum of $n\log\sigma$ bits. Two landmark solutions are the FM-index, which achieves succinct space and supports $\SA$ and $\ISA$ queries in roughly logarithmic time, and the Compressed Suffix Array (CSA), which uses $O(n\log\sigma)$ bits and answers both queries in $O(\log_\sigma^\epsilon n)$ time. Nearly all subsequent compressed indexes, including entropy-compressed and repetitiveness-aware variants, support $\SA$ and $\ISA$ using essentially the same techniques, leading to similar space--time trade-offs. This raises a fundamental question: under the same asymptotic space bound, do $\SA$ and $\ISA$ have the same inherent query complexity? We provide evidence that this symmetry is not intrinsic. Under an $O(n\log\sigma)$-bit space bound, we show that $\SA$ queries are unlikely to admit $\log^{o(1)} n$ query time, suggesting that improving the classical CSA bound would require a major breakthrough. In contrast, we present a new encoding supporting $\ISA$ queries in $O(\tau+\log\log n/\log\log\sigma)$ time using $(1+1/\tau+o(1))n\log\sigma$ bits, for any $\tau\ge1$. Our main insight is that the $\LF$-mapping, traditionally implemented using the Burrows--Wheeler Transform, can be adapted to support $\ISA$ queries directly from the packed text, eliminating the need to store the BWT while achieving substantially faster query times.
arXiv:2607.18169v1 Announce Type: new
Abstract: Edge Artificial Intelligence of Things (AIoT) systems often collect sensitive data in situ, raising serious privacy concerns. Resistive-switching random-access memory (RRAM) is an attractive substrate for efficient AIoT thanks to its multi-bit storage and compute-in-memory (CiM) capabilities, while its inherently stochastic write behavior provides a natural source of randomness that can be leveraged for differential privacy (DP) protection. Yet how to transform this device-level randomness-typically viewed as detrimental to accuracy-into a principled randomized mechanism while preserving model utility remains underexplored. We propose RRAM-DP, a hardware-algorithm co-design that relaxes RRAM write-verify operations to inject calibrated noise for inherently (epsilon, delta)-DP with formal DP analysis; together with pretraining techniques, it renders a novel private, high-utility CiM training paradigm. On CIFAR-10/100, STS-B, and SST-2, RRAM-DP-SGD incurs at best only a 3.8% accuracy drop at (epsilon=2, delta=O(1/n))-DP relative to non-private SGD. At the same privacy level, RRAM-DP-SGD delivers up to 57x and 3.2x energy savings and 2.7x and 1.8x speedups over A100 and DiVa-GEMM, respectively. These results point toward efficient, privacy-preserving in-memory training on RRAM at the edge.
arXiv:2607.16525v1 Announce Type: new
Abstract: We investigate plasmonic resonances and Fano-like interference in Au-coated Ag nanoislands fabricated by solid-state dewetting followed by Au overgrowth. By combining electrostatic spectral analysis, full-wave simulations, and linear transmission spectroscopy, we show that the optical response is governed by hybridization between plasmonic modes supported by the Ag-island and the Au-coating. Increasing the Au-coating thickness red-shifts the low-energy resonance and transfers spectral weight from high-energy to low-energy resonances, while a pronounced anti-resonant dip remains nearly fixed. The eigenmode analysis identifies this dip as the signature of destructive interference between super-radiant and sub-radiant hybridized modes. These results establish coated bimetallic nanoislands as promising platforms for tunable Fano-like optical responses accessible through standard far-field spectroscopy, using a fabrication route that requires no lithographic patterning and is compatible with large-area, low-cost production.
arXiv:2607.16527v1 Announce Type: new
Abstract: Linepack is a critical buffer in gas networks, providing short-term storage and operational flexibility. This paper presents a comparative dynamic analysis of the linepack impact in hydrogen (H2) and natural gas (CH4) networks under compressor contingency conditions. A three-day dynamic simulation is conducted for a CH4 network and a H2 network integrated with a power system. Two cases are investigated: Case 1 with identical and Case 2 with different pipe inner diameters in CH4 and H2 networks. The results in both cases show that H2 exhibits faster transient recovery after the compressor contingency, although its linepack is less than that of CH4. On the other hand, depending on the selected pipe diameter, pressure losses in the two networks can differ significantly. With identical pipe diameters, H2 exhibits lower pressure drop than CH4, and its demand therefore experiences less curtailment. However, when the H2 pipe diameter is reduced, the pressure drop across the H2 pipes increases and the curtailed load becomes higher than in the CH4 network. These results can be used by gas TSOs in designing and operating their grid more efficiently.
arXiv:2607.17036v1 Announce Type: new
Abstract: We propose a linear variable-step exponential time-differencing method for the incompressible Navier--Stokes equations in vorticity--streamfunction formulation on a two-dimensional periodic box. The method consists of a second-order scheme and an embedded first-order variant, yielding a natural mechanism for adaptive time stepping and a posteriori error control. Each time step requires only uniquely solvable linear problems: two heat equation solves, efficiently handled by Fourier methods in the periodic setting, and one linear scalar auxiliary-variable equation, evaluated via Laplace transform and Talbot's numerical inverse transform.
The construction combines the ETD framework, a mean-reverting scalar auxiliary variable (mr-SAV), and second-order extrapolation of the nonlinear term. The mean-reverting correction enables long-time stability while preserving full linearity, distinguishing the method from related mr-SAV schemes that require nonlinear algebraic solves. We prove unconditional long-time stability: for uniformly bounded $L^2$ forcing, the discrete vorticity remains bounded in $L^\infty(0,\infty;L^2)$ for all Reynolds numbers and time-step sizes. Numerical experiments
arXiv:2607.18064v1 Announce Type: new
Abstract: Coding agents can now be left alone to improve software against a score. In this pattern--recently popularized as "autoresearch"--the agent receives a dataset, an evaluation script, and one editable file, and iterates without supervision: modify the code, measure, keep the change if the score improves. But what does the agent actually optimize--the developer's intent, or the literal number? We ran this loop on a real production task: deciding which Quranic verses appear in a noisy speech-recognition transcript and splitting the transcript by verse. Two frontier coding agents, Claude Code and OpenAI Codex, started from the same blank file with the same instructions, budget, and reasoning effort, three runs each. Both independently invented the same algorithm (canonicalization, n-gram anchoring, dynamic-programming alignment)--and then diverged. Claude stopped early with compact, general code. Codex drove the score ~10x lower, largely by memorizing answers to individual evaluation rows (19-41 hardcoded verse ids per run): a clean natural instance of specification gaming by a production agent. In a preregistered second study, we added a held-out test set and told both agents it existed. The memorization vanished, and the score gap vanished with it--yet Codex's general core transferred better and more consistently (held-out detection+split 0.085+/-0.004 vs. 0.121+/-0.031), losing only on one missed rejection of non-recitation input. Two exploratory community arms (Cursor, Antigravity) are consistent with the pattern. Every agent's held-out solution matched or beat the hand-engineered pipeline it was built to replace--the best by an order of magnitude--and now runs in production. From the ways agents exploited our harness--reading sibling runs through shared git state, leaving notes to "future runs" in persistent memory--we distill five design rules for evaluating autonomous agents.
arXiv:2607.16351v1 Announce Type: new
Abstract: Publicly shareable construction-video benchmarks remain scarce, especially for safety-critical hazards that are rare, dangerous to stage, and difficult to release. We study worker under suspended load, a relational hazard that depends on worker-load geometry and temporal persistence rather than object detection alone. We introduce SynthSite, a focused synthetic video benchmark of 55 clips spanning varied load configurations, viewpoints, clutter, occlusions, and surveillance conditions, together with a privacy-aware hybrid generation workflow that supports both publicly shareable benchmark creation and privacy-constrained synthetic video generation.
We then ask whether worker appearance can be suppressed without undermining downstream hazard recognition. Under five whole-body privacy conditions, we evaluate worker and load retention, localization stability, and clip-level hazard recognition. We find that structure-preserving obfuscations retain substantially more downstream utility than appearance-smoothing baselines, and that preserving a raw visual reference alone does not guarantee the strongest agreement with human hazard labels. These findings suggest that privacy evaluation for construction safety analytics should assess not only appearance suppression, but also preservation of the geometric cues required for hazard reasoning. Our dataset and code are available at https://huggingface.co/datasets/govtech/SynthSite .
arXiv:2607.17836v1 Announce Type: new
Abstract: We present a one-way coupled Eulerian-Lagrangian computational framework for simulating fluid and particle dynamics in two-dimensional incompressible flows. The framework extends the GPU-accelerated GHD2D Fourier pseudospectral Navier-Stokes solver \cite{Mukherjee2018,Biswas2024} by incorporating passive tracer and finite-inertia particle modules. The Eulerian fluid equations are integrated using a second-order Adams-Bashforth scheme, while particle trajectories are advanced with a classical fourth-order Runge-Kutta method. Coupling between the Eulerian and Lagrangian descriptions is achieved through spatial and temporal interpolation of the fluid fields using bilinear, bicubic Catmull-Rom, and bicubic B-spline schemes. The framework is verified using analytical solutions and benchmark problems for the fluid solver, tracer transport, and inertial-particle dynamics. Bilinear interpolation produces transport statistics nearly identical to higher-order schemes while providing greater computational efficiency, and particle-number convergence demonstrates statistical robustness. Simulations of tracer and inertial particles in decaying two-dimensional turbulence capture long-time transport, turbulent dispersion, vortex trapping, coherent-structure interactions, preferential concentration, and inertia-dependent transport. The solver exhibits stable scaling with grid resolution and particle number while maintaining efficient single-GPU performance. The modular architecture and computational efficiency make the framework suitable for Eulerian-Lagrangian studies of turbulent transport and particle-laden incompressible flows.
arXiv:2607.16662v1 Announce Type: new
Abstract: Accurate emergency triage decision is critical to avoid clinical deterioration, morbidity, and mortality. Machine learning-based triage system involves acquiring the main presenting complaint in text form and assessing vital signs in numerical data, enabling an automated and efficient analysis of patient information for timely and accurate prioritization of medical attention. However, modelling the intricacies of both data types requires a comprehensive understanding of the temporal structure and dependencies within the data. Thus, the aim of this study is to propose a multimodal deep learning architecture that can effectively handle both tabular and textual data. Furthermore, the proposed model exploits self-attention to to capture both local and global relationships between the features. A dataset consisting of 11,102 triage data collected from emergency department of Hospital Universiti Sains Malaysia is used for model development and validation. The proposed model demonstrated an increase of 1.95% in accuracy, 2.49% in F1-score, and 1.41% in ROC AUC compared to the baseline model. The experimental results demonstrated the potential of the proposed model in predicting triage decisions.
arXiv:2607.16357v1 Announce Type: new
Abstract: Security rating platforms summarize externally observable cyber exposure and are expected to help organizations prioritize remediation. A platform may want to tell an organization how a candidate remediation action would affect its score, but repeatedly exposing exact score responses can reveal information about the hidden scoring engine. We propose a surrogate based approach for remediation score impact prediction that is designed to respect this opacity constraint. The surrogate predicts scores from organization configurations while explicitly representing checkpoint (i.e., a security check) applicability and the observed checkpoint set. A main challenge is that such predictions are not uniformly reliable: they depend on the amount and structure of the observable checkpoint evidence available for a given configuration. To address this, the approach combines applicability-aware surrogate construction, sensitivity analysis under controlled checkpoint restriction, a reliability layer for identifying unstable predictions, and score-impact prediction for supported remediation actions. Explicit modeling of checkpoint applicability is central throughout: it improves score prediction and provides the feature basis used by the reliability layer to identify unstable cases. We evaluate the approach on a real-world dataset of 5,188 organization configurations from a commercial security rating platform. The results show that the applicability-aware surrogate improves score prediction over simpler feature representations. For remediation, the surrogate predicts the score impact of supported actions, while the reliability layer helps identify cases in which these predicted impacts should be interpreted cautiously.
arXiv:2607.17514v1 Announce Type: new
Abstract: The surge of GPU-intensive workloads in artificial intelligence (AI) data centers drives massive energy demands, leading to soaring costs and significant stress on local power distribution networks. Coordinating delay-tolerant workload scheduling with power grid conditions via precise workload prediction can mitigate these issues. However, a critical gap remains in conventional approaches, i.e., minimizing prediction error does not necessarily lead to minimized downstream operational loss. Hence, this paper proposes an end-to-end Predict-Then-Schedule (PTS) framework that integrates upstream workload prediction with downstream scheduling optimization. By leveraging differentiable convex optimization, the PTS framework maps input features directly to optimal scheduling and enables gradient-based training. Furthermore, to respect the data center's capacity, a workload over-shifted loss combining electricity cost with a penalty for load-shedding is introduced to evaluate scheduling quality. Experiments demonstrate that the proposed framework significantly reduces operational cost and enhances system security compared to the conventional two-stage baseline.
arXiv:2607.16968v1 Announce Type: new
Abstract: Under stated assumptions, a static surface-code patch that adds no fold or \mbox{self-dual} structure cannot perform the magic-axis check that magic-state cultivation relies on while still accepting often. This is a conditional no-go. Fault-tolerant machines spend much of their cost making magic states, and cultivation makes them in place by measuring the magic axis, which every known construction does through a fold or \mbox{self-dual} patch that it is folklore to call necessary. We test the folklore. The no-go says that a useful check must pay for the magic axis somewhere. It can add a charge-converting resource, it can leave the dilute regime of its accepted history, or it can accept only exponentially rarely. For a single stabilizer-measurement transcript this is proved outright, from a topological reading of the accepted outcome. For adaptive, post-selected protocols in a bounded-depth (polynomial spacetime-volume) model, it holds under two structural assumptions plus a subcriticality assumption. We isolate the one open assumption, show that protection alone does not force it, and give the threshold any resolution must address. What remains is a single conjecture.
arXiv:2607.16261v1 Announce Type: new
Abstract: Modern optimizers combine gradients from the current mini-batch with historical optimization state, such as momentum or adaptive moments. While highly effective, aggregating across the batch and incorporating this history can produce parameter updates that increase the loss of individual samples. We term this effect harm and formalize the parameter update as an optimization problem that explicitly minimizes the conflicting impact of both batch averaging and past optimization state on current data.
Because the exact formulation is intractable, we introduce a highly efficient proxy. We first reduce the problem's dimensionality to the batch size, and then drastically cut memory and speed bottlenecks by successfully restricting the optimization to the last linear layer. This hinges on the unexpected finding that this layer alone reliably captures the second-order statistics of the per-sample gradients. The resulting surrogate problem integrates readily into standard optimizers like SGD and AdamW, and can be solved using a small number of GPU-friendly iterations. Crucially, the method exhibits favorable scaling properties, as the relative computational overhead shrinks as the model size or input grows. Experiments on image classification benchmarks confirm reduced per-sample interference and improved generalization.
arXiv:2607.16846v1 Announce Type: cross
Abstract: Motivated by programmable tweezer arrays, we develop an exactly solvable shape-space theory for near-equilateral atomic trimers. The Higgs oscillator on Kendall's shape sphere gives a nonresonant spectral lattice whose fixed-angular-momentum relative-stationary minimizers are supported on two adjacent admissible sites. These symmetry-selected doublets are separated from higher relative-stationary branches by a finite branch gap. With phase-coherent shape-mode driving and Rydberg-mediated conditional phases, they furnish a candidate route to geometric qubits and entangling operations.
arXiv:2607.16361v1 Announce Type: new
Abstract: A trained flow or diffusion model is usually run with only a handful of solver steps, and the integration error this leaves behind is unevenly distributed across the image. We ask where that error is injected and how it reaches the endpoint, and answer with a signed source-and-transport accounting of few-step integration error, tested to first order. A perturbation experiment on five models at 256^2 resolution shows the learned dynamics spread local disturbances widely: near the start of sampling, under 10% of the summed endpoint response remains at the source. Signed one-step truncation residuals, propagated through the model's own linearized dynamics, reconstruct much of the endpoint error's direction and regional structure (cosine 0.81-0.87), and a region's error owes more to what arrives from elsewhere than to its own injection. Structure-destroying nulls, with protocols frozen before evaluation, locate what carries the account: randomizing contribution signs halves it, and reassigning which region receives each contribution, with content, norms, and signs intact, destroys it entirely. Where the injections land is readable from the model itself. The variation of its velocity or prediction field along the trajectory, a structure that emerges during training, predicts the final per-region gap (within-image rho of 0.57-0.70 on fine trajectories, weaker from the cheap solve alone). The prediction is partial because endpoint error depends not only on injected magnitude but on its sign, timing, and transport through the learned dynamics. A training penalty on the injected variation lowers few-step error, so the structure is one a model can be trained to change.
arXiv:2607.17522v1 Announce Type: new
Abstract: Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model. A locally dependent nonnegative score field represents position wise uncertainty, and the scheduler selects the K positions with the smallest scores. Dependence among the selected positions is measured through a distance-dependent Gaussian correlation model. This separation provides a tractable framework for quantifying how the geometry of low-score locations affects the dependence cost of factorized parallel decoding. We establish two complementary results. In a conservative sub-square-root regime, the conditional Gaussian total correlation of the selected block vanishes in probability. At the square-root scale, it remains non-negligible with positive asymptotic probability and admits a strictly positive expectation lower bound. Synthetic experiments support the predicted finite-size behavior. These results provide a rigorous stochastic-geometry baseline for understanding how budget size, score dependence, and spatial correlation jointly shape one-step confidence-based selection in masked discrete diffusion.