arXiv:2605.09391v2 Announce Type: replace Abstract: It is becoming increasingly necessary to have monitors check for harmful behaviors during language model interactions, but text-only monitoring has not been sufficient. This is because models sometimes exhibit strategic deception and sandbagging, changing their behavior during evaluation. This motivates the use of white-box monitors like linear probes, which can read the model internals directly. Currently, such probes can fail under distribution shift, limiting their usefulness in real settings. We study whether there exists a low-dimensional subspace of the model internals that captures harmful behaviors more robustly, while leaving out spuriously correlative features. Inspired by the Assistant Axis and Persona Selection Model, we construct persona axes for deception and sycophancy using contrastive persona prompts. The first principal components, obtained by unsupervised PCA of the persona-specific vectors, cleanly separate harmful and harmless personas. Across 10 evaluation datasets, we show that persona-derived directions transfer non-trivially and probes trained on persona-PC projections generalize better than probes trained on raw activations. We also find that a unified axis consisting of multiple harmful and harmless behaviors improves generalization across behaviors and datasets. Overall, persona vectors provide a useful inductive bias for building more transferable behavior probes.
Science Journals
arXiv:2506.15255v3 Announce Type: replace Abstract: Scalar mixing fronts develop at the interface of agitated fluids of different solute concentrations. In such fronts, scalar fluctuations form at both microscopic and macroscopic scales, due to stretching-enhanced molecular diffusion and hydrodynamic dispersion respectively. While these two elementary processes are well understood separately, predicting how their coupling governs the evolution of concentration statistics within dispersing fronts remains a challenge. Here, we propose a theoretical framework to describe scalar fluctuations in fronts mixed by smooth chaotic flows. We find that the transfer of energy between the macroscopic and microscopic scalar fluctuation scales operates at a characteristic length scale $s_i$, for which dispersion and stretching-enhanced diffusion are of equal strength. This leads to a closed expression for the concentration variance, which captures the results of direct numerical simulations with no fitting parameters, for a broad range of P\'eclet numbers. These findings open a new avenue for predicting both conservative and reactive mixing in smooth chaotic flows such as porous media or microfluidic flows.
arXiv:2605.15799v1 Announce Type: new Abstract: Multi-agent pathfinding (MAPF) under one-shot planning is a core component of warehouse automation, yet classical formulations typically assume four-connected 2D grids with unit-time moves in four directions. To fill reality gaps while still being trackable with discrete combinatorial search, this work proposes a more practical counterpart tailored to differential-drive AGVs. We term this multi-agent warehouse pathfinding (MAWPF), featured with four constraints: (i) agent actions are restricted to straight motion and in-place rotation; (ii) rotations require multi-step costs; (iii) acceleration and deceleration are considered, and; (iv) follower collisions are prohibited to prevent rear-end crashes. To solve MAWPF efficiently, we adapt representative suboptimal MAPF algorithms-PP, LNS2, PIBT, and LaCAM-and conduct comprehensive benchmarking. Our experiments reveal that PP and LNS2 struggle to solve instances with many agents, while PIBT-based approaches achieve preferable scalability with increased solution cost. We believe that these constitute an important step toward adapting classical gridworld MAPF to operational warehouse setups.
arXiv:2605.15803v1 Announce Type: new Abstract: Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: the rapid decay of intra-group variance. As the distinctiveness among samples within a group diminishes, the variance approaches zero. This eliminates the very learning signal required for optimization, rendering the process unstable and forcing the policy into premature stagnation or reward hacking. Existing strategies, such as varying the initial noise or increasing group sizes, often fail to address this fundamental issue, resulting in training instability or diminishing returns. To overcome these challenges, we propose $\textbf{Embedding-perturbed Exploration Preference Optimization (}E^2\textbf{PO)}$, a novel framework that sustains optimization through embedding-level perturbation. Our method introduces structured, embedding-level perturbations within sample groups, guaranteeing a robust variance that preserves the discriminative signal throughout the training process. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art baselines, achieving a more faithful alignment with human preference.
arXiv:2306.08793v5 Announce Type: replace Abstract: Imaging through complex scattering media is severely limited by aberrations and scattering which obscure images and reduce resolution. Confocal and temporal gatings partly filter out multiple scattering but are severely degraded by wavefront distortions. Adaptive optics restore resolution by correcting low-order aberrations and matrix-based imaging enables more complex wavefront corrections. However, they struggle to undo high-order aberrations under strong scattering, preventing imaging at greater depths. To address these challenges, we present Scattering Matrix Tomography (SMT), an approach that makes full use of the wavefront engineering capability of scattering matrix and extreme adaptive optics. SMT reformulates imaging through complex media as a numerical optimization and employs Zernike-mode wavefront regularization and coarse-to-fine nonconvex optimization strategy to reverse severe aberrations, enabling noninvasive high-resolution volumetric imaging in multiple scattering regime. Based on the spectrally-resolved matrix measurement, SMT achieves a depth-over-resolution ratio above 900 beneath $ex~vivo$ mouse brain tissue and volumetric imaging at over three transport mean free paths inside an opaque colloid, where conventional methods fail to correct strong aberrations under these challenging conditions. SMT is noninvasive, label-free, and works both inside and outside the scattering media, making it suitable for various applications, including medical imaging, biological science, device inspection, and colloidal physics.
arXiv:2605.15418v1 Announce Type: new Abstract: Hybrid optical systems combining refractive and diffractive optical responses have the potential to support new types of optical behavior, but they are difficult to model and optimize due to the disparate spatial scales and physics exhibited by ray and wave phenomena. In this work, we present a differentiable ray-wave framework that serves as a general model for hybrid refractive-diffractive optical systems and that operates as a plug-and-play module within standard ray tracing pipelines. Our model uniquely applies to both planar and curvilinear diffractive surfaces and can accommodate arbitrary holographic diffractive profiles with high spatial frequency responses. We analyze ray-wave modeling regimes that optimally account for the spatial frequency properties and spatial curvature of the diffractive surfaces, and we demonstrate the gradient-based end-to-end optimization of hybrid refractive-diffractive systems featuring planar and conformal diffractive surfaces. We anticipate that these modeling capabilities will enable new classes of hybrid optical systems relevant to computational imaging and display applications.
arXiv:2603.08962v2 Announce Type: replace Abstract: This letter investigates the use of differential space-time block coding (DSTBC) to address antenna array calibration impairments at multi-antenna user equipment (UE) in the downlink (DL) of cell-free massive MIMO (CF-mMIMO) systems. We show that, by exploiting DSTBC, reliable DL communication can be achieved without explicit UE-side calibration or channel phase knowledge. Simulation results demonstrate that the proposed DSTBC-based transmission effectively mitigates the impact of antenna-dependent phase offsets, restoring near-coherent performance in CF-mMIMO networks.
arXiv:2506.14829v2 Announce Type: replace Abstract: AI for Social Impact (AI4SI) is an emergent field harnessing interdisciplinarities between the fields of artificial intelligence (AI), machine learning (ML), and the social sciences to address societal issues aligned with the United Nations Sustainable Development Goals (UN SDGs), such as universal healthcare, climate action, etc. Despite AI4SI's rising popularity, achieving tangible, on-the-ground impact remains a significant challenge. In particular, identifying collaborators open to co-designing and deploying AI4SI-based solutions in real-world settings is often difficult. Thus, many projects stall at the proof-of-concept stage, unable to scale to production-level deployment. Drawing on twenty-six AI4SI researchers' interviews, primarily from academic institutions though also including some industry researchers and practitioners, and the authors' own lived experiences, this paper employs thematic analysis to highlight structural, organizational, communication, collaboration, and operational challenges hindering socially impactful AI4SI deployments. While there are no easy fixes, the authors synthesize best practices and actionable strategies from interviews and personal experiences, positioning this paper as a practical guide for AI4SI researchers and organizations pursuing socially impactful collaborations$^1$. $^1$We note that our findings are most directly applicable to academic research groups in the global north, as governmental, startup, and global south researchers' perspectives are underrepresented in our sample.
arXiv:2605.16100v1 Announce Type: new Abstract: We study the role of retardation in the energy shift of Rydberg states induced by thermal radiation, focusing on the case of temperatures higher than those for which the electric-dipole approximation is expected to apply. As anticipated by Farley and Wing [Phys. Rev. A {\bf 23}, 2397 (1981)], retardation needs to be taken into account in calculations of this energy shift at and above the temperature $\alpha\, mc^2/(3k_{\rm B}\,n^2)$, where $n$ is the principal quantum number of the state considered, $m$ is the mass of the electron and $k_{\rm B}$ is Boltzmann constant.The corresponding non-dipole shift dominates the electric-dipole shift at about 2.5 times that characteristic temperature. We also show that the electric-quadrupole thermal shift is of the same order of magnitude as the diamagnetic thermal shift and would thus need to be taken into account in the circumstances where the latter is relevant.
arXiv:2605.15547v1 Announce Type: new Abstract: Following recent interest in correctly rounded math library functions (as currently recommended by the IEEE 754 standard), we have designed several SIMD algorithms for one-input single precision functions and integrated them into our CPU math library; these will form the core of the first correctly rounded vector math library, to be available to users in mid-2026. To take advantage of the cross-platform bitwise reproducibility afforded by correct rounding, we adapted and evaluated a few SIMD implementations on graphics processing units (GPU). In addition, we designed and evaluated proof-of-concept SIMD implementations of two correctly rounded double precision functions.
arXiv:2605.15938v1 Announce Type: new Abstract: Finding an odor source in a turbulent flow requires effectively leveraging the history of olfactory observations into a robust navigation strategy. In this work, we use tabular Q-learning to train an olfactory search agent with a minimal memory of past observations: only a running clock since the last whiff. This agent learns an interpretable strategy to recover the plume which combines well-known behaviors observed in insects: surging, casting, and a return downwind. While achieving good performance on data from direct numerical simulations of turbulence, the agent is limited by an inability to adapt its strategy to the local intermittency level; we show that providing more flexibility improves robustness.
arXiv:2605.02609v2 Announce Type: replace Abstract: The effectiveness of active learning hinges on the choice of the acquisition criterion by which a learning algorithm selects potentially informative data points whose label is subsequently queried. This paper proposes a novel gradient-based acquisition criterion, derived from a generalization bound introduced by Luo et al. (2022). This criterion can be applied in lieu of uncertainty measures in uncertainty sampling, or incorporated into diversity-based methods that consider the spread of sampled points in addition to the uncertainty of their labels. We provide a theoretical justification of the proposed acquisition criterion, and demonstrate its effectiveness in an empirical evaluation.
arXiv:2605.14716v2 Announce Type: replace Abstract: Sparse anchors provide a compact interface for human motion authoring: users specify a few root positions, planar trajectory samples, or body-point targets, while the system synthesizes the full-body motion that completes the under-specified intent. We present AnchorRoute, a sparse-anchor motion synthesis framework that uses anchors as a shared scaffold for both generation and refinement. Before generation, AnchorRoute converts sparse anchors into anchor-condition features and injects the resulting condition memory into a frozen Transition Masked Diffusion prior through AnchorKV and dual-context conditioning. This preserves the generation quality of the pretrained text-to-motion prior while learning sparse spatial control. After generation, the same anchors are evaluated as residuals: their timestamps define refinement intervals, and their residuals determine where correction should be concentrated. RouteSolver then refines the motion by projecting soft-token updates onto anchor-defined piecewise-affine interval bases. This couples generation-time anchor conditioning with residual-routed refinement under one anchor scaffold. AnchorRoute supports root-3D, planar-root, and body-point control within the same formulation. In benchmark evaluations, AnchorRoute outperforms prior sparse-control methods under the sparse keyjoint protocol and consistently improves anchor adherence across control families. The results show that the learned anchor-conditioned generator and RouteSolver refinement are complementary: the generator preserves text-motion quality, while RouteSolver provides a controllable path toward stronger anchor adherence.
arXiv:2605.00674v2 Announce Type: replace Abstract: Large language models (LLMs) are becoming increasingly capable mathematical collaborators, but static benchmarks are no longer sufficient for evaluating progress: they are often narrow in scope, quickly saturated, and rarely updated. This makes it hard to compare models reliably and track progress over time. Instead, we need evaluation platforms: continuously maintained systems that run, aggregate, and analyze evaluations across many benchmarks to give a comprehensive picture of model performance within a broad domain. In this work, we build on the original MathArena benchmark by substantially broadening its scope from final-answer olympiad problems to a continuously maintained evaluation platform for mathematical reasoning with LLMs. MathArena now covers a much wider range of tasks, including proof-based competitions, research-level arXiv problems, and formal proof generation in Lean. Additionally, we maintain a clear evaluation protocol for all models and regularly design new benchmarks as model capabilities improve to ensure that MathArena remains challenging. Notably, the strongest model, GPT-5.5, now reaches 98% on the 2026 USA Math Olympiad and 74% on research-level questions, showing that frontier models can now comfortably solve extremely challenging mathematical problems. This highlights the importance of continuously maintained evaluation platforms like MathArena to track the rapid progress of LLMs in mathematical reasoning.
arXiv:2605.14087v2 Announce Type: replace Abstract: Large Language Models (LLMs) trained on web-scale corpora inherently absorb toxic patterns from their training data. This leads to toxic degeneration where even innocuous prompts can trigger harmful outputs. This phenomenon poses significant risks for real-world deployments. Thus, necessitating effective mitigation strategies that should maintain model utility while ensuring safety. In this comprehensive replication study, we evaluate the efficacy of DExperts (Decoding-time Experts), which is an inference-time mitigation technique that steers generation without requiring model retraining. We structured our research into three systematic phases: (1) establishing baseline toxicity measurements using RealToxicityPrompts on standard GPT-2 models; then (2) implementing and evaluating DExperts to mitigate explicit toxicity; and finally (3) stress-testing the method against implicit hate speech using the adversarial ToxiGen dataset. Our empirical results confirm that while DExperts achieves near-perfect safety rates (100%) on explicit toxicity benchmarks, it exhibits brittleness against adversarial, implicit hate speech, with safety rates dropping to 98.5%. Furthermore, we quantify a critical trade-off. The method introduces a 10x latency penalty (from 0.2s to 2.0s per generation), posing challenges for real-time deployment scenarios. This study contributes to the growing body of work on AI safety by highlighting the robustness gap between explicit and implicit toxicity mitigation. We emphasize the need for more sophisticated approaches that generalize across diverse hate-speech patterns without incurring prohibitive computational costs.
arXiv:2605.15535v1 Announce Type: new Abstract: Underwater salient object detection (USOD) has attracted increasing attention for underwater visual scene understanding and vision-guided robotic applications. However, existing USOD methods still struggle with underwater image degradations, which often lead to inaccurate object localization, fragmented salient regions, and coarse boundary prediction. To address these challenges, this paper proposes DSS-USOD, a novel RGB-based USOD method built upon dynamic structural specialization. DSS-USOD extracts a shared base representation from a single underwater image, decomposes it into boundary-sensitive and region-coherent structural features, and dynamically coordinates their contributions according to local structural context. Specifically, the extracted shared base representation is decomposed into a boundary-sensitive branch for modeling fine-grained boundary details and a region-coherent branch for capturing region-level structural consistency. A spatial coordination module is then introduced to adaptively regulate the relative contributions of the two branches according to local structural context. Moreover, cooperative structural supervision is introduced to promote branch specialization and stabilize spatial coordination, enabling DSS-USOD to better balance boundary precision and region coherence under degraded underwater conditions. Extensive experiments show that DSS-USOD achieves superior performance on benchmark datasets. Finally, real-world deployment on an underwater robot validates the practical effectiveness of DSS-USOD for underwater object inspection.
arXiv:2507.15778v2 Announce Type: replace Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has become an effective post-training method for improving the reasoning abilities of Large Language Models (LLMs). However, existing methods mainly apply uniform optimization constraints across all tokens, ignoring their heterogeneous roles. Prior work shows that high-entropy tokens are closely tied to reasoning, while low-entropy tokens primarily encode factual knowledge, and recent approaches attempt to exploit this distinction by isolating token updates via masking or asynchronous training. We argue that such isolation breaks the sequential dependency structure of autoregressive generation, leading to suboptimal learning. To address this, we propose \textbf{Archer}, an entropy-aware RLVR framework with \textbf{dual-token constraints} that preserves joint optimization while modulating update strength across token types. Our method introduces response-level entropy normalization for stable token classification and applies differentiated clipping ranges and KL regularization to encourage exploration on reasoning tokens while preserving knowledge tokens. Experiments on mathematical reasoning and code generation benchmarks show that Archer consistently outperforms strong baselines across multiple model scales, improving both \textit{pass@1} and \textit{pass@K} performance. These results highlight the importance of respecting sequence-level dependencies when designing fine-grained RL optimization strategies for LLMs.
arXiv:2605.02689v2 Announce Type: replace Abstract: Long-term time series forecasting requires models that simultaneously capture rapid oscillations, medium-range periodicities, and slowly evolving macro-trends from a fixed look-back window. Existing lightweight MLP-based models typically operate on a single temporal resolution, limiting their ability to explicitly model patterns at multiple scales. We propose MSMixer, a channel-independent multi-scale MLP architecture that addresses this limitation through three complementary innovations: (i) three parallel scale branches at down-sample factors {1x, 4x, 16x} with independent MLP blocks, (ii) a learnable softmax gate that dynamically weighs branch outputs, and (iii) a DLinear complementary shortcut that provides full-window trend and seasonality context. MSMixer contains only 112K parameters at H=96 and runs at O(T) complexity. Evaluated on four ETT benchmarks with standard chronological splits and three random seeds, MSMixer achieves the lowest average MSE (0.357) among lightweight models, outperforming DLinear (0.386, -7.4%) and NLinear (0.365, -2.1%), winning 12 of 16 configurations. Against five Transformer-based baselines from the literature, MSMixer achieves best or second-best MSE in 9 of 16 configurations while using 5x fewer parameters than PatchTST. Ablation and sensitivity analyses confirm the complementary contributions of the multi-scale branches and the DLinear shortcut.
arXiv:2601.21294v2 Announce Type: replace Abstract: Partial Least Squares (PLS) learns shared structure from paired data via the top singular vectors of the empirical cross-covariance (PLS-SVD), but multimodal datasets often have missing entries in both views. We study PLS-SVD under independent entry-wise missing-completely-at-random masking in a proportional high-dimensional spiked model. After appropriate normalization, the masked cross-covariance behaves like a spiked rectangular random matrix whose effective signal strength is attenuated by $\sqrt{\rho}$, where $\rho$ is the joint entry retention probability. The replica-symmetric analysis predicts a sharp BBP-type phase transition: below a critical signal-to-noise threshold the leading singular vectors are asymptotically uninformative, while above it they achieve nontrivial alignment with the latent shared directions, with closed-form asymptotic overlap formulas. We also state a finite-rank extension as a conjecture, predicting that the same missingness-adjusted threshold applies componentwise when the latent spikes are separated. Simulations and semi-synthetic multimodal experiments agree with the predicted phase diagram and recovery curves across aspect ratios, signal strengths, and missingness levels.
arXiv:2605.15529v1 Announce Type: new Abstract: Process Reward Models (PRMs) provide step-level feedback for reasoning, but current PRMs usually output only a single reward score for each step. Downstream methods must therefore treat imperfect step-level reward predictions as reliable decision signals, with no indication of when these predictions should be trusted. We propose BetaPRM, a distributional PRM that predicts both a step-level success probability and the reliability of that prediction. Given step-success supervision from Monte Carlo continuations, BetaPRM learns a Beta belief that explains the observed number of successful continuations through a Beta-Binomial likelihood, rather than regressing to the finite-sample success ratio as a point target. This learned reliability signal indicates when a step reward should be trusted, enabling downstream applications to distinguish reliable rewards from uncertain ones. As one application, we introduce Adaptive Computation Allocation (ACA) for PRM-guided Best-of-N reasoning. ACA uses the learned reliability signal to stop when a high-reward solution is reliable and to spend additional computation on uncertain candidate prefixes. Experiments across four backbones and four reasoning benchmarks show that BetaPRM improves PRM-guided Best-of-N selection while preserving standard step-level error detection. Built on this signal, ACA improves the accuracy--token tradeoff over fixed-budget Best-of-16, reducing token usage by up to 33.57% while improving final-answer accuracy.
arXiv:2605.15053v2 Announce Type: replace Abstract: Continually pre-training a large language model on heterogeneous text domains, without replay or task labels, has remained an unsolved architectural problem at LLM scale. Existing methods rely on replay buffers, task identifiers, regularization penalties that scale poorly, or sentence-classification-scale evaluation. We introduce TFGN, an architectural overlay for transformer language models that produces input-conditioned, parameter-efficient updates while leaving the rest of the transformer unchanged. On six heterogeneous text domains (Prose, Python, Math, Biomedical, Chinese, JavaScript) at 1B tokens per phase across three model scales (~398M, ~739M, ~9B) and two regimes (From-Scratch and Retrofit), TFGN achieves backward transfer of -0.007 at LLaMA 3.1 8B Retrofit, HellaSwag retention 0.506/0.504/0.510, and >=99.59% L2-orthogonal gradient separation between domain pairs - with no replay, no task IDs, no Fisher penalty. The same matrices show positive cross-domain forward transfer: held-out JavaScript PPL drops 26.8% at LLaMA-8B Retrofit and 62.0% at GPT-2 Medium From-Scratch purely from Python training. Two extensions on the same substrate close further open problems. A closed-loop meta-control layer (Extension A) reduces forgetting by an additional 81% at ~398M, mapping onto the System A and System M roles of Dupoux et al. (arXiv:2603.15381). An operator-level plan vector (Extension B) reshapes forward-pass behavior at 99.96% cosine fidelity over 30 source->target pairs. The architectural insight is a Read/Write decomposition: the forward pass is fully dense, while cross-domain parameter updates are structured so prior-domain subspaces are not written to. To our knowledge, TFGN is the first architecture that simultaneously closes catastrophic forgetting at LLM scale, realizes a closed-loop autonomous-learning meta-controller, and carries an operator-level latent planner.
arXiv:2605.05179v2 Announce Type: replace Abstract: By far the most common way to estimate an expected loss in machine learning is to draw samples, compute the loss on each one, and take the empirical average. However, sampling is not necessarily optimal. Given an MLP at initialization, we show how to estimate its expected output over Gaussian inputs without running samples through the network at all. Instead, we produce approximate representations of the distributions of activations at each layer, leveraging tools such as cumulants and Hermite expansions. We show both theoretically and empirically that for sufficiently wide networks, our estimator achieves a target mean squared error using substantially fewer FLOPs than Monte Carlo sampling. We find moreover that our methods perform particularly well at estimating the probabilities of rare events, and additionally demonstrate how they can be used for model training. Together, these findings suggest a path to producing models with a greatly reduced probability of catastrophic tail risks.
arXiv:2605.15528v1 Announce Type: new Abstract: Autonomous underwater vehicle (AUV) swarms are emerging as intelligent underwater networks, where each node must sense, communicate, process local data, and make decisions under severe acoustic constraints. Persistent underwater target tracking is a typical task with moving targets, changing communication topology, intermittent acoustic links, and limited observation for each AUV. Multi-agent reinforcement learning (MARL) is a natural candidate for distributed tracking, yet existing studies still lack a unified open-source platform for evaluating different MARL algorithms under six-degree-of-freedom AUV dynamics. In addition, policies trained with raw geometric states and low-level force actions often struggle to represent task phases, observation reliability, link quality, and local cooperation roles. This paper addresses these issues by developing an open-source MARL-AUV platform that integrates DI-engine with a six-degree-of-freedom underwater AUV target-tracking simulator. To the best of our knowledge, it is the first open platform that connects a public MARL training framework with physically modeled AUV swarm-based tasks, and provides a unified experimental protocol for fair training, testing, and comparison of representative RL and MARL algorithms. Based on this platform, we propose STG-MAPPO, a Semantic Task Graph-enhanced variant of Multi-Agent Proximal Policy Optimization. STG-MAPPO builds semantic policy inputs from tracking diagnostics, task phases, observation confidence, link availability, neighbor tracking quality, and local role advantage. A compact semantic task graph links communication-constrained network states to decentralized actor decisions, and a velocity-level action abstraction maps high-level cooperative decisions to executable six-degree-offreedom AUV control inputs.The code is available at https://github.com/dasjsaj/MARL-AUV.
arXiv:2605.15648v1 Announce Type: new Abstract: Differentially Private Stochastic Gradient Descent (DP-SGD) is widely used to protect training data in machine learning. Its privacy guarantee is commonly analyzed through a security game in which an adversary infers whether a target record is included in the training dataset from the mechanism output. The resulting privacy leakage is characterized by a privacy curve, which reports the false negative rate as a function of the false positive rate. We identify a mismatch between this formal analysis and common DP-SGD implementations. Existing analyses often model DP-SGD and its variants as the Subsampled Gaussian Mechanism (SGM), where Gaussian noise is added to the sum of clipped gradients computed from a Poisson-sampled batch. In practice, however, many implementations apply an additional normalization step: the noisy gradient sum is divided either by the expected batch size or by the sampled batch size. These mechanisms are therefore better formalized as the Expected-Averaged SGM (EASGM) or the Batch-Averaged SGM (ASGM), respectively. We re-analyze the privacy guarantees of DP-SGD under the EASGM and ASGM formulations. Our theoretical results show that these guarantees can be weaker than the standard SGM-based guarantee, implying that the true privacy leakage may exceed the reported guarantee in some regimes. We further audit four state-of-the-art DP-SGD implementations, including Meta's Opacus library, and observe empirical leakage beyond the SGM-based guarantees. Finally, we audit Opacus versions v0.9.0 to v1.5.4 and derive a corrected privacy guarantee for the latest implementation.
arXiv:2506.05878v3 Announce Type: replace Abstract: We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.