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01.
arXiv (CS.AI) 2026-06-12

ARROW: Augmented Replay for RObust World models

arXiv:2603.11395v3 Announce Type: replace-cross Abstract: Continual reinforcement learning challenges agents to acquire new skills while retaining previously learned ones with the goal of improving performance in both past and future tasks. Most existing approaches rely on model-free methods with replay buffers to mitigate catastrophic forgetting; however, these solutions often face significant scalability challenges due to large memory demands. Drawing inspiration from neuroscience, where the brain replays experiences to a predictive World Model rather than directly to the policy, we present ARROW (Augmented Replay for RObust World models), a model-based continual RL algorithm that extends DreamerV3 with a memory-efficient, distribution-matching replay buffer. Unlike standard fixed-size FIFO buffers, ARROW maintains two complementary buffers: a short-term buffer for recent experiences and a long-term buffer that preserves task diversity through intelligent sampling. We evaluate ARROW on two challenging continual RL settings: Tasks without shared structure (Atari), and tasks with shared structure, where knowledge transfer is possible (Procgen CoinRun variants). Compared to model-free and model-based baselines with replay buffers of the same-size, ARROW demonstrates substantially less forgetting on tasks without shared structure, while maintaining comparable forward transfer. Our findings highlight the potential of model-based RL and bio-inspired approaches for continual reinforcement learning, warranting further research.

02.
arXiv (quant-ph) 2026-06-16

Twisted (co)homology of non-orientable Weyl semimetals

arXiv:2511.22303v3 Announce Type: replace-cross Abstract: The quasi-particle excitations in Weyl semimetals, known as Weyl fermions, are usually forced to emerge in charge-conjugate pairs by the Nielsen–Ninomiya theorem. When the Brillouin zone is non-orientable, this constraint is replaced by a $\mathbb{Z}_2$ charge cancellation, as a result of the chirality becoming ill-defined on such manifolds; this results in configurations with seemingly non-zero total chirality. Here, we set out to explain this behaviour from a purely topological perspective, and provide a classification of non-orientable Weyl semimetal topology in terms of exact sequences of twisted (co)homology groups. This leads to several discoveries of direct physical importance: in particular, we recover the $\mathbb{Z}_2$ charge cancellation in a coordinate-independent way, allowing meaningful limits to be set on its physical interpretation. A detailed discussion is provided on a specific Klein bottle-like topology induced by a momentum-space glide symmetry, including a full review of the insulating and semimetallic invariants of the system and a classification of the surface states on the non-orientable boundary. Beyond this, we provide a complete survey of all possible non-orientable Brillouin zones and their associated invariants, and extend our formalism into the realm of non-Hermitian topological physics and inversion-symmetric Weyl semimetals. Our work exemplifies the vast potential of fundamental mathematical descriptions to not only aid the corresponding physical intuition, but also predict novel and hitherto overlooked phenomena of great relevance throughout the physics research forefront.

03.
arXiv (CS.CV) 2026-06-11

Right Regions, Wrong Labels: Semantic Label Flips in Segmentation under Correlation Shift

The robustness of machine learning models can be compromised by spurious correlations between non-causal features in the input data and target labels. A common way to test for such correlations is to train on data where the label is strongly tied to some non-causal cue, then evaluate on examples where that tie no longer holds. This idea is well established for classification tasks, but for semantic segmentation the specific failure modes are not well understood. We show that a model may achieve reasonable overlap while assigning the wrong semantic label, swapping one plausible foreground class for another, even when object boundaries are largely correct. We focus on this semantic label-flip behaviour and quantify it with a simple diagnostic (Flip) that counts how often ground truth foreground pixels are assigned the wrong foreground identity while remaining predicted as foreground. In a setting where category and scene are correlated during training, increasing the correlation consistently widens the gap between common and rare test conditions and increases these within-object label swaps on counterfactual groups. Overall, our results motivate assessing segmentation robustness under distribution shift beyond overlap by decomposing foreground errors into correct pixels, flipped-identity pixels, and missed-to-background pixels. We also propose an entropy-based, ground truth label-free `flip-risk' score, which is computed from foreground identity uncertainty, and show that it can flag flip-prone cases at inference time. Code is available at https://github.com/acharaakshit/label-flips.

04.
arXiv (CS.CV) 2026-06-17

4DSloMo: 4D Reconstruction for High Speed Scene with Asynchronous Capture

Reconstructing fast-dynamic scenes from multi-view videos is crucial for high-speed motion analysis and realistic 4D reconstruction. However, the majority of 4D capture systems are limited to frame rates below 30 FPS (frames per second), and a direct 4D reconstruction of high-speed motion from low FPS input may lead to undesirable results. In this work, we propose a high-speed 4D capturing system only using low FPS cameras, through novel capturing and processing modules. On the capturing side, we propose an asynchronous capture scheme that increases the effective frame rate by staggering the start times of cameras. By grouping cameras and leveraging a base frame rate of 25 FPS, our method achieves an equivalent frame rate of 100-200 FPS without requiring specialized high-speed cameras. On processing side, we also propose a novel generative model to fix artifacts caused by 4D sparse-view reconstruction, as asynchrony reduces the number of viewpoints at each timestamp. Specifically, we propose to train a video-diffusion-based artifact-fix model for sparse 4D reconstruction, which refines missing details, maintains temporal consistency, and improves overall reconstruction quality. Experimental results demonstrate that our method significantly enhances high-speed 4D reconstruction compared to synchronous capture.

05.
arXiv (CS.AI) 2026-06-11

DiffCold: A Diffusion-based Generative Model for Cold-Start Item Recommendation

arXiv:2606.12245v1 Announce Type: cross Abstract: Cold-start item recommendation remains a persistent challenge in real-world systems due to the absence of interaction histories. While prior models attempt to bridge this gap using item content features, they universally suffer from the seesaw dilemma: enhancing performance for cold items inevitably degrades performance for warm items, and vice versa. We identify that this dilemma stems from a fundamental distributional disparity: warm item embeddings occupy a complex ``behavioral manifold" shaped by rich interaction signals, whereas cold item embeddings are constrained to a ``semantic manifold" derived solely from auxiliary content. Existing methods often force a rigid mapping between these inconsistent spaces, causing the model to sacrifice the precision of warm representations to accommodate cold ones. To address this, we propose DiffCold, a diffusion-based generative model that unifies warm and cold representations. Unlike GANs or VAEs, DiffCold leverages conditional diffusion to reconstruct warm item embeddings from content, preserving the underlying manifold structure without degradation. We further tailor this paradigm with two specific designs: a Retrieval-enhanced Aggregator that initializes generation using semantically similar warm items to bypass inefficient noise, and a Simulation-based Representation Alignment module that enforces distribution consistency between generated and real embeddings via contrastive learning. Experiments on three benchmarks confirm that DiffCold resolves the seesaw dilemma, consistently outperforming state-of-the-art methods across all metrics.

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

High-Fidelity Two-Step Image Generation via Teacher-Aligned End-to-End Distillation

Few-step diffusion distillation has become increasingly mature for 4-8-step generation, yet pushing further to 2 steps remains challenging. In this work, we introduce Z-Image Turbo++, a high-quality 2-step image generation model distilled from the 8-step Z-Image Turbo teacher. Our method addresses the central bottlenecks of increased task difficulty and limited model capacity in 2-step generation through three simple but effective design choices tailored to this regime. First, we propose Distribution-Aligned Adversarial Learning, which uses teacher-generated images rather than external real images as real samples for GAN training, providing a more attainable and informative adversarial target. Second, we adopt Step-Decoupled Parameterization, assigning independent model parameters to the two denoising steps to better match their distinct capacity demands. Third, we perform End-to-End Training with Iterative Regularization, allowing the first step to receive gradients from final image quality while preserving a meaningful intermediate generation through an explicit step-1 loss. Together, these designs substantially narrow the quality gap between 2-step and 8-step generation in both qualitative and quantitative evaluations, highlighting the potential of carefully tailored distillation strategies for improving the quality-efficiency trade-off in few-step generation.

07.
arXiv (CS.AI) 2026-06-19

Bidirectional Tutoring for Developmental Motor Learning in Robots: Co-Developed Interaction Dynamics Support Stable Learning

arXiv:2606.19728v1 Announce Type: cross Abstract: Infants are well known to develop their motor skills through dense interaction with caregivers. Although such social interaction is crucial for human development, motor-skill learning in robots is often treated as a unidirectional process in which robots passively receive demonstrations from tutors. This overlooks a key property of social interaction: it is inherently bidirectional, with tutor and learner dynamically adapting to each other. In such interactions, the robot's past experiences may function as prior constraints that shape the dynamics of their co-developed trajectories. We hypothesize that bidirectional tutoring allows such constraints to guide the formation of consistent behavioral patterns that preserve behavioral coherence and support generalization, whereas unidirectional interaction lacks such constraints and leads to broader, less consistent behavioral patterns. To examine this hypothesis, we conducted two experiments with a physical humanoid robot performing an object manipulation task: one involving human-robot interaction and another employing an AI tutor interacting with the real robot through an adaptive intervention mechanism designed to examine whether similar effects would emerge under more controlled conditions. We implement the developmental learning framework using a free-energy-principle-based neural network extended with generative replay, which supports stable sequence-by-sequence learning from single tutored episodes. Across both settings, bidirectional tutoring fostered consistent behaviors and stage-wise generalization, while the robot gradually required less tutor guidance. These results suggest that bidirectional tutoring, as an embodied and socially grounded approach, provides an effective scaffold for developmental motor learning in robots.

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

Track2View: 4D-Consistent Camera-Controlled Video Generation via Paired 3D Point Tracks

Re-rendering an existing video from a novel camera viewpoint requires the output to follow the prescribed camera trajectory while preserving the appearance and dynamics of the original scene across every frame. Existing methods rely on per-frame pose embeddings, noisy point-cloud renderings, or implicit learned correspondences, none of which provides an explicit, temporally continuous link between source and target pixels. We propose Track2View, which conditions a video diffusion transformer on paired 3D point tracks: sparse trajectories of scene points projected into both the source and target camera views. These tracks provide explicit spatiotemporal correspondences that are temporally continuous by construction, encoding what content should appear where and when. At the core of Track2View is a dual-view track conditioner that transfers visual context from source to target view through parameter-free geometric operations and learned temporal aggregation, ensuring generalization to arbitrary camera trajectories without memorizing specific motions. We further introduce a data curation pipeline that extracts one-to-one track correspondences by running a 3D point tracker on temporally concatenated multi-camera view pairs. On a 400-video benchmark spanning static and dynamic scenes, Track2View achieves state-of-the-art results across visual quality, view synchronization, and camera accuracy, reducing rotation error by 30-65% and translation error by 61-72% relative to leading baselines. Project page is available at this https URL: https://qjizhi.github.io/track2view

09.
arXiv (quant-ph) 2026-06-16

Weak continuous measurements require more work than strong ones

arXiv:2502.09732v4 Announce Type: replace Abstract: Understanding the energy cost of quantum measurement process and its connection to the measurement performance faces the challenge of modeling the objectification process. The latter, turns the measurement result into an objective fact, available to independent observers, and is responsible for the measurement irreversibility. To address this issue, we propose and analyze a dynamical model of quantum measurement, able to capture nonideal (weak and inefficient) measurements. In this model, the objectification is induced by a contact with a macroscopic reservoir at equilibrium which is responsible for the redundant broadcast of the measurement outcome (producing a Spectrum Broadcast Structure (SBS) state) while inducing decoherence in the pointer basis, in the line of the theory of quantum Darwinism. We analyze the performance of the obtained measurement process by introducing figures of merit to quantify the strength of the measurement and its efficiency. We also derive and a lower bound on the measurement work cost that we can relate to the measurement quality. We take as an illustration the readout of a qubit via its coupling to a harmonic oscillator. We investigate the long sequences of extremely short and weak measurements (a.k.a continuous measurements), to find under which conditions they converge to an ideal (projective) measurement and analyze their work cost. Surprisingly, we find that a sequence converging to projective measurement has a much larger work cost than an equivalent strong measurement obtained from a single intense interaction with the apparatus. We extend this result to a large class of models owing to scaling arguments. Our analysis offers new insights into the trade-offs between measurement strength, energy consumption, and information extraction in quantum measurement protocols.

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

StereoGeo: an end-to-end stereo camera calibration method

In this work, we propose StereoGeo, an end-to-end network-based approach for stereo camera calibration. Our method estimates the focal lengths and gravity directions of the left and right cameras, as well as the relative extrinsic transformation relating them. Existing methods often rely on calibration patterns in structured environments or address only a single camera configuration, being limited to either intrinsic or extrinsic estimation, and depending on a multi-view setups. StereoGeo extends the GeoCalib algorithm, integrating deep neural network feature extraction with a differentiable optimizer. Extensive experiments on real-world benchmarks demonstrate that StereoGeo achieves competitive performance for intrinsic calibration and provides accurate stereo extrinsic estimation, outperforming existing methods that are limited to monocular settings. The dataset used in this work is partially publicly available at https://github.com/meddourimane/StereoGeo-dataset.

11.
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/ .

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

A solvable model for unsupervised federated learning

arXiv:2606.13045v1 Announce Type: cross Abstract: We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larger overlap with the ground-truth signal. We derive the optimal Bayesian conditions for teacher recovery as functions of the sample complexity, noise level, and interaction strength, and validate these predictions through numerical simulations. The resulting dynamics can be mapped onto equilibrium sampling in a Restricted Boltzmann Machine with a structured hidden layer, providing a principled theoretical understanding of how interactions improve distributed generative modeling.

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

A DeepLearning Framework for Dynamic Estimation of Origin-Destination Sequence

arXiv:2307.05623v2 Announce Type: replace-cross Abstract: OD matrix estimation is a critical problem in the transportation domain. The principle method uses the traffic sensor measured information such as traffic counts to estimate the traffic demand represented by the OD matrix. The problem is divided into two categories: static OD matrix estimation and dynamic OD matrices sequence(OD sequence for short) estimation. The above two face the underdetermination problem caused by abundant estimated parameters and insufficient constraint information. In addition, OD sequence estimation also faces the lag challenge: due to different traffic conditions such as congestion, identical vehicle will appear on different road sections during the same observation period, resulting in identical OD demands correspond to different trips. To this end, this paper proposes an integrated method, which uses deep learning methods to infer the structure of OD sequence and uses structural constraints to guide traditional numerical optimization. Our experiments show that the neural network(NN) can effectively infer the structure of the OD sequence and provide practical constraints for numerical optimization to obtain better results. Moreover, the experiments show that provided structural information contains not only constraints on the spatial structure of OD matrices but also provides constraints on the temporal structure of OD sequence, which solve the effect of the lagging problem well.

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

Toward Controllable Catalyst Inverse Design via Large-Scale Autoregressive Pretraining

arXiv:2606.17445v1 Announce Type: new Abstract: Inverse design of heterogeneous catalysts remains challenging because catalyst surfaces exhibit substantial structural complexity with coupled surface-adsorbate interactions across a vast chemical space that is difficult to explore efficiently through conventional screening alone. Although machine learning-based high-throughput screening has accelerated catalyst discovery, its efficiency inevitably declines as the search space grows, motivating the development of generative models that can directly construct catalysts with target properties. Here, we present a conditional catalyst generative model based on the Generative Pretrained Transformer architecture with a numerical embedding layer that enables the generation of catalyst structures conditioned on both categorical and continuous properties within a single autoregressive framework. The model was pretrained on 133 million catalyst structures and subsequently fine-tuned on approximately 460,000 optimized structures with associated categorical properties and binding energies for conditional generation. The resulting model achieved 98% structural validity, 95% optimization validity, and high categorical condition fidelity, with a 93 % joint match rate for adsorbate type and composition. For binding energy conditioning, the match rate of approximately 20% represents a four-fold improvement over the baseline training distribution, and the generated distributions shift systematically toward the target values, enabling a 1.5 to 4-fold improvement in screening efficiency for reaction-targeted catalyst discovery without additional fine-tuning. These results show that large-scale autoregressive pre-training, combined with explicit property conditioning, provides a practical route toward controllable catalyst generation and accelerated catalysts discovery.

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

Triangular-Reference Schrödinger Bridges for Time Series Generation

arXiv:2605.27478v3 Announce Type: replace-cross Abstract: Schrödinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid. The Brownian reference, however, fixes the quadratic variation of the generated paths, which is restrictive when stochastic volatility, correlated noise, or rank-deficient covariance structures must be reproduced. We introduce "Triangular-Reference Schrödinger Bridges for Time Series" (TR-SBTS), which keeps the entropy-projection backbone of SBTS but replaces the Brownian reference by a triangular, volatility-informed, intervalwise frozen reference on a state augmented with latent covariance descriptors. The construction remains a single entropy projection on the augmented state: the minimiser is the \(h\)-transform of the reference, and on each frozen interval the optimal drift has the logarithmic-gradient form \(b^\star(t,x)=A\,\nabla\log H(t,x)\), intrinsic to the active covariance directions when the frozen covariance \(A\) is degenerate. We prove stability of the frozen approximation and consistency of the associated regularised kernel estimators, describe a reference-aware Nadaraya–Watson implementation of the conditional next-increment law, and evaluate the construction on numerical experiments.

16.
Nature (Science) 2026-06-08

Daily briefing: Human embryo genomes precisely altered

作者:

The use of ‘base editing’ to precisely tweak human embryos has divided researchers. Plus, the number of lives saved by less-polluting cars in China and how to tip the world towards a sustainable future. The use of ‘base editing’ to precisely tweak human embryos has divided researchers. Plus, the number of lives saved by less-polluting cars in China and how to tip the world towards a sustainable future.

17.
arXiv (CS.LG) 2026-06-16

Scalable and Interpretable Representation Alignment with Ordinal Similarity

arXiv:2606.16379v1 Announce Type: new Abstract: Evaluating representation similarity is fundamental to representation learning. However, existing metrics suffer from significant limitations: they lack interpretability due to shifting baselines, lack robustness to outliers, and are computationally intractable for large datasets, forcing reliance on heuristic approximations. To address this, we develop an ordinal-similarity framework, instantiated by the Triplet (TSI) and Quadruplet (QSI) Similarity Indices, which measure alignment by quantifying the consistency of ordinal relationships. We theoretically demonstrate this formulation is inherently interpretable, robust to outliers, and computationally efficient. Finally, we establish a formal equivalence between TSI and local neighborhood alignment, measured by Mutual Nearest Neighbors. Empirically, we validate these properties and show that ordinal similarity offers a scalable approach to measuring alignment, enabling practitioners to better understand and design representations.

18.
arXiv (CS.AI) 2026-06-11

Diffusing to Coordinate: Efficient Online Multi-Agent Diffusion Policies

arXiv:2602.18291v2 Announce Type: replace Abstract: Online Multi-Agent Reinforcement Learning (MARL) is a prominent framework for efficient agent coordination. Crucially, enhancing policy expressiveness is pivotal for achieving superior performance. Diffusion-based generative models are well-positioned to meet this demand, having demonstrated remarkable expressiveness and multimodal representation in image generation and offline settings. Yet, their potential in online MARL remains largely under-explored. A major obstacle is that the intractable likelihoods of diffusion models impede entropy-based exploration and coordination. To tackle this challenge, we propose among the first \underline{O}nline off-policy \underline{MA}RL framework using \underline{D}iffusion policies (OMAD) to orchestrate coordination. Our key innovation is a relaxed policy objective that maximizes scaled joint entropy, facilitating effective exploration without relying on tractable likelihood. Complementing this, within the centralized training with decentralized execution (CTDE) paradigm, we employ a joint distributional value function to optimize decentralized diffusion policies. It leverages tractable entropy-augmented targets to guide the simultaneous updates of diffusion policies, thereby ensuring stable coordination. Extensive evaluations on MPE and MAMuJoCo establish our method as the new state-of-the-art across $10$ diverse tasks, demonstrating a remarkable $2.5\times$ to $5\times$ improvement in sample efficiency.

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

ToolChain-CRC: Conformal Risk Control for Agentic AI Under Retrieval and Tool-Use Drift

arXiv:2606.18467v1 Announce Type: cross Abstract: Modern AI agents retrieve documents, call tools, check intermediate information, and then produce a final answer or action. This creates a risk-control problem that is not visible from the final answer alone. A final response may look acceptable even when the retrieval was weak, a tool output was wrong, or an earlier step was unsupported. We propose ToolChain-CRC, a conformal risk-control method for retrieval-augmented and tool-using agents under drift. The method treats each agent run as a full trajectory of actions, observations, and final output. It builds step-level risk scores, combines them into a trajectory risk score, calibrates an accept-or-intervene rule, and adds an anytime alarm that can stop risky runs before the final answer. We prove trajectory-level risk control under exchangeable calibration runs, give a drift-aware extension with auditable constants, and prove an anytime escalation rule through a supermartingale construction. Experiments cover synthetic tool-chain drift, RAG/tool-use stress tests, public SQuAD-derived retrieval tasks, an API-free agentic QA case study, ablations, target-risk sensitivity checks, 20-seed robustness checks, a drift-margin audit, and a live RAG/tool-use agent benchmark. Across these settings, final-answer-only calibration can miss retrieval and tool failures, while trajectory-level calibration keeps accepted-trajectory risk below the target.

20.
arXiv (CS.LG) 2026-06-18

P$^2$CE: Model-Agnostic Plausible Pareto-Optimal Counterfactual Explanations

arXiv:2606.18418v1 Announce Type: new Abstract: The increasing use of machine learning algorithms in social applications has raised concerns about fairness and transparency, leading to the development of counterfactual explanations. These explanations supports individuals to understand and potentially alter unfavorable decisions in areas such as loan applications, job selections, and more, by providing actionable changes to input features that would lead to a desired outcome. Existing methods often struggle to balance feasibility, plausibility, and computational efficiency. To address this, we introduce P$^2$CE, an algorithm for generating plausible Pareto-optimal counterfactual explanations, offering users a diverse set of optimal trade-offs between different notions of feasibility. P$^2$CE employs an auxiliary isolation forest outlier detector to ensure that explanations are in accordance with the data distribution and leverages SHAP values to obtain optimal results with short computing times, regardless of the underlying model. Our algorithm was empirically evaluated on three datasets, demonstrating superior performance in terms of both solution quality and computational efficiency compared to related techniques.

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

Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization

arXiv:2604.03146v3 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max characterization of key statistics, enabling approximation of the mean $\mu_{\hat{\theta}}$ and covariance $C_{\hat{\theta}}$ of the ERM estimator $\hat{\theta}$. Specifically, under a concentration assumption on the data matrix and standard regularity conditions on the loss and regularizer, we show that for a test covariate $x$ independent of the training data, the projection $\hat{\theta}^\top x$ approximately follows the convolution of the generally non-Gaussian distribution of $\mu_{\hat{\theta}}^\top x$ with an independent centered Gaussian variable of variance $\mathrm{tr}(C_{\hat{\theta}} \mathbb{E}[xx^\top])$. This result clarifies the scope and limits of Gaussian universality for ERMs. Additionally, we prove that any $\mathcal{C}^2$ regularizer is asymptotically equivalent to a quadratic form determined solely by its Hessian at zero and gradient at $\mu_{\hat{\theta}}$. Numerical simulations across diverse losses and models are provided to validate our theoretical predictions and qualitative insights.

22.
arXiv (quant-ph) 2026-06-11

Handbook of Error-Correcting Codes

arXiv:2606.11484v1 Announce Type: new Abstract: Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during storage and transmission. The handbook includes descriptions of these error-correcting codes and a classification according to the symbols they use. It also catalogues relations among codes and related objects such as sphere packings, lattices, designs, groups, and classical and quantum phases of matter. The collection is intended both as a rigorous reference and as a practical aid for tracing the web of code relationships and uncovering new connections.

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

Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs

arXiv:2605.26631v2 Announce Type: replace-cross Abstract: We propose KO-PDE-IDENT, a data-driven framework for identifying parsimonious partial differential equations (PDEs) with false discovery rate (FDR) control. PDE discovery from noisy observations is often hindered by extreme multicollinearity among candidate terms, which causes typical sparse-regression methods to select spurious terms. To address this problem, KO-PDE-IDENT initially mines a support set of potential candidate terms via model-X knockoff filters with finite-sample FDR control, then refines and ranks the surviving PDE alternatives. The framework integrates three components. First, knockoff feature statistics are constructed by coupling $\ell_{0}$-constrained adaptive best-subset selection with SHapley Additive exPlanations (SHAP), yielding an effective and computationally efficient difference statistic. Second, a recursive feature elimination (RFE) procedure removes terms whose marginal contributions are dispensable and assesses statistical necessity through knockoff-perturbed hypothesis testing. Third, the final model selection is formulated as a multi-criteria decision-making (MCDM) problem, where the optimal governing equation is the alternative that best balances a wide range of criteria such as predictive accuracy, model complexity and coefficient uncertainty. We evaluate KO-PDE-IDENT on five canonical PDEs under severe noise corruption. Empirical results show that our framework can exactly recover the true PDE structure, eliminating false discoveries while retaining all true underlying terms, with low coefficient estimation error.

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

RODS: Reward-Driven Online Data Synthesis for Multi-Turn Tool-Use Agents

arXiv:2606.19047v1 Announce Type: new Abstract: Multi-turn tool-use RL is bottlenecked by the rapid depletion of informative samples in static datasets. We observe that the gradient signal in GRPO concentrates on tasks with the highest rollout reward variance, a consequence of the Popoviciu upper bound. Consequently, samples near the agent's capability boundary – where successes and failures are roughly balanced – contribute disproportionately large policy gradients. As training progresses, this boundary continuously shifts, which gradually depletes the pool of informative samples in a static dataset. We propose RODS (Reward-driven Online Data Synthesis) to resolve this depletion. RODS closes the loop between RL training and data generation by repurposing the progress reward variance as a practical, zero-cost boundary detector that requires no extra inference beyond the rollouts already computed for training. It continuously identifies such boundary samples, synthesizes new multi-turn variants matching their structural complexity (e.g., API topology and dependency depth) via a skill-aligned resampling pipeline, and manages a dynamic replay buffer that co-evolves with the policy. Starting from 400 human seeds and maintaining an active training pool of ~800 samples, RODS achieves comparable performance to a 17K-sample offline pipeline while requiring roughly 20x fewer trajectories, and improves over fixed-data RL and environment augmentation in our controlled setting.