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01.
arXiv (CS.CL) 2026-06-17

SuCo: Sufficiency-guided Continuous Adaptive Reasoning

Despite remarkable performance on complex tasks, Large Reasoning Models (LRMs) often generate excessively long Chain-of-Thoughts (CoT), inflating computational costs even for simple queries. Existing efforts to mitigate this inefficiency typically rely on discrete reasoning modes or fixed budget tiers, lacking a principled criterion of when reasoning is sufficient. In this work, we introduce Minimal Sufficient CoT (MSC), defined as the shortest prefix of a CoT trajectory which is adequate for producing the correct answer. We empirically show that MSC not only reduces reasoning tokens, but also improves accuracy across difficulty levels. Building on MSC, we propose Sufficiency-guided Continuous Adaptive Reasoning (SuCo), a two-stage training framework for autonomous reasoning control along a continuous spectrum. In stage 1, MSC-Aligned Fine-Tuning (MFT) constructs MSC data using problem-adaptive sufficiency thresholds that naturally scale with question difficulty, then fine-tunes the model to internalize concise yet sufficient reasoning patterns. In stage 2, Sufficiency-Aware Policy Optimization (SAPO) further optimizes the model through reinforcement learning with dynamic complexity tracking and sufficiency-aware rewards that penalize both over- and under-thinking. Extensive experiments across mathematics, code, and science benchmarks show that SuCo consistently achieves improvements in both accuracy and reasoning efficiency.

02.
arXiv (math.PR) 2026-06-16

Transposition Approach to Optimal Control of McKean-Vlasov SPDEs

arXiv:2603.06245v2 Announce Type: replace Abstract: In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a Pontryagin-type stochastic maximum principle that provides necessary optimality conditions for admissible controls. The analysis is based on the classical spike variation method together with the introduction of an adjoint backward stochastic partial differential equation involving Lions derivatives with respect to probability measures. Our results extend the stochastic maximum principle for McKean-Vlasov controlled stochastic differential equations to the infinite-dimensional SPDE setting.

03.
arXiv (CS.LG) 2026-06-12

DynamicPTQ: Mitigating Activation Quantization Collapse via Residual-Stream Dynamics

arXiv:2606.12487v1 Announce Type: new Abstract: Post-training quantization (PTQ) is essential for efficient large language model inference, but reliably quantizing activations remains challenging when weights, activations, and KV caches are all quantized to 4-bit precision. A key difficulty lies in massive activations, whose extreme values dominate the activation range and amplify quantization errors. State-of-the-art methods mainly mitigate massive activations through transformation-based smoothing, such as orthogonal rotations and affine scaling, but overlook the cross-layer dynamics of the residual stream. In this paper, we show that massive activations emerge and disappear in a phase-wise pattern across network depth, triggering large residual changes. These changes cause newly injected layer-wise updates to dominate the 4-bit quantization scale and weaken historical residual information. To characterize this behavior, we introduce Jump Ratio and Historical Feature SNR. This suggests that static transformation-based smoothing cannot fully resolve dynamic quantization instability caused by cross-layer residual changes. Based on this analysis, we propose DynamicPTQ, a Dynamic Post-Training Quantization policy for phase-aware mixed-precision activation quantization. DynamicPTQ identifies quantization-sensitive layers from residual-stream dynamics and assigns 8-bit activation precision only to these layers, while keeping weights, KV caches, and other activations in 4-bit precision. It can be directly integrated with strong PTQ baselines such as QuaRot, SpinQuant, and FlatQuant. Experiments on LLaMA-2 and LLaMA-3 show that DynamicPTQ consistently improves perplexity and zero-shot QA performance under W4A4KV4 quantization, while achieving 1.05 to 1.07 times throughput improvement with modest memory overhead. These results demonstrate a practical path toward robust low-bit LLM inference.

04.
arXiv (CS.LG) 2026-06-16

BRICKS-WM: Building Reusability via Interface Composition Kinetics for Structured World Models

arXiv:2606.16489v1 Announce Type: new Abstract: Model-based Reinforcement Learning (MBRL) has achieved remarkable success in continuous control by leveraging latent world models. However, prevailing approaches typically rely on monolithic latent dynamics, entangling environment dynamics into a coupled process. This coupling severely limits reusability: altering the agent necessitates retraining the entire world from scratch, even if the environment remains constant. To address this, we introduce BRICKS-WM (Building Reusability via Interface Composition Kinetics for Structured World Models), a framework for the modular assembly of structured world models. Driven by the insight that the physical world is composed of independent entities, we posit that global dynamics can be modeled as a composition of distinct dynamical modules interacting via latent interfaces. As a minimal instantiation, we factorize the latent state space into an actuated Agent module and an external Background module, bridged by a learned latent interface. Unlike prior object-centric methods that prioritize visual segmentation, BRICKS-WM enforces a functional separation in transition dynamics, ensuring that background dynamics remains agnostic to the agent's dynamics. Empirically, BRICKS-WM achieves control performance comparable to strong monolithic baselines when trained from scratch, and enables the reuse of frozen background dynamics across agents.

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

Cost-Optimal LLM Routing with Limited User Feedback under User Satisfaction Guarantees

arXiv:2606.19376v1 Announce Type: cross Abstract: Inference costs for large language model (LLM) applications are rapidly growing, driven by surging demand and rising infrastructure cost. Users expect high-quality responses, and in commercial settings this is formally codified in Service Level Agreements (SLAs), creating a fundamental tension between cost and quality. Recent progress on cost-aware LLM request routing has shown potential to resolve this tension, but existing approaches rely on complete feedback signals, offline training, extensive per-workload tuning, and most lack SLA guarantees or inference-time adaptivity. We introduce SLARouter, an online routing algorithm that learns a cost-optimal policy from the sparse, one-sided user feedback available in production systems. SLARouter provides theoretical guarantees for both cost optimality and strict SLA compliance. Experiments across a wide range of LLM benchmarks show that SLARouter satisfies SLA constraints without the need for per-benchmark tuning, reducing operating cost by up to 2.2x over existing baselines.

07.
arXiv (CS.CL) 2026-06-11

Organize then Retrieve: Hierarchical Memory Navigation for Efficient Agents

Large language model (LLM) agents struggle with long-horizon tasks due to their inherent statelessness, requiring all task-relevant information to be encoded in growing input contexts. The resulting degraded reasoning quality, increased inference cost, and higher latency necessitate efficient working memory mechanisms. However, existing approaches either rely on lossy compression or similarity-based retrieval, which often fail to capture temporal structure and causal dependencies required for multi-step agentic tasks. In this work, we present HORMA, a Hierarchical Organize-and-Retrieve Memory Agent that organizes experience into a file-system-like hierarchical structure, where summarized entities are linked to the corresponding raw trajectories, enabling efficient access without losing detailed information. HORMA decomposes working memory into two stages: structured memory construction and navigation-based retrieval. The construction module iteratively refines how experiences are structured by distinguishing between failures caused by missing information and those caused by misleading or overloaded context. The navigation module retrieves task-relevant context by traversing the hierarchy using a lightweight agent trained with reinforcement learning to select minimal yet sufficient context, thereby reducing latency along the critical execution path. Across ALFWorld, LoCoMo, and LongMemEval, HORMA improves task performance under constrained context budgets while requiring at most 22.17% of the baseline token usage in long conversation tasks. Compared to existing methods, it consistently achieves better efficiency-performance trade-offs and generalizes effectively to unseen tasks.

08.
arXiv (CS.CV) 2026-06-18

Global Offshore Wind Infrastructure: Deployment and Operational Dynamics from Dense Sentinel-1 Time Series

The offshore wind energy sector is expanding rapidly, increasing the need for independent, high-temporal-resolution monitoring of infrastructure deployment and operation at global scale. While Earth Observation based offshore wind infrastructure mapping has matured for spatial localization, existing open datasets lack temporally dense and semantically fine-grained information on construction and operational dynamics. We introduce a global Sentinel-1 synthetic aperture radar (SAR) time series data corpus that resolves deployment and operational phases of offshore wind infrastructure from 2016Q1 to 2025Q1. Building on an updated object detection workflow, we compile 15,606 time series at detected infrastructure locations, with overall 14,840,637 events as analysis-ready 1D SAR backscatter profiles, one profile per Sentinel-1 acquisition and location. To enable direct use and benchmarking, we release (i) the analysis ready 1D SAR profiles, (ii) event-level baseline semantic labels generated by a rule-based classifier, and (iii) an expert-annotated benchmark dataset of 553 time series with 328,657 event labels. The baseline classifier achieves a macro F1 score of 0.84 in event-wise evaluation and an area under the collapsed edit similarity-quality threshold curve (AUC) of 0.785, indicating temporal coherence. We demonstrate that the resulting corpus supports global-scale analyses of deployment dynamics, the identification of differences in regional deployment patterns, vessel interactions, and operational events, and provides a reference for developing and comparing time series classification methods for offshore wind infrastructure monitoring.

09.
arXiv (CS.CV) 2026-06-11

Time-Conditioned and Multi-Time Survival Prediction from 2D PET/CT Projections in Lung Cancer

Accurate prediction of overall survival (OS) from positron emission tomography/computed tomography (PET/CT) can support personalized treatment and follow-up strategies in oncology. However, the impact of temporal modeling on imaging-based survival prediction remains insufficiently explored. We investigate how different temporal formulations influence survival prediction by developing two complementary approaches: Attention-guided Time-Conditioned Survival (ATCS) and Multi-Time Survival (MTS). We retrospectively analyzed pre-treatment PET/CT images from 848 patients with non-small cell lung cancer (NSCLC), including 556 for model development and 292 for held-out testing. A previously proposed Time-Conditioned Survival (TCS) model was used as a baseline. Models were trained using 5-fold cross-validation and evaluated on the test set using time-dependent area under the curve (AUC) at 6-month intervals from 0.5 to 5 years. Both ATCS and MTS outperformed the baseline TCS model, achieving mean AUCs of 0.794 and 0.793, respectively, compared to 0.767. ATCS performed better at earlier time points (0.5-3 years), whereas MTS performed better at later intervals (3.5-5 years). Combining tumor-specific and tissue-wise PET/CT features improved performance over either input alone. Finer temporal discretization improved short-term prediction, while coarser intervals provided more stable long-term estimates. These findings demonstrate that temporal modeling and input design influence PET/CT-based survival prediction. The proposed approaches enable time-specific survival estimation from pre-treatment imaging and may support improved risk stratification and clinical decision-making.

10.
arXiv (CS.AI) 2026-06-11

AutoMine Solution for AV2 2026 Scenario Mining Challenge

arXiv:2606.11874v1 Announce Type: new Abstract: With the development of autonomous driving systems, mining high-value, safety-critical, and planning-relevant scenarios from large-scale driving logs has become essential for data-driven evaluation. In this paper, we propose AutoMine, a robust self-refining scenario mining method based on LLMs and VLMs. AutoMine uses semantics-preserving prompt augmentation to reduce LLM prompt sensitivity, combines robust trajectory atomic functions with VLM-based functions to handle perception noise and open-world visual cues, and refines generated code through execution feedback from real logs. In the Argoverse 2 Scenario Mining Competition at CVPR 2026, AutoMine achieves a HOTA-Temporal score of 36.38 and a Timestamp BA score of 77.21.

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

Position: AI Must Become Planet-Centered, Not Just Human-Centered

arXiv:2606.13704v1 Announce Type: cross Abstract: This position paper argues that contemporary AI paradigms are insufficient for supporting complex global goals and introduces Planet-Centered AI (PCAI) as a design philosophy and research agenda that reorients AI toward planetary-scale socio-ecological systems and their long-term trajectories. A planet-centered approach is grounded in systems thinking, treating Earth as an interconnected whole of which humans are part. We diagnose recurring limitations across AI frameworks, many of which remain human-centered, and show why these become especially consequential under current planetary conditions characterized by systemic risk, non-stationarity, and deep uncertainty. We then articulate how PCAI reshapes the AI lifecycle, from problem formulation and model design to evaluation and deployment, by emphasizing alignment with global agendas, developing system-aware AI foundations, trajectory-oriented evaluation, and monitorability. Finally, we advance a falsifiable claim: AI systems optimized without explicit consideration of systemic consequences are more likely to exacerbate systemic instability than to mitigate it.

12.
arXiv (CS.CL) 2026-06-11

APEX: Automated Prompt Engineering eXpert with Dynamic Data Selection

Large Language Models are highly sensitive to prompt formulation, necessitating automatic prompt optimization to unlock their full potential. While evolutionary algorithms have emerged as the dominant paradigm, they suffer from a critical bottleneck: data efficiency. Current methods treat the development dataset as a static benchmark, wasting significant compute budget on uninformative data. In this work, we introduce APEX (Automatic Prompt Engineering eXpert), a novel framework that optimizes the data usage alongside the prompt search. APEX dynamically stratifies the dataset into Easy, Hard, and Mixed tiers based on the optimization lineage. By prioritizing the Mixed tier, which identifies the data where the LLM has mixed performance, we identify two high-leverage subsets: the addressable frontier for generating informative mutations and the rank-sensitive frontier for distinguishing candidate quality. We evaluate APEX across three diverse benchmarks: IFBench, SimpleQA Verified, and FACTS Grounding. Under a fixed budget of 5,000 evaluation calls, due to its data efficiency, APEX outperforms the initial prompt by an average of 11.2% on Gemini 2.5 Flash and 6.8% on Gemma 3 27B, demonstrating that a data-centric approach is key to efficient and effective prompt optimization.

13.
arXiv (CS.CV) 2026-06-12

An Extensible and Lightweight Unified Architecture for Demosaicing Pixel-bin Image Sensors

Pixel-bin image sensors are becoming the default choice for smartphone cameras due to their resolution vs light-gathering trade-off. However, their larger inter-color separation compared to the Bayer color filter array (CFA) makes them challenging to demosaic. Furthermore, existing deep learning-based demosaicing methods are CFA-specific, requiring multiple individual models that take up precious onboard resources and demand larger development and maintenance efforts. In this work, we propose a modular unified architecture for demosaicing various pixel-bin sensors that provides higher image quality while being extensible and lightweight. Additionally, to enable plug-and-play operation, we introduce a learning-free CFA-identification module to detect the CFA type of raw data accurately.

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

Pruning via Causal Attribution Preserves Reasoning Performance in Large Language Models

Large language models (LLMs) excel at multi-step reasoning but incur substantial inference cost. We introduce Causal Attribution Pruning (CAP), a training-free method that identifies critical attention heads by measuring their causal impact on reasoning tasks and uses these head-level scores to guide fine-grained weight pruning. For each attention head, CAP estimates the expected performance degradation when the head is masked during forward passes on a small calibration set of reasoning problems. These causal scores are then converted into weight-level importance values for the corresponding projection matrices. Unlike magnitude-only or activation-based criteria, CAP's interventional measurement directly captures each head's functional contribution, yielding relative accuracy gains of up to 61% over Wanda on ARC-Challenge at 20% sparsity. We evaluate CAP on GSM8K, StrategyQA, and ARC-Challenge using Llama-3-8B-Instruct and Mistral-7B-Instruct at 10%, 20%, and 50% sparsity. At moderate sparsity (10-20%), CAP improves over Wanda in most model-benchmark configurations. with especially large gains on ARC-Challenge for Llama-3. Our results suggest that attention-head-level causal attribution can better preserve reasoning performance on downstream benchmarks than correlational pruning criteria at equivalent sparsity, while remaining limited by coarse MLP attribution at 50% sparsity.

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

Kairos: A Native World Model Stack for Physical AI

World models are transitioning from passive visual generators to foundational, operational infrastructure for Physical AI: they must natively acquire world knowledge from heterogeneous experience, maintain persistent states over long horizons, and execute efficiently within real deployment constraints. We introduce Kairos, a native world model stack designed around these requirements. (1) Kairos learns the world by pioneering a Native Pre-training Paradigm governed by a Cross-Embodiment Data Curriculum, which organizes open-world videos, human behavioral data, and robot interactions into a progressive developmental pathway. (2) Kairos maintains the world by unified world understanding, generation, and prediction within a Native Unified Architecture equipped with Hybrid Linear Temporal Attention, where sliding-window attention captures local dynamics, dilated sliding windows capture mid-range dependencies, and gated linear attention maintains persistent global memory. We establish formal theoretical bounds demonstrating that this temporal factorization strictly limits error accumulation, mathematically guaranteeing state propagation across extended horizons. (3) Kairos runs the world by incorporating a Deployment-Aware System Co-Design to support low-latency rollout generation on server and consumer-grade hardware for real-world observation-action-feedback loops. Experiments on embodied world-model, long-horizon, and action-policy benchmarks show that Kairos achieves top level performance while offering a strong efficiency-capability trade-off. Together, these results position Kairos as a cohesive operational foundation for future self-evolving physical intelligence.

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

A Prototypical Signature Approach for Writer-Independent Offline Signature Verification

Offline handwritten signature verification aims to distinguish genuine from forged signatures using static images. Since real forgeries are rarely available, negative samples are usually randomly drawn from genuine signatures of other users to create training data. However, this random selection often lacks diversity, increases redundancy, and escalates computational cost, leading to inefficient training. We propose a data-driven strategy to generate diverse, informative negative samples using prototypical signatures, which are compact, non-identifiable summaries of genuine signature features. Based on the experiments results, we conclude that (i) prototypical signatures yield more informative negative samples, improving the detection of skilled forgeries; (ii) the proposed approach is backbone-agnostic, showing robustness across architectures; and (iii) when combined with a primal-form linear SVM, it serves as an alternative to RBF-based models while significantly improving scalability and computational efficiency. Implementation of the method is available at https://github.com/kdmoura/proto_hsv.

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

EvoMemBench: Benchmarking Agent Memory from a Self-Evolving Perspective

Recent benchmarks for Large Language Model (LLM) agents mainly evaluate reasoning, planning, and execution. However, memory is also essential for agents, as it enables them to store, update, and retrieve information over time. This ability remains under-evaluated, largely because existing benchmarks do not provide a systematic way to assess memory mechanisms. In this paper, we study agent memory from a self-evolving perspective and introduce EvoMemBench, a unified benchmark organized along two axes: memory scope (in-episode vs. cross-episode) and memory content (knowledge-oriented vs. execution-oriented). We compare 15 representative memory methods with strong long-context baselines under a standardized protocol. Results show that current memory systems are still far from a general solution: long-context baselines remain highly competitive, memory helps most when the current context is insufficient or tasks are difficult, and no single memory form works consistently across all settings. Retrieval-based methods remain strong for knowledge-intensive settings, whereas procedural and long-term memory methods are more effective for execution-oriented tasks when their stored experience matches the task structure. We hope EvoMemBench facilitates future research on more effective memory systems for LLM-based agents. Our code is available at https://github.com/DSAIL-Memory/EvoMemBench.

18.
arXiv (quant-ph) 2026-06-16

Atom–photon Entanglement with a Single Trapped Cesium Atom

arXiv:2605.28968v2 Announce Type: replace Abstract: We demonstrate atom–photon entanglement using a single cesium atom trapped in an optical tweezer. Entanglement is generated by resonant excitation and subsequent spontaneous decay, which entangles the atomic Zeeman state with photon polarization. The photon is collected with a high numerical aperture objective (NA = 0.55) and coupled into a single-mode fiber, enabling atom photon measurements and measurement of the Bell-state fidelity. We obtain raw entanglement fidelity of ${\mathcal F} = 0.942(16)$ and inferred fidelity of ${\mathcal F}_inf = 0.962(26)$ after correcting independently characterized atom measurement errors. Compared with related free-space experiments using $^{87}$Rb, the multilevel structure of the relevant excited state in $^{133}$Cs requires the use of a single short excitation pulse in each entanglement attempt in order to suppress unwanted re-excitation. These results establish a free-space Cs atom–photon interface and provide a step toward dual-species Rb–Cs quantum networking.

19.
Nature (Science) 2026-06-17

The EU needs to back its ambition to end animal testing with cash

作者: 未知作者

The European Union has declared that it wants to stop using animals in chemical safety testing. Its goal will need a timeline and a serious funding commitment. The European Union has declared that it wants to stop using animals in chemical safety testing. Its goal will need a timeline and a serious funding commitment.

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

Two-Phase Bilevel Search for the Moving-Target Traveling Salesman Problem with Moving Obstacles

arXiv:2606.18730v1 Announce Type: cross Abstract: The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a minimum cost trajectory for an agent that departs from a static depot, visits a set of moving targets, each within one of their assigned time windows, and returns to the depot. In this article, we study the Moving-Target Traveling Salesman Problem with Moving Obstacles (MT-TSP-MO), a generalization of the MT-TSP where the agent trajectory must avoid moving obstacles. We present a Mixed-Integer Conic Programming (MICP) formulation that can be solved using off-the-shelf solvers, as well as a fast and scalable Two-Phase Bilevel Search (TPBS) algorithm that computes high-quality feasible solutions for the problem. We evaluate our approaches against an existing baseline algorithm on a broad range of problem instances with up to 40 targets and 40 obstacles. The results demonstrate that both the proposed methods significantly outperform the baseline with respect to success rates, solution costs, and computation time.

21.
arXiv (CS.LG) 2026-06-18

Measurement noise limits the advantage of nonlinear models over linear models in biomedical prediction

arXiv:2606.18420v1 Announce Type: new Abstract: On biomedical tabular data, flexible models such as deep networks, gradient-boosted trees, and kernel methods are repeatedly matched or beaten by linear and logistic regression given the same features. The usual reaction is to treat this as a model-side shortfall, to be fixed with more data, a better architecture, or tuning, on the assumption that the nonlinear structure is there and the model has failed to capture it. We argue that these fixes cannot help when the binding limit is the measurement rather than the model, as it frequently is in biomedicine. Additive noise blurs the population-optimal predictor, and because blurring removes a function's fine, rapidly varying detail before its broad shape, it erases nonlinear structure faster than linear structure. A degree-$k$ interaction is attenuated by the $k$-th power of feature reliability, while the linear part is attenuated only once. At the reliabilities typical of biomedical measurement, the nonlinear advantage can vanish even when the underlying biology is strongly nonlinear, and what the noise removes cannot be recovered by a larger cohort or a more flexible model, only by better measurement. The nonlinearity is hidden, not absent, and a tie between linear and flexible models is not by itself a verdict on the biology. These pieces are classical, drawn from measurement-error statistics, psychometrics, and Gaussian analysis, and we assemble them into an exact excess-risk identity. Measurement reliability is one of three conditions, alongside sample size and feature representation, that must align for a flexible model to help, and together they leave only a narrow window that most biomedical tasks fall outside. Across 140 UK Biobank tasks, the gap between flexible and linear models, where it exists, carries the predicted noise signature, and the three conditions can be separated by intervention but not by a benchmark alone.

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

LoLA: Low-Rank Linear Attention With Sparse Caching

The per-token cost of transformer inference scales with context length, preventing its application to lifelong in-context learning. Linear attention is an efficient alternative that maintains a constant memory footprint, even on infinite context lengths. While this is a potential candidate for lifelong learning, it falls short in memory capacity. In this paper, we propose LoLA, a training-free augmentation to linear attention that boosts associative recall. LoLA distributes past key-value pairs from context into three memory systems: (i) recent pairs in a local sliding window cache; (ii) difficult-to-memorize pairs in a sparse, global cache; and (iii) generic pairs in the recurrent hidden state of linear attention. We show through ablations that our self-recall error metric is crucial to efficiently manage long-term associative memories. On pass-key retrieval tasks, LoLA improves the base model's performance from 0.6% to 97.4% accuracy. This is achieved with a 4.6x smaller cache than Llama-3.1 8B on 4K context length. LoLA also outperforms other 1B and 8B parameter subquadratic models on zero-shot commonsense reasoning tasks.

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

Optimal classical shadow estimation of unitary channels at Heisenberg limit

arXiv:2606.13638v1 Announce Type: new Abstract: Full tomography of an unknown quantum evolution is resource-intensive and often unnecessary when the goal is only to predict selected properties. This motivates the study of classical shadow estimation of unitary channels (CSEU), a task in which one queries an unknown $d$-dimensional unitary $U$ and stores classical data that can later be used to predict expectation values $\mathrm{tr}[O \cdot U\rho U^\dagger]$ up to additive error $\varepsilon$ for arbitrary input states $\rho$ and observables $O$. We propose a parallel, non-adaptive CSEU protocol using $\mathcal{O}(d\varepsilon^{-1})$ queries when the input states or observables have constant rank. This achieves Heisenberg scaling with respect to $\varepsilon$ and is query-optimal, as we prove a matching $\Omega(d\varepsilon^{-1})$ lower bound that remains valid even with stronger access to the unknown unitary. Our query-optimal CSEU protocol provides a versatile and powerful tool for quantum learning theory, pushing the performance limits of several fundamental learning tasks, including unitary channel tomography, Hamiltonian learning, boundary-regime quantum channel tomography, Pauli transfer matrix learning, inverse-free amplitude estimation, pure-state property estimation, and shallow-circuit learning. Remarkably, we show that optimal unitary channel tomography can be achieved using only parallel queries, closing the gap between the best achievable efficiency of parallel and sequential tomography protocols. Together, these applications establish our framework as a fundamental tool for learning properties of quantum processes, particularly for certain key tasks that require high precision.

24.
arXiv (math.PR) 2026-06-16

Stein's method for the matrix normal distribution

arXiv:2601.11422v2 Announce Type: replace-cross Abstract: This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive an extended-generator-based Stein identity from a matrix Ornstein-Uhlenbeck diffusion with two-sided scales, provide an explicit semigroup representation for the solution of the Stein equation, and obtain regularity estimates for the solution. The new methodology is demonstrated in three examples: (i) smooth Wasserstein distance bounds to quantify the matrix central limit theorem (a didactic example), (ii) a Wasserstein distance bound for the matrix normal approximation of the centered matrix $T$ distribution, and (iii) a Stein's method-of-moments approach to estimating the row and column covariance factors of the matrix normal, yielding a flexible class of weighted flip-flop Stein estimators that generalize Dutilleul's classical flip-flop algorithm and naturally accommodate row/column importance weights, systematic missingness, and projection onto structured covariance families. The latter two examples are intrinsically matrix-valued and cannot be treated using naive vectorization.

25.
arXiv (CS.LG) 2026-06-18

On the Residual Scaling of Looped Transformers: Stability and Transferability

arXiv:2606.18524v1 Announce Type: new Abstract: Looped (weight-tied) Transformers apply a shared residual block $N$ times ($h \leftarrow h + \varepsilon\,f(h)$, same $f$ at each step), increasing effective depth without adding parameters. Prior depth-scaling analyses prescribe $\varepsilon = 1/\!\sqrt{L}$ for depth-$L$ residual networks. We show that this is insufficient for looped architectures: weight sharing makes residual updates correlated across iterations, requiring the stronger scaling $\varepsilon = 1/N$. For multi-layer blocks ($L$ unique layers looped $N$ times), we derive a factored parameterization $\varepsilon = \lambda/(N\!\sqrt{L})$ that separates the two sources of growth: $1/N$ controls the within-layer loop correlation, and $1/\!\sqrt{L}$ controls the across-layer variance. A key consequence is that the optimal learning rate depends only on the number of unique layers $L$, not on the loop count $N$, enabling direct hyperparameter transfer from small to large $N$ without retuning. Experiments on looped Transformers confirm that $1/N$ scaling improves trainability and yields better loss than $1/\!\sqrt{N}$ scaling across loop counts.