arXiv:2606.25818v2 Announce Type: replace Abstract: Shift-variant image degradation is frequently encountered in practical imaging systems where the point spread function (PSF) varies across the image field due to motion, optical aberrations, atmospheric turbulence, or sensor-related effects. Unlike shift-invariant, shift-variant degradation presents significant challenges for image restoration because the degradation process cannot be represented by a single convolution kernel. This paper proposes a singular value decomposition (SVD)-based framework for restoring images degraded by shift-variant motion blur. The proposed approach determines the contribution of small singular values using a singular-value energy retention criterion. Specifically, the number of small singular values is selected based on a specified percentage of cumulative singular-value energy, providing a systematic approach for controlling noise amplification while preserving useful image information. The degradation model is formulated using a position-dependent PSF represented by a shift-variant imaging operator. Three representative one dimensional shift-variant motion PSFs are considered: bidirectional linear motion, Gaussian motion, and simple harmonic motion. The image degradation process is modeled as a linear system, and SVD is employed to analyze and invert the corresponding degradation operator. The singular-value representation provides insight into the ill-conditioned nature of the restoration problem and enables the development of stable inversion techniques. The proposed SVD-based restoration algorithm is applied to three degraded images. Experimental results demonstrate the effectiveness of the proposed approach in recovering image details and reducing blur artifacts under different motion models.
Science Journals
arXiv:2606.26297v4 Announce Type: replace Abstract: This paper presents a Qiskit-compatible distributed quantum approximate optimization algorithm (DQAOA) simulator for quadratic unconstrained binary optimization (QUBO) problems arising in engineering design and decision applications. The open-source simulator is available through the RAISE LAB website and GitHub repository, with README documentation for installation, input formatting, configurable parameters, and example workflows. The package addresses the need for a reusable simulator that can solve and compare QUBO instances across different QAOA execution modes. It supports monolithic QAOA on a single quantum processing unit (QPU) and distributed QAOA across a user-specified number of QPUs with configurable capacities. The workflow canonicalizes the QUBO model, maps it to a cost Hamiltonian, allocates variables across QPUs, identifies local and cross-QPU couplings, and constructs the corresponding circuits. Runtime optimizations, including parameterized circuit reuse, objective reuse at fixed depth, batched evaluations, and parallel multi-start execution, reduce repeated overhead. A Streamlit graphical user interface is also provided for entering or uploading QUBO instances, configuring solver settings, running selected modes, and visualizing solution-quality metrics without editing Python scripts. The package is demonstrated on standalone QUBO benchmarks and a power generation unit commitment application. In the unit commitment case, brute force, monolithic QAOA, and distributed QAOA recover the same commitment bitstring and operating cost. Across multiple case studies, the simulator produces results consistent with classical monolithic QAOA references in terms of optimal bitstrings and costs. Staged runtime analysis shows substantial runtime reduction across implementation stages, while distributed QAOA remains more demanding because cross-QPU couplings require remote operations.
arXiv:2607.01120v2 Announce Type: replace Abstract: LLM agents are rapidly being deployed in production, including coding assistants, customer-support chatbots, and scientific research assistants, yet they remain fundamentally static in enterprise deployment. The LLM weights, system prompts, tool repertoires, and in-context harnesses are frozen at deployment time, and any improvement requires a manual loop of human-curated data collection, offline fine-tuning, modification of the agentic paradigm, and re-deployment. Recent work on self-evolving agents, such as OpenClaw for individual users, indicates that the next leap in agent capability will come from agents that continually learn from their own experience. In this paper, we argue that this vision for self-evolving agent deployment is being held back for enterprise-level large-scale agentic service not by reinforcement learning (RL) algorithms but by agentic online RL systems. Specifically, current agentic RL systems and the surrounding observability software stack are inadequate along three essential aspects: (i) there is no standardized agent trajectory data protocol capable of carrying RL learning signals at step granularity across heterogeneous agent paradigms; (ii) there is no enterprise-grade comprehensive data proxy that converts real workloads into governed learning substrates; and (iii) there is no unified agent evolution control plane that automatically decides, based on trajectory statistics, when to update policy weights or evolve the in-context harness. The next generation of agentic RL systems must be co-designed around these three pillars, and we sketch concrete architectures, case studies, and counter-arguments. We instantiate one branch through AReaL2.0, reorganizing existing RL infrastructure into an agent-oriented online RL loop for policy weight updates from deployed workloads.
arXiv:2607.02423v1 Announce Type: new Abstract: Active Few-Shot Learning (AFSL) adapts LLMs to specialized domains by identifying the most valuable unlabeled samples for annotation and use as few-shot demonstrations, effectively reducing human annotation costs while promoting high performance. However, existing methods typically rely on output-level signals for sample identification, such as predictive entropy or semantic similarities with test-time data based on external embeddings, which often overlook models' internal dynamics, which could pinpoint specific knowledge gaps. To bridge this gap, we propose NeuFS, a Neuron-Aware Active Few-Shot Learning framework that shifts the selection paradigm from output-level proxies to models' internal dynamics. NeuFS utilizes neuron activation patterns to represent sample directly, and includes a dual-criteria selection strategy that: (1) ensures few-shot sample diversity with neuron patterns for broader example coverage, while (2) prioritizing on identifying informative and challenging few-shot samples LLMs tend to hallucinate by quantifying neuron consensus. Experiments on three datasets demonstrate that NeuFS excels in both reasoning and text classification tasks, outperforming existing AFSL baselines. Ablation studies further highlight that internal neuron activations provide a more principled and effective selection signal than external embeddings, validating the superiority of the proposed NeuFS.
arXiv:2607.01478v1 Announce Type: cross Abstract: We measured quantization-induced decision-boundary changes using local logit-margin radii, first-order boundary displacement, normal variation, slice-boundary Jaccard distance, grid prediction changes, multiclass junction counts, and low-margin boundary-band flips. On the digits benchmark, 8-bit weight quantization preserved all test labels while producing boundary-mask Jaccard \(0.428\) on the PCA slice; at 4 bits, accuracy remained \(0.9733\), while boundary Jaccard rose to \(0.970\) and median local boundary shift reached \(0.0290\). Interpolation between adjacent quantization levels localized the visible reconfigurations at multiclass junctions, with 12, 34, and 17 triple-junction cells in the selected transitions. Calibration-to-test stopping reduced the digits held-out flip rate from \(0.0094\) to \(0.0022\) and boundary Jaccard from \(0.825\) to \(0.524\); the same stopping rule also reduced flips on MNIST and Fashion-MNIST. On official CIFAR-10 subsets, PTQ-W selected by accuracy gave 6-bit flip \(0.0367\) and boundary Jaccard \(0.184\), whereas boundary-aware stopping selected 8-bit flip \(0.0083\) and boundary Jaccard \(0.048\). On full CIFAR-10 with three seeds, 6-bit PTQ-W lost \(0.0029\) accuracy relative to float, changed \(5.3\%\) of held-out decisions, and changed \(24.5\%\) of low-margin boundary-band decisions. A fixed-bit boundary-gap rounding term changed the trade-off at 4 bits by reducing boundary Jaccard from \(0.457\) to \(0.435\) and boundary-band pair-order flip from \(0.3600\) to \(0.3558\), with an accuracy trade-off; the 3-bit stress test exposed the tuning limit of this surrogate. Calibration boundary Jaccard predicted held-out boundary Jaccard across PTQ-W and optimized rounding variants with \(r=0.947\)--\(0.994\).
arXiv:2505.03303v5 Announce Type: replace Abstract: Lightweight convolutional neural networks are often compared using results obtained with different training recipes, input settings, and pretrained checkpoints. Such differences make architecture rankings difficult to interpret. This study presents a controlled benchmark of seven established CNNs across CIFAR-10, CIFAR-100, and Tiny ImageNet under a shared fine tuning protocol. The evaluation reports top-1 accuracy, macro F1, top-5 accuracy, parameter count, FP32 parameter storage, and multiply accumulate operations. EfficientNetV2-S records the highest observed top-1 accuracy on all three datasets, reaching 97.57%, 86.98%, and 78.73%. EfficientNet-B0 remains within 0.85 percentage points of EfficientNetV2-S across the three datasets while requiring only about 21% of its parameters and 14% of its multiply accumulate operations on Tiny ImageNet. It therefore offers a favorable general balance between predictive performance and computational demand. MobileNetV3-Small is a strong candidate for ultra low resource settings. It uses about 40% of the parameters and 15% of the multiply accumulate operations of EfficientNet-B0 while retaining competitive accuracy. A matched comparison of ImageNet pretrained and randomly initialized EfficientNet-B0 and MobileNetV3-Small models shows that the pretrained advantage is substantially larger on CIFAR-100 and Tiny ImageNet than on CIFAR-10 under the fixed protocol. The results provide a focused reference for selecting established lightweight CNNs when predictive quality, parameter storage, and theoretical computation must be considered together.
arXiv:2607.01232v2 Announce Type: replace Abstract: Reinforcement learning (RL) has become a central component of post-training large language models (LLMs), yet little is understood about how RL adaptation is distributed across transformer layers. Existing approaches typically update all model parameters uniformly, implicitly assuming that every layer contributes similarly to the gains obtained during RL post-training. In this work, we challenge this assumption through a systematic layer-wise study of RL training. Surprisingly, we find that training a single transformer layer can recover most of the gains achieved by full-parameter RL training, and in some cases even surpass it. To quantify this phenomenon, we introduce the quantity layer contribution, which measures the fraction of full RL improvement recovered by training a layer in isolation. Across seven models spanning two model families (Qwen3, Qwen2.5), three RL algorithms (GRPO, GiGPO, Dr. GRPO), and multiple task domains including mathematical reasoning, code generation, and agentic decision-making, we observe a remarkably stable pattern: RL gains are highly concentrated in a small subset of, and in many cases even a single, transformer layers. More strikingly, the same structural pattern consistently emerges: high-contribution layers concentrate in the middle of the transformer stack, while layers near the input and output ends contribute substantially less. The resulting layer rankings remain strongly correlated across datasets, tasks, model families, and RL algorithms.
arXiv:2209.04942v2 Announce Type: replace-cross Abstract: Problem definition: This paper studies the problem of estimating consumer preferences from bundle sales data. Product bundling is a widely used pricing strategy in retail markets. To set profitable bundle selection and prices, the seller needs to learn the distribution of consumers' valuations for individual products from the transaction data. When customers purchase bundles or multiple products, classical methods such as discrete choice models cannot be used to estimate consumers' valuations. In this paper, we propose an approach to learn the distribution of consumers' valuations toward the products using bundle sales data. Methodology/results: Our approach is to define a utility model for customer choices and estimate the parameters of a valuation distribution that maximizes the likelihood of observing the transaction data. Our approach reduces this problem to an estimation problem where the samples are censored by polyhedral regions on the valuation space of customers. Using the EM algorithm and Monte Carlo simulation, our approach can recover the distribution of consumers' valuations. We extend the framework to allow for unobserved no-purchases, clustered market segments and to incorporate non-additive bundle utilities with synergy effects. In addition, we provide theoretical results on the identifiability of the probability model and sufficient conditions for local convergence of the EM algorithm. Moreover, the performance of the approach is also demonstrated numerically with synthetic and real datasets. Managerial implications: This study demonstrates the challenge to leverage the transaction data of bundle sales to learn customers' preferences. The proposed algorithm provides a practical guidance for retailers.
arXiv:2404.06937v2 Announce Type: replace-cross Abstract: $\Lambda$, $V$, $\Xi$ (ladder), and other three-level quantum systems with one forbidden transition (referred here as $\Lambda$-type systems) play an important role in quantum physics. Various applications require manipulation of such systems using as control shaped laser field. In this work, we study how degeneracy of energy states or of Bohr frequencies in these systems affects the efficiency or difficulty of finding optimal shape of the control field. For this, we adopt the notion of higher order traps, which was introduced in [A.N. Pechen and D.J. Tannor, Are there traps in quantum control landscapes? Phys. Rev. Lett. {\bf 106}, 120402 (2011)], where second/third order traps were discovered for $\Lambda$-atom with one forbidden transition and with non-degenerate energy levels. We theoretically study control of such systems with and without degeneracy in their eigenstates and Bohr frequencies, and investigate numerically using GRAPE and l-BFGS algorithms how this degeneracy influences on the efficiency of optimizing the control laser field. We find that the degeneracy of the Bohr frequencies in the $\Xi$ system, which makes the system energy levels symmetrically distributed, leads to the appearance of a seventh order trap with a more significant attracting domain resulting in a more difficult optimization, while the degeneracy of energy states in generic $\Lambda$-type systems does not lead to an increase of the order of the zero control trap compared to the non-degenerate case. We also find that when not only the Bohr frequencies are degenerate in the system $\Xi$, but also the dipole moments for the two allowed transitions coincide (in this case $\Xi$ system is not controllable), then true traps arise in the quantum control landscape. In particular, the constant zero control becomes a trap.
arXiv:2510.21705v2 Announce Type: replace-cross Abstract: Here we address the fundamental question of whether an idealized system of $N$ atoms will show collective behavior and superradiance when it emits fermions instead of photons. We show that for single-fermion emission processes, the maximum emission is $\propto N$ and not $\propto N^2$, which proves the absence of superradiance and shows that the recent proposal to realize a superradiant neutrino laser is impossible. This can be understood as either destructive interference of fermionic transition amplitudes, or Pauli blockade by collective excitations with fermionic nature. We derive the exact solution of the fermionic Dicke problem and analyze the decay dynamics in various regimes. We extend the proof to arbitrary Hamiltonians and show that the jump rate operator for neutrino emission has a maximum eigenvalue of $N$ times the single-particle rate $\Gamma_0$. States with low excitation can show collective behavior and emit at a rate of $N \Gamma_0$.
arXiv:2602.15966v2 Announce Type: replace-cross Abstract: We study a sequential coherent side-channel model in which an adversarial probe qubit interacts with a target qubit during a hidden gate sequence. Repeating the same hidden sequence for $N$ shots yields an empirical \emph{full-correlation record}: the joint histogram $\widehat{P}_g(b)$ over probe bit-strings $b\in\{0,1\}^k$, which is a sufficient statistic for classical post-processing under identically and independently distributed (i.i.d.)\ shots but grows exponentially with circuit depth. We first describe this sequential probe framework in a coupling- and measurement-agnostic form, emphasizing the scaling of the observation space and why exact analytic distinguishability becomes intractable with circuit depth. We then specialize to a representative instantiation (a controlled-rotation probe coupling with fixed projective readout and a commuting $R_x$ gate alphabet) where we (i) derive a depth-dependent leakage envelope whose maximizer predicts a coupling band as a function of depth {if the measurement data is reduced to marginal statistics}, and (ii) provide an operational decoder, via machine learning, a single parameter-conditioned map from $\widehat{P}_g$ to Alice's per-step gate labels, generalizing across coupling and noise settings without retraining.
arXiv:2510.06288v4 Announce Type: replace Abstract: Today's AI models learn primarily through mimicry and refining, so it is not surprising that they struggle to solve problems beyond the limits set by existing data. To solve novel problems, agents should acquire skills by exploring and learning through experience. Finding a scalable learning mechanism for developing agents that learn through interaction remains a major open problem. In this work, we introduce BuilderBench, a benchmark to accelerate research into agent training that centers open-ended exploration. BuilderBench requires agents to learn how to build any structure using blocks. BuilderBench is equipped with (1) a simulator of a robot interacting with various physical blocks, and (2) a task-suite with over 50 diverse target structures that are carefully curated to test an understanding of physics, mathematics, and long-horizon planning. Agents are provided with a target structure at the start, and can interact with the environment for multiple episodes to experiment and learn various skills for building the structure. Solving these tasks requires \emph{embodied reasoning} in a way that is not reflected in words but rather in actions, experimenting with different strategies and piecing them together. Our experiments with multiple state-of-the-art frontier language model based agents and tabula rasa reinforcement learning algorithms show that these agents cannot solve any of the non-trivial tasks in the BuilderBench. Our analysis throws light on the lack of exploration abilities in these models.
arXiv:2601.02813v3 Announce Type: replace Abstract: Aligning language models to qualitative behavioral traits, such as human-likeness, remains difficult because they are hard to define, measure, and optimize. As a result, improvements in human-like behavior are largely driven by scale or broad supervised training, rather than targeted alignment. We introduce Human Aligning LLMs (HAL), a framework for aligning language models to conversational human-likeness using an interpretable, data-driven reward. HAL derives explicit conversational traits from contrastive dialogue data, combines them into a compact scalar score, and uses this score as a transparent reward signal for alignment with standard preference optimization methods. Using this approach, we align models of varying sizes without affecting their overall performance. In large-scale Chatbot Arena-style human evaluations, a model aligned with HAL is more frequently perceived as human-like in conversation. Because HAL operates over explicit, interpretable traits, it enables inspection of alignment behavior and diagnosis of unintended effects. More broadly, HAL demonstrates how soft, qualitative properties of language--previously outside the scope for alignment--can be made measurable and aligned in an interpretable and explainable way.
arXiv:2607.01752v1 Announce Type: new Abstract: Temporal point processes (TPPs) have widespread applications across various domains. Compared to modeling the conditional intensity of a TPP, modeling its cumulative conditional intensity function (CCIF) improves computational efficiency and eliminates numerical approximation errors. However, current CCIF parameterizations uniformly rely on Monotone Neural Networks (MNNs), which we identify as suffering from three structural deadlocks--convexity restrictions, saturation limits, and violations of CCIF modeling requirements--that fundamentally restrict their representational capacity for complex temporal dynamics. To resolve these bottlenecks, this paper proposes a novel framework called Monotone Alternating Splines (MAS). By leveraging distinct interpolation and extrapolation components, MAS provides a flexible and efficient framework for modeling CCIFs. Theoretically, MAS's interpolation provides strong fitting accuracy, while its extrapolation supports robust generalization, reducing the irreducible approximation gaps of MNNs. Extensive experiments show that MAS achieves superior performance on both synthetic and real-world datasets.
arXiv:2511.05150v2 Announce Type: replace Abstract: Molecular biomarker testing in pathology is often costly and tissue-consuming, limiting scalable clinical deployment. Artificial intelligence applied to hematoxylin and eosin (HE)-stained histology could enable rapid biomarker screening, but clinical translation requires models that are both accurate and interpretable. Here we introduce Hireca, a biomarker-focused pathology foundation model pretrained on more than 80,000 whole-slide images spanning 38 organ types from three medical centers, together with CytoMap, an interpretability module that localizes cellular-scale evidence underlying predictions. Across 10 biomarker tasks encompassing morphological, molecular, genetic, and spatial-transcriptomic-proxy readouts, Hireca ranked first in five tasks and outperformed comparable models overall. In evaluation by eight pathologists from two countries, CytoMap was consistently preferred over alternative visualization approaches and revealed error patterns in difficult cases. These results position Hireca and CytoMap as a transparent framework for clinically reviewable biomarker assessment directly from routine HE histology.
arXiv:2511.11437v2 Announce Type: replace Abstract: Reconstructing natural images from fMRI requires bridging neural activity with both the structural and semantic representations used by modern generative models. Existing diffusion-based decoders often condition on a single global fMRI embedding, which limits their ability to exploit the hierarchical organization of the visual cortex and makes the contribution of different visual areas difficult to inspect. We propose Hi-DREAM, a brain-inspired hierarchical diffusion framework that structures fMRI conditioning according to early, middle, and late visual Regions of Interest (ROI) streams. A ROI adapter converts these streams into a multi-scale cortical pyramid, and a lightweight ROI-conditioned ControlNet injects the resulting anatomy-aware priors into matched U-Net depths during denoising. Experiments on the Natural Scenes Dataset (NSD) show that Hi-DREAM achieves state-of-the-art high-level semantic reconstruction while retaining strong low-level structure. Further ablation and attribution analyses show that the proposed hierarchy-aware conditioning is effective, and that different ROI streams provide complementary, inspectable contributions to reconstruction.
arXiv:2607.01245v1 Announce Type: new Abstract: We introduce Office Comprehension Bench (OCB), the first public benchmark to jointly evaluate LLM systems on Word, Excel, and PowerPoint comprehension over native file formats (.docx, .xlsx, .pptx) and their variants. OCB consists of two tracks. File Fidelity Q&A tests structural and visual perception of office artifacts - tables, charts, embedded images, formulas, and app-specific elements such as headers, speaker notes, and named ranges. Domain Q&A tests expert-level reasoning grounded in real-world industry documents across 12 professional domains, with queries requiring multi-step analysis and synthesis across documents. Each reference answer is decomposed into atomic, binary-gradable claims, and an ensemble of LLM judges scores responses against each claim independently. Even the strongest frontier system in its default reasoning mode reaches only about 59.3% on Domain Q&A; increasing thinking depth within a tier does not move performance materially, while moving to a higher product tier yields modest gains. We release the dataset, evaluation tooling, judge prompt, and a public leaderboard.
arXiv:2607.01247v1 Announce Type: new Abstract: Open-ended mathematics exams are valuable because they assess reasoning, proof construction, algorithmic thinking, and communication of intermediate steps. They are also difficult to grade at scale because instructors must apply partial-credit rubrics consistently while giving feedback that helps students repair misconceptions. This paper evaluates six contemporary large language model (LLM) configurations, Gemini 3.1 Pro Extended, Gemini 3.5 Flash, ChatGPT 5.5 Pro Extended, ChatGPT 5.5 Thinking, Claude Pro Opus 4.7, and Claude Sonnet 4.6, as grading assistants for an undergraduate discrete mathematics examination. The study compares two grading policies. The BASELINE policy uses a stricter rubric-following prompt that emphasizes explicit evidence and complete justification. The LIBERAL policy was added after preliminary grading showed that the baseline condition sometimes applied harsh point deductions and failed to recognize valid partial reasoning. Agreement with human grading is measured at both the question and exam-total levels using mean absolute error, root mean squared error, normalized root mean squared error, Pearson correlation, and exact agreement. The results show that liberal partial-credit prompting reduces average question-level error for every evaluated model family. ChatGPT 5.5 Thinking (LIBERAL) has the lowest average question-level MAE (1.87) and RMSE (2.53), while Gemini 3.1 Pro Extended (LIBERAL) has the lowest total-score MAE (8.00) and RMSE (10.66). However, the strongest total-score Pearson correlation occurs under Gemini 3.1 Pro Extended (BASELINE) at 0.58, showing that point calibration and rank preservation remain distinct goals. We also report practical usability observations.
arXiv:2607.00920v2 Announce Type: replace Abstract: Real-world e-commerce image editing often requires multiple, localized, and auditable operations rather than global restyling. This compositional nature poses a dual challenge: models must precisely apply all requested edits to the correct regions while preserving unmodified content, even under ambiguous instructions. Existing one-shot editors conflate intent resolution, spatial grounding, and synthesis into a single step, frequently resulting in partial execution failures, which is unacceptable for commercial scenarios. To address this, we introduce GMO-E$^2$DIT, an agentic editing framework that couples a Vision-Language Model (VLM) with a mask-conditioned image editor to tackle structured multi-turn task completion. Given an underspecified instruction, the VLM agent constructs a region-grounded edit agenda, effectively decoupling cognitive reasoning from generative rendering. The framework then executes sub-programs via operation-aware masks and references, utilizing a reflection-driven loop to inspect intermediate results and determine the subsequent state. This iterative mechanism reliably preserves safe partial progress, retries unfinished operations, and recovers from errors. Furthermore, we develop a unified data pipeline providing aligned supervision for planning, execution, and reflection, alongside EComEditBench, a comprehensive benchmark for instruction-driven evaluation. Extensive experiments demonstrate that GMO-E$^2$DIT achieves competitive performance compared to strong closed-source models, yielding superior instruction accuracy and edit fidelity over existing baselines.
arXiv:2604.08580v2 Announce Type: replace-cross Abstract: Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing a control under SDE constraints. In this work, we revisit and generalize Adjoint Matching, a recently proposed SOC-based method for learning optimal controls, and place it on a rigorous footing by deriving it from the Stochastic Maximum Principle (SMP). We formulate a general Hamiltonian adjoint matching objective for SOC problems with control-dependent drift and diffusion and convex running costs, and show that its expected value has the same first variation as the original SOC objective. As a consequence, critical points satisfy the Hamilton--Jacobi--Bellman (HJB) stationarity conditions. In the important practical case of state- and control-independent diffusion, we recover the lean adjoint matching loss previously introduced, which avoids second-order terms and whose critical points coincide with the optimal control under mild uniqueness assumptions. Numerical experiments confirm that the extra terms it discards become necessary once the diffusion is state-dependent. Finally, we show that adjoint matching can be precisely interpreted as a continuous-time method of successive approximations induced by the SMP, yielding a practical and implementable alternative to classical SMP-based algorithms, which are obstructed by intractable martingale terms in the stochastic setting. These results are also of independent interest to the stochastic control community, providing new implementable objectives and a viable pathway for SMP-based iterations in stochastic problems.
arXiv:2606.12623v3 Announce Type: replace-cross Abstract: Personalized medicine in acute ischemic stroke requires moving beyond average treatment effects (ATE) to individualized treatment effect (ITE) estimates to support treatment decisions. In acute ischemic stroke, mechanical thrombectomy has been shown to be more effective on average than lysis in randomized controlled trials (RCTs), such as the MR CLEAN study. We aim to identify which individual patients benefit most from mechanical thrombectomy compared to lysis. The outcome of interest is the modified Rankin Scale (mRS) at three months, an ordinal measure of functional disability (0: no symptoms, 6: death). We demonstrate that causal transformation models on directed acyclic graphs (TRAM-DAG) can be used for ITE estimation after being fitted on observational MAGIC multi-center stroke patient data. To ensure comparability with the MR CLEAN population, which we use for validation, we train the TRAM-DAG on a MAGIC sub-population with NIHSS at admission >= 6, corresponding to one inclusion criterion of MR CLEAN. The fitted model is then used to estimate ITEs for stroke patients in the MR CLEAN population. While these ITE estimates cannot be confirmed experimentally, we show that their average is consistent with the trial's reported ATE. Furthermore, the ITE estimates correctly rank trial patients by their observed frequency of a good outcome (mRS at three months <= 2). These findings support the use of causal models like TRAM-DAG for personalized decision-making in stroke care and highlight their ability to bridge the gap between observational evidence and clinical trials.
arXiv:2606.19268v2 Announce Type: replace-cross Abstract: We define a new measure of intrinsic dimension of a data manifold, which we call the Patnaik-Pearson dimension, and apply this to internal representations of neural networks, in particular transformers. The inspiration for this comes from the HTSR and SETOL work of Martin, Mahoney and Hinrichs, combined with the TwoNN intrinsic dimension estimator of Facco et al. We prove various properties of this intrinsic dimension estimator. Treating weight matrices of neural networks as data manifolds, for weight matrices whose Empirical Spectral Density follows a Pareto (Power Law) distribution, we relate the Patnaik-Pearson dimension to the HTSR and SETOL analysis, and show that critical values of the tail exponent coincide for the two approaches. Using a combination of theoretical and numerical techniques, we study the behaviour of the Patnaik-Pearson dimension of a data manifold under the transformations typical to neural networks. We apply this machinery to the BERT-base and DeepSeek-R1-Distill-Qwen-1 models, to investigate first the Patnaik-Pearson dimension of the initial data manifold of token embeddings, and second the evolution of the Patnaik-Pearson dimension as token embeddings pass through the layers of the model. Code and notebooks used for the numerical results presented here is available at https://github.com/tdhadfield/PatnaikPearson
arXiv:2606.31738v2 Announce Type: replace-cross Abstract: We propose Regularized Newton-SLRA (RN-SLRA), a regularized Newton-type method for local manifold--affine intersection problems motivated by structured low-rank approximation. Classical Newton-SLRA achieves fast local convergence under transversality, but its tangent-space intersection step may become ill-defined, singular, or severely ill-conditioned when transversality fails. RN-SLRA overcomes this difficulty by replacing the exact tangent-space intersection step with a regularized quadratic subproblem over the affine space. Under intrinsic transversality, we prove local linear convergence to the intersection. Under transversality, we show that a residual-dependent choice of the regularization parameter yields higher-order local convergence; in particular, the method converges quadratically for the linear residual rule. We also analyze an inexact variant based on quasioptimal manifold projections. When the quasioptimality constant is sufficiently accurate, the inexact method retains local residual convergence. Numerical experiments on constructed degenerate SLRA instances and Hankel-structured examples illustrate the robustness of RN-SLRA in settings where Newton-SLRA may fail, and show that the inexact variant can reduce the projection cost in large-scale problems.
arXiv:2607.00224v2 Announce Type: replace-cross Abstract: Watermarking promises statistical traceability of large language model (LLM) uses, but real documents rarely arrive as purely human-written or purely LLM-generated. This motivates a quantitative question beyond detection: what proportion of a document is generated from a pre-specified watermarked LLM? We study this watermark proportion estimation problem under the Gumbel--max watermarking mechanism, treating the next-token prediction distributions as unknown and arbitrary nuisance parameters subject to a non-degeneracy condition. We compare two observation regimes: in the full observation regime, the estimator observes the pseudorandom vector and the selected token at each position; in the more prevalent setting of pivotal reduction, it observes only a scalar pivot, which follows a one-dimensional Uniform--Beta mixture distribution. Under pivotal reduction, we develop a Laguerre-polynomial estimator and establish a matching information-theoretic lower bound for the sample complexity. For full observation, we introduce an event-counting estimator and show a matching lower bound, yielding a substantially smaller sample complexity. As our results imply, although reducing to pivotal statistics is an elegant and prevalent choice, it is not always sample-efficient for estimating the proportion of watermarks.
arXiv:2601.03390v2 Announce Type: replace Abstract: As Byzantine Fault Tolerant (BFT) protocols are increasingly adopted for user-facing applications such as payments and smart contracts, it is crucial that they provide low latency. To reduce latency, some BFT consensus protocols use a leaderless, speculative, fast path where clients broadcast requests directly to replicas, enabling end-to-end commit latency of two message delays ($2\Delta$). However, such a fast path is extremely fragile: concurrent requests can cause replicas to diverge when they receive requests in different orders, triggering costly recovery procedures. This paper presents Aspen, a leaderless speculative BFT protocol that handles concurrent requests while achieving near-optimal latency of $2\Delta + \epsilon$. The $\epsilon$ term is a short waiting delay introduced by Aspen's best effort ordering layer, which uses loosely synchronized clocks and network delay estimates to provide a tentative order. To make its fast path even more robust to intermittent divergence, Aspen adds extra replicas ($n = 3f + 2p + 1$) as well as novel recovery mechanisms that allow the system to tolerate divergence while preserving safety and performance. In experiments with geo-distributed replicas, Aspen reduces the median latency of requests by $1.1\times$--$3.8\times$ compared to state-of-the-art BFT protocols, while sustaining up to $0.75\times$ the peak throughput of throughput-optimized designs.