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01.
arXiv (CS.CL) 2026-06-16

Mechanistic Analysis of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning

Sequential fine-tuning of Large Language Models (LLMs) adaptation to target tasks often triggers catastrophic forgetting, where the acquisition of novel target skills degrades ancestral capabilities. This paper presents a systematic comparative study of catastrophic forgetting across twenty premier models representing the state-of-the-art in mid-2026. We categorize our investigation into two primary research lines: (i) a behavioral and semantic output drift analysis of ten leading closed-source models (including Claude Fable 5, GPT-5.5 High, and Gemini 3.5 Flash), and (ii) a deep mechanistic interpretation of ten prominent open-weight architectures (such as DeepSeek-V4-Pro, Llama 4 Maverick, and Qwen 3.6-27B). Through weight-space trajectory tracking, Centered Kernel Alignment (CKA), and routing gate drift calculations in Mixture-of-Experts (MoE) layers, we localize the neural circuits highly susceptible to parameter overwriting. Our findings indicate that early-layer attention heads exhibit systemic entropic dispersion, while mid-to-deep feed-forward networks (or sparse expert blocks) suffer localized representation collapse. Informed by these insights, we introduce Low-Rank Circuit Projection (LRCP), a subspace-regularized training intervention. Empirical evaluations show that LRCP successfully mitigates up to 94.2% of ancestral capabilities in open-weight configurations and matches the adaptation velocity of standard PEFT baselines.

02.
arXiv (CS.CV) 2026-06-24

Neural Particle Automata: Learning Self-Organizing Particle Dynamics

We introduce Neural Particle Automata (NPA), a Lagrangian generalization of Neural Cellular Automata (NCA) from static lattices to dynamic particle systems. Unlike classical Eulerian NCA where cells are pinned to pixels or voxels, NPA model each cell as a particle with a continuous position and internal state, both updated by a shared, learnable neural rule. This particle-based formulation yields clear individuation of cells, allows heterogeneous dynamics, and concentrates computation only on regions where activity is present. At the same time, particle systems pose challenges: neighborhoods are dynamic, and a naive implementation of local interactions scale quadratically with the number of particles. We address these challenges by replacing grid-based neighborhood perception with differentiable Smoothed Particle Hydrodynamics (SPH) operators backed by memory-efficient, CUDA-accelerated kernels, enabling scalable end-to-end training. Across tasks including morphogenesis, point-cloud classification, and particle-based texture synthesis, we show that NPA retain key NCA behaviors such as robustness and self-regeneration, while enabling new behaviors specific to particle systems. Together, these results position NPA as a compact neural model for learning self-organizing particle dynamics.

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

An Ontology-Guided Multi-Anchor Graph Retrieval Framework for Traffic Legal Liability Determination

Traffic law liability determination is critical for assigning legal penalties, requiring the simultaneous identification of interdependent statutory provisions across multiple legal dimensions. However, existing retrieval-augmented generation methods suffer from a multi-dimensional retrieval bottleneck: single axis architectures compress complex legal queries into a single pathway, causing interdependent statutory dimensions to be overlooked. To address this, we propose OMAGR, an ontology-guided framework that decomposes queries into ontology-aligned anchors and executes parallel graph retrieval across each dimension, ensuring independent retrieval across dimensions before fusion. To evaluate the proposed method, we created the TrafficLaw-QA dataset, an expert-validated benchmark dataset containing 200 questions and 527 legal provisions. Results show that TrafficOmni-RAG outperforms baselines on Context Precision and Faithfulness metrics. The findings demonstrate that parallel multi-anchor retrieval effectively resolves the multi-dimensional retrieval bottleneck, offering a promising direction for traffic law liability determination research.

04.
arXiv (math.PR) 2026-06-15

Stationary measures for higher spin vertex models on a strip

Authors:

arXiv:2309.04897v2 Announce Type: replace-cross Abstract: We introduce a higher spin vertex model on a strip with fused vertex weights. This model can be regarded as a generalization of both the unfused six-vertex model on a strip arXiv:2212.09111 and an 'integrable two-step Floquet dynamics' model introduced in arXiv:1711.08884. We solve for the stationary measure using a fused version of the matrix product ansatz and then characterize it in terms of the Askey-Wilson process. Using this characterization, we obtain the limits of the mean density along an arbitrary down-right path. It turns out that all these models share a common phase diagram, which, after an appropriate mapping, matches the phase diagram of open ASEP. This provides evidence for the universality of this phase diagram.

05.
Nature (Science) 2026-06-17

A blastoporal organizer in a ctenophore

In an iconic experiment in 1924, Hilde Mangold and Hans Spemann established that the dorsal blastopore lip of amphibian embryos functions as an organizer and induces a secondary body axis when transplanted into a host embryo1. This discovery demonstrated that specific embryonic regions can regulate embryonic patterning and lead to the establishment of an entire body axis. Subsequent studies have revealed that cnidarians, the sister group to Bilateria, also possess a blastoporal embryonic organizer2,3. However, the evolutionary origin of the organizer remains unclear. Here we report that the blastopore lip of the ctenophore Mnemiopsis leidyi, a member of the evolutionary sister group to all other metazoans4,5, exhibits organizer activity. We show that transplanted fragments of blastopore lip tissue from M. leidyi gastrula induce secondary pharynx and mouth formation. Moreover, transphyletic transplantation experiments show that the blastopore lip of M. leidyi leads to the generation of a secondary body axis in embryos of the cnidarian Nematostella vectensis. Organizer function in M. leidyi requires both β-catenin and TGFβ signalling, and the TGFβ-family ligands probably provide this inductive capacity. These findings reveal the deep homology of the blastoporal organizer in ctenophores, cnidarians and vertebrates, implying the ancestral organizer role of the blastopore lip. We propose that the emergence of the organizer was an essential innovation that facilitated the change from the temporal cell differentiation of unicellular relatives to the spatial cell differentiation of the first multicellular embryo. Experiments using the comb jelly Mnemiopsis leidyi and the sea anemone Nematostella vectensis reveal that the emergence of a core signalling pathway may have been a key innovation enabling the transition to multicellularity in animals.

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

Towards a future space-based, highly scalable AI infrastructure system design

arXiv:2511.19468v2 Announce Type: replace-cross Abstract: If AI is a foundational general-purpose technology, we should anticipate that demand for AI compute – and energy – will continue to grow. The Sun is by far the largest energy source in our solar system, and thus it warrants consideration how future AI infrastructure could most efficiently tap into that power. This work explores a scalable compute system for machine learning in space, using fleets of satellites equipped with solar arrays, inter-satellite links using free-space optics, and Google tensor processing unit (TPU) accelerator chips. To facilitate high-bandwidth, low-latency inter-satellite communication, the satellites would be flown in close proximity. We illustrate the basic approach to formation flight via an 81-satellite cluster of 1 km radius, and describe an approach for using high-precision ML-based models to control large-scale constellations. Trillium TPUs are radiation tested. They survive a total ionizing dose equivalent to a 5 year mission life without permanent failures, and are characterized for bit-flip errors. Launch costs are a critical part of overall system cost; a learning curve analysis suggests launch to low-Earth orbit (LEO) may reach $\lesssim$\$200/kg by the mid-2030s.

07.
arXiv (CS.CV) 2026-06-25

CoGeoAD: Hierarchical Color-Geometric Fusion with Multi-View Attention for Zero-Shot 3D Anomaly Detection

Zero-shot 3D anomaly detection is essential for industrial quality inspection, where labeled anomaly samples are scarce. Meanwhile, existing methods lack an effective mechanism to fuse complementary 2D color images with 3D geometric structures, limiting their ability to detect both surface and structural defects in a unified framework. To address these issues, we propose CoGeoAD, a unified CLIP-based framework that fuses color and geometric features by constructing pixel-aligned paired multi-view images. The framework introduces a Data-Driven Multi-View Attention (MVA) mechanism to adaptively aggregate 3D features and a Multi-Stage Color-Geometric Fusion (MS-CGF) module to hierarchically integrate multi-level features from both modalities. Extensive experiments on the MVTec3D-AD and Eyecandies benchmarks demonstrate that CoGeoAD achieves state-of-the-art performance, effectively capturing both structural and textural anomalies in complex industrial scenarios. our source code is available at https://github.com/kingdomShu/CoGeoAD.

08.
arXiv (CS.LG) 2026-06-24

Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs

arXiv:2606.23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradients, and Hessians of the value function, where Hessian information is obtained from a matrix Riccati equation along optimal trajectories. These quantities augment a weighted least-squares regression over sparse polynomial bases on hyperbolic cross index sets, with gradients and Hessians contributing additional linear equations per sample and substantially reducing sample complexity compared to value-only regression. Feedback laws are recovered analytically from the learned value function. In high dimensions, a partial Hessian strategy controls the cost of data generation. The approach is validated on problems of increasing state dimension, where second-order data augmentation is shown to improve approximation accuracy and closed-loop performance, with up to an order-of-magnitude reduction in the number of training samples required relative to lower-order methods.

09.
arXiv (quant-ph) 2026-06-24

Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling

arXiv:2606.24713v1 Announce Type: cross Abstract: Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$, making it relevant for $K

10.
bioRxiv (Bioinfo) 2026-06-23

Comorbidity structure as an inductive bias: Comparing output-head designs for multi-label prediction of diabetes and myocardial infarction complications

Background: Clinical complications are often predicted with separate sigmoid outputs, even when the target labels arise from related pathophysiological processes. This paper asks whether output-layer choice should reflect both predictive convenience and the biological structure assumed among complications. The central premise is that label-dependence mechanisms are explicit hypotheses about comorbidity, not generic modelling additions. Methods: Output-head assumptions were compared across two clinically distinct multi-label prediction tasks. In Type 2 diabetes (T2D), six heads were evaluated for nephropathy, neuropathy, and retinopathy: independent baseline, linear additive, multiplicative, symmetric conditional random field (CRF), residual multilayer perceptron (MLP), and combined additive-multiplicative. In myocardial infarction (MI), four heads were evaluated for ventricular tachycardia, ventricular fibrillation, and atrioventricular block: independent baseline, linear additive, multiplicative, and symmetric CRF. All experiments used five training data fractions and seven independent seeds, with the same shared-backbone protocol within each disease setting. Results: In T2D, the symmetric CRF gave the most consistent improvement pattern, ranking highest at full data and at the two lowest data fractions while adding only three interaction parameters. At 20% training data, it was the only interaction head whose aggregate mean exceeded the independent baseline. The residual MLP, despite 123 interaction parameters, remained below the baseline across all T2D fractions. In MI, rankings changed across fractions: the multiplicative head led at 80% and 60%, the CRF led at 100% and 20%, and the baseline led at 40%. The combined additive-multiplicative head did not improve robustness in T2D and showed the largest negative baseline-relative deviations at lower fractions. Conclusions: The findings support a biology-guided view of output-layer design. A small constrained mechanism was most useful when its symmetry matched the shared microvascular structure of T2D, whereas the heterogeneous electrophysiology of MI produced no stable winner. Output-layer choice should therefore be reported and defended as an assumption about disease structure instead of a routine hyperparameter decision.

11.
arXiv (quant-ph) 2026-06-16

Morphology-resolved scrambling in a chaotic quantum billiard

arXiv:2606.16865v1 Announce Type: new Abstract: Chaotic quantum systems can retain spatial memory through scarred eigenstates, but whether these static structures control scrambling remains unclear. This work establishes a morphology-resolved connection between scarred eigenstates and eigenstate-resolved OTOCs in a peanut-shaped quantum billiard. Scalar localisation diagnostics, including differential entropy and continuum participation ratios, detect anomalous concentration but discard spatial architecture. A scale-normalised density overlap, in contrast, directly compares probability density profiles, revealing families of orthogonal eigenstates with nearly identical spatial morphology. Comparing the complete OTOC time traces of these orthogonal eigenstates reveals that morphological recurrence has dynamical content: moderate density overlap yields no universal prediction, whereas strongly recurring morphologies exhibit nearly identical OTOC growth and saturation. Thus, scarred structures act as spatial templates for operator growth, not merely static violations of ergodicity. This morphology-resolved framework turns eigenstate shape into a quantitative predictor of scrambling and provides a scale-controlled diagnostic of weak ergodicity breaking in quantum chaos.

12.
arXiv (quant-ph) 2026-06-19

Single-Step Phase-Engineered Pulse for Active Readout Cavity Reset in Superconducting Circuits

arXiv:2512.08393v2 Announce Type: replace Abstract: In a circuit QED architecture, we experimentally demonstrate a hardware-efficient and qubit-state-dependent Single-Step Phase-Engineered (SSPE) pulse scheme for actively depopulating a readout cavity. The protocol appends a reset segment with tailored amplitude and phase to a standard square readout pulse. Within the linear-response regime, the optimal reset amplitude scales proportionally with the readout amplitude, while the optimal reset phase remains invariant, significantly simplifying the experimental calibration procedure. Time-resolved measurements of the cavity photon number dynamics demonstrate that the SSPE scheme significantly outperforms the CLEAR protocol in terms of reset speed. Crucially, this approach enables arbitrarily fast, overshoot-free depletion of the cavity photon population, with the ultimate reset rate constrained by the finite analog bandwidth of the measurement chain. Furthermore, a comprehensive evaluation of the QND nature demonstrates that the SSPE scheme introduces no additional non-QND measurement errors. It exhibits non-QNDness comparable to both the free-decay and CLEAR protocols, with residual errors predominantly governed by state switching induced by qubit relaxation during the readout process. Thses results establish the SSPE scheme as a practical and scalable approach for achieving rapid and smooth cavity reset in superconducting quantum circuits.

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

ECA: Efficient Continual Alignment for Open-Ended Image-to-Text Generation

Incremental Learning (IL) for Open-ended Image-to-Text Generation (OpenITG) enables models to continuously generate accurate, contextually relevant text for new images while preserving previously acquired knowledge. Unlike prior studies, this paper addresses a more practical scenario in which the predominant category of visual data shifts over time as environments evolve. In this context, we introduce a new notion of continual alignment, which incrementally adapts the alignment module within pre-trained VLMs to preserve high-quality cross-modal representations. Based on this idea, we propose Efficient Continual Alignment (ECA), a novel exemplar-free IL approach for OpenITG. The key challenge is enabling the model to acquire new, task-specific features while minimizing interference with the established alignment without accessing raw data from previous tasks. To address this, ECA employs three core mechanisms: a Mixture of Query (MoQ) module that adapts task-specific query tokens, a Fisher Dynamic Expansion (FeDEx) that dynamically expands model structure based on a Fisher Information Matrix (FIM)-based metric, and an embedding dictionary with Dictionary Replay (DR) to retain past knowledge. To evaluate ECA's performance, we construct four new IL OpenITG benchmarks that better reflect real-world scenarios. Experimental results demonstrate that ECA significantly mitigates catastrophic forgetting and improves IL performance compared to baseline methods. Code and benchmarks are available at https://github.com/Snowball0823/ECA.

14.
arXiv (CS.LG) 2026-06-15

CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data

arXiv:2606.14565v1 Announce Type: cross Abstract: Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests. Because each test samples only a narrow loading path and provides homogenized rather than local stress information, robust discovery typically requires multiple loading modes to constrain the multidimensional response. This is challenging for soft biological tissues, where repeated testing, damage, and sample variability limit reliable information from a single specimen. Here, we combine CANNs with the stress-unsupervised full-field discovery framework EUCLID to identify sparse hyperelastic laws directly from displacement fields and reaction forces in one heterogeneity-inducing loading case. CANN-EUCLID minimizes equilibrium imbalance with sparsity-promoting regularization selecting compact active terms, without local stress measurements or a prescribed law. We evaluate the approach on isotropic and anisotropic benchmarks with prescribed ground-truth laws. When the ground truth is representable by the chosen CANN basis, our method recovers the correct terms with near-exact accuracy, including exponential terms with embedded parameters. When it is not contained in the basis, the method retains shared terms and approximates missing contributions using available basis functions. Generalization depends strongly on sampled deformation states: exponential strain-stiffening terms can be recovered accurately when sufficiently probed, but can produce large extrapolation errors when the stiffening regime lies outside the sampled domain. Forward FE validation simulations show that the discovered behavior accurately replicates the ground truth. These results establish stress-unsupervised CANN discovery as a promising framework for interpretable full-field constitutive model identification.

15.
medRxiv (Medicine) 2026-06-18

Multicluster measles outbreak with a substantial proportion of modified cases in Tokyo, Japan, January-May 2026

Tokyo experienced a measles outbreak (260 cases) in early 2026 despite elimination status. Adults aged 20-39 years were most affected, and 38% of cases were modified measles, increasing with prior vaccination. Although incidence rose until April, the effective reproduction number; R(t) fell below 1, consistent with outbreak control. Multiple clusters were identified, but many cases lacked epidemiological links, suggesting that modified measles is less likely to be considered in differential diagnosis. Intensive contact tracing and surveillance contributed to limiting transmission.

16.
arXiv (CS.CV) 2026-06-19

Exploring Multi-Modal Large Language Models and Two-Stage Fine-Tuning for Fashion Image Retrieval

Composed image retrieval retrieves a target image using a composed query of a reference image and a modified text description. In the fashion domain, this task requires understanding subtle attribute variations such as color, pattern, and texture. However, existing approaches face limitations due to scarce annotated data and simplistic negative sampling. We propose a novel framework that integrates a multi-modal large language model (LLaVA) to generate attribute-aware triplets and introduces a two-stage fine-tuning strategy to enhance contrastive learning. We leverage pretrained vision-language models, such as CLIP-ViT/B32, to generate and concatenate sentence-level prompts with the relative caption and to scale the number of negatives using static representations. Experimental results demonstrate enhanced compositional reasoning and improved fine-grained retrieval behavior, underscoring the feasibility and potential of the proposed framework for fashion retrieval.

17.
arXiv (CS.AI) 2026-06-12

A Study of Belief Revision Postulates in Multi-Agent Systems (Extended Version)

arXiv:2605.02249v2 Announce Type: replace Abstract: We investigate the belief revision problem in epistemic planning, i.e., what will be the beliefs of all agents in a multi-agent system after an agent gains the belief in some state property. Based on the standard representation in epistemic planning of agents' beliefs via a single multi-agent Kripke model, we generalize the classical AGM belief revision postulates to the multi-agent setting, with the aim to provide a formal framework for evaluating dynamic epistemic reasoning frameworks in which the beliefs of all agents as the result of actions are computed. As an example of a simple operator that satisfies all of the generalized AGM postulates, we present generalized full-meet multi-agent belief revision. We moreover define a generalization of the standard postulates for iterated revision, present a more sophisticated, event model based revision operator, and discuss the potential issues in defining an epistemic operator on Kripke models that can satisfy all of the generalized postulates for iterated multi-agent belief revision.

18.
arXiv (quant-ph) 2026-06-11

Observable signatures of exceptional points from left-right eigenstate distinction

arXiv:2606.11333v1 Announce Type: new Abstract: Non-Hermitian quantum systems exhibit qualitatively distinct physical behavior compared to Hermitian systems, a prime example being spectral singularities known as exceptional points. Their relevance in, e.g., quantum sensing, unidirectional transport, and robust lasing makes it important to be able to identify exceptional points through observable features of a many-body system. Here, using as an example a one-dimensional complex XY spin chain realizing both rotation-time RT- and parity-time PT-symmetric regimes, we develop a framework for detecting exceptional points based on the distinction between left and right eigenvectors of the Hamiltonian, which in a non-Hermitian system are no longer the adjoint of each other. We first show that a global measure constructed from the difference between the Hamiltonian and its adjoint locates exceptional points via distinct non-analytic behavior. At the level of observables, differences in local spin correlations evaluated on the right and left eigenstates provide a reliable static detection scheme. In contrast, static bipartite entanglement measures fail to capture this distinction, urging us to study the quantum dynamics of the model. Following a sudden quench, we demonstrate that the time-averaged right-left entanglement entropy difference directly encodes signatures of the exceptional point. In the RT-symmetric regime, it exhibits a pronounced peak at the exceptional point, whereas in the PT-symmetric regime it behaves as an order-parameter-like quantity, remaining finite in one phase and vanishing at the transition. Our results establish a direct link between the structure of non-Hermitian eigenstates and observable signatures of exceptional points, providing a practical route to identify them in existing quantum simulators.

19.
arXiv (CS.CV) 2026-06-24

VistaRef: Boosting Visual Spatial Orientation Awareness for Pointing-to-Object Detection

Grounding deictic gestures in natural images is fundamental to AR and human-robot collaboration, providing a basis for seamless spatial interaction. While Transformer-based visual models have achieved significant progress in general object detection, their global attention mechanisms often neglect micro-geometric relationships, degrading orientation accuracy. In pointing tasks, this deficiency manifests as an inability to accurately capture the pointing ray implied by finger poses, which results in pointing drift and localization ambiguity when dealing with distant or densely packed objects. To address this, we propose VistaRef, a framework designed to explicitly enhance spatial orientation awareness. First, we develop the Local Hand Entity Modeling (LHEM) module, which incorporates hand-pose embeddings to strengthen the model's capability to capture subtle finger deviations. Second, drawing inspiration from multi-view geometry, we construct the Geometric Ray Modeling (GRM) module to transform implicit orientation information into explicit spatial geometric features, guiding feature aggregation and deep fusion via attention mechanisms. Furthermore, we introduce a novel Orientation-Consistent Alignment Loss (OCAL) to synergistically supervise hand presence and pointing consistency, ensuring that all architectural improvements collectively serve the core objective of spatial localization. Experimental results demonstrate that VistaRef significantly outperforms the baseline, achieving a 14-point absolute gain in grounding accuracy. Qualitative analysis further confirms that VistaRef effectively models the geometric correlation from hand to target, bridging the spatial perception gap inherent in traditional Transformers for complex scenarios. Code: https://github.com/lingli1724/VistaRef.

20.
arXiv (CS.AI) 2026-06-16

AC-ODM: Actor–Critic Online Data Mixing for Sample-Efficient LLM Pretraining

arXiv:2505.23878v2 Announce Type: replace-cross Abstract: Optimizing pretraining data composition is pivotal for LLM generalization. While dynamic mixing outperforms static strategies by capturing evolving training dynamics, current methods fail to reconcile computational efficiency with sample efficiency and structural flexibility for diverse pipelines.We introduce Actor–Critic Online Data Mixing (AC-ODM), which approaches data mixing from a reinforcement learning perspective with a parameterized policy that we theoretically prove to act as a dynamic linear surrogate maximizing the constructive interference of gradients. To enhance practical flexibility, AC-ODM supports two operational modes: (i) a proxy mode for fixed, pre-prepared corpora, where a policy learned on a small model is transferred to a larger target; and (ii) a non-proxy mode for direct end-to-end training from scratch without priors. Empirically, AC-ODM significantly outperforms prior methods in convergence speed and downstream accuracy across various architectures. On Pythia-1B, it reaches optimal validation perplexity using up to 66% fewer training steps than competitive baselines, delivering a 27.5% relative improvement in MMLU accuracy and a 2.23 x higher pass@1 on HumanEval, all while incurring a virtually negligible (0.4%) per-step wall-clock increase and only 2% additional memory overhead. Code is available at https://github.com/DANG-ai/AC-ODM.

21.
arXiv (CS.LG) 2026-06-15

Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It

arXiv:2606.14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity. We identify a sharp regularity-dependent boundary. In a rate-determining normal form where the slow drift contains a locally linear leakage and a nonlinear remainder of order $1+\rho$ ($\rho\in[0,1]$), the uncorrected recursion satisfies \[ \mathbb{E}\|Y_k\|^2 \le C\bigl(k^{-1}+k^{-a(1+\rho)}\bigr), \] and a matching scalar Gaussian lower bound shows that the slower term is unavoidable without modifying the update. Thus the decoupled $k^{-1}$ rate is guaranteed for the uncorrected recursion exactly when $a(1+\rho)\ge 1$. This lower bound concerns only the naive update; it is not an information-theoretic obstruction. We demonstrate this by equipping the normal-form recursion with an auxiliary online bias estimator \[ M_{k+1}=M_k+\gamma_k(R(X_k)-M_k),\qquad \beta_k\ll\gamma_k\ll\alpha_k, \] and subtracting $M_k$ from the slow update. Under the same stability, moment, and remainder assumptions, the corrected recursion achieves $\mathbb{E}\|\widetilde Y_k\|^2=O(k^{-1})$ for every $\rho\in[0,1]$, including regimes where the uncorrected update provably suffers the slower rate. Finally, we prove localized transfer theorems that extend the phase-transition mechanism to general nonlinear TTSA in fast-manifold coordinates. The proofs are non-asymptotic and rely on two Abel-transform cancellations: one for the locally linear fast-error leakage, and one for the tracked nonlinear bias.

22.
PLOS Computational Biology 2026-06-01

A statistical framework for comparing epidemic forests

Authors:

by Cyril Geismar, Peter J. White, Anne Cori, Thibaut Jombart Inferring who infected whom in an outbreak is essential for characterising transmission dynamics and guiding public health interventions. However, this task is challenging due to limited surveillance data and the complexity of immunological and social interactions. Instead of a single definitive transmission tree, epidemiologists often consider multiple plausible trees forming epidemic forests. Various inference methods and assumptions can yield different epidemic forests, yet no formal test exists to assess whether these differences are statistically significant. We propose such a framework using a chi-square test and permutational multivariate analysis of variance (PERMANOVA). We assessed each method’s ability to distinguish simulated epidemic forests generated under different offspring distributions. While both methods achieved perfect specificity for forests with 100+ trees, PERMANOVA consistently outperformed the chi-square test in sensitivity across all epidemic and forest sizes. Implemented in the R package mixtree, we provide the first statistical framework to robustly compare epidemic forests.

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

Visual-OPSD: Cross-Modal On-Policy Self-Distillation for Efficient Unified Multimodal Reasoning

Unified multimodal models (UMMs) interleave generated ''visual thoughts'' (VTs) with text reasoning to improve spatial tasks. This incurs roughly an order-of-magnitude inference cost from multi-step diffusion. We find this cost yields limited direct benefit. On ThinkMorph, removing or noising VTs barely changes accuracy across nine benchmarks. Once rendered, attention concentrates on the VT regardless of content. Yet a KL diagnostic shows that conditioning on a privileged VT trace shifts the model's completion distribution. This suggests the generation pathway encodes useful reasoning beyond the rendered pixels. Motivated by this gap, we propose Visual On-Policy Self-Distillation(Visual-OPSD). Teacher and student share identical weights but differ in context: the teacher sees privileged VTs while the student sees only the question. Token-level JSD distillation on on-policy student trajectories transfers the teacher's reasoning to a text-only student. Across nine benchmarks, Visual-OPSD improves over its generative teacher by $+3.40$pp with $14.3\times$ speedup (10.0s vs. 142.8s per sample) and outperforms same-scale VLMs by $+63.83$pp on VSP. A Gaussian-noise control ($+0.40$pp vs. $+10.28$pp for real VTs) and $58.4\%$ closure of the KL gap confirm that gains come from the semantic content of the generation pathway.

24.
arXiv (CS.LG) 2026-06-16

Convergence Rate Analysis of the AdamW-style Shampoo: Unifying One-Sided and Two-Sided Preconditioning

arXiv:2601.07326v4 Announce Type: replace-cross Abstract: This paper studies AdamW-style Shampoo, an effective variant of the classical Shampoo that won the external tuning track of the AlgoPerf neural network training competition. Our analysis unifies one-sided and two-sided preconditioning. When the exponents of the two preconditioners sum to $1/2$, we establish the convergence rate $\frac{1}{K}\sum_{k=1}^KE\left[||\nabla f(X_k)||_*\right]\leq O(\frac{\sqrt{m+n}C}{K^{1/4}})$, where $K$ represents the number of iterations, $(m,n)$ denotes the dimensions of the matrix-valued parameters, and $C$ matches the constant appearing in the optimal convergence rate of SGD. Theoretically, the nuclear norm and Frobenius norm satisfy $||\nabla f(X)||_F\leq ||\nabla f(X)||_*\leq \sqrt{\min\{m,n\}}||\nabla f(X)||_F$, which suggests that our convergence rate is analogous to the optimal $\frac{1}{K}\sum_{k=1}^KE\left[||\nabla f(X_k)||_F\right]\leq O(\frac{C}{K^{1/4}})$ convergence rate of SGD in the ideal case where $||\nabla f(X)||_*= \Theta(\sqrt{\min\{m,n\}})||\nabla f(X)||_F$ and $m$ and $n$ are of comparable magnitude. Then, we extend our analysis to settings where the preconditioning exponents do not sum to 1/2, and establish convergence with an explicit but more involved rate.

25.
arXiv (CS.CV) 2026-06-17

Similarity-based representation factorization for revealing interpretable dimensions in representational data

The study of representations is widespread across fields, including neuroscience, psychology, and artificial intelligence. While representations are often studied and compared through similarities between stimuli, current methods provide only limited access to the dimensions that shape these representations and are often limited in interpretability. To overcome these challenges, here we introduce Similarity-Based Representation Factorization (SRF), a general computational method for recovering low-dimensional, non-negative, interpretable embeddings from similarity matrices derived from measured data. Across simulations and many neural, behavioral, and computational datasets, SRF recovers interpretable dimensions from diverse forms of representational data, even for very sparsely sampled, incomplete data. The dimensions derived from these datasets match those obtained by task-specific models, predict independent behavioral properties, improve exploratory analysis, and offer higher power for confirmatory hypothesis testing than comparing similarity matrices. Together, these results establish SRF as a general-purpose method with broad applications for uncovering, understanding, and using the dimensions underlying representations.