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01.
arXiv (CS.CL) 2026-06-18

LegalWorld: A Life-Cycle Interactive Environment for Legal Agents

作者:
Songhan Zuo↗Shengbin Yue↗Tao Chiang↗Guanying Li↗Yun Song↗Xuanjing Huang↗Zhongyu Wei↗

Civil litigation is inherently a life-cycle process: what a lawyer drafts on day one constrains what unfolds at trial months later. Yet existing legal benchmarks evaluate isolated subtasks, and prior legal-agent simulators reinitialize each scenario from shared ground truth, leaving cross-stage causal dependencies unmodeled. We present LegalWorld, a life-cycle interactive environment that models Chinese civil litigation as a causally connected state chain of five stages (seven sub-scenarios), grounded in 75,309 paired Chinese civil judgments. We pair it with reusable infrastructure (local memory, global case memory, a Skill/Tool library) that keeps each dispute consistent across its full life cycle. Building on this environment, we construct LongJud-Bench to evaluate agent capability across all five connected stages. 18,992 ratings from 217 legal-background evaluators confirm that LegalWorld trajectories are procedurally faithful and role-consistent; and a capability-level cross-model evaluation reveals sharp divergences that aggregate scores cannot expose, with no single backbone leading across consultation, drafting, and courtroom advocacy. Detailed resources will be released publicly.

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02.
arXiv (CS.LG) 2026-06-16

On the Energy Distribution of the Galactic Center Excess' Sources

作者:
Florian List↗Yujin Park↗Nicholas L. Rodd↗Eve Schoen↗Florian Wolf↗

arXiv:2507.17804v2 Announce Type: replace-cross Abstract: The Galactic Center Excess (GCE) may yet herald the discovery of annihilating dark matter. Weighing against that conclusion are analyses showing evidence for dim point sources within the spatial structure of the emission. Due to technical limitations these analyses are purely spatial with all spectral information that could disentangle the excess from astrophysical backgrounds discarded. Here, we demonstrate that a neural network simulation-based inference approach can jointly analyze the spatial and spectra data. The addition is profound: energy information drives the putative point sources to be significantly dimmer, indicating either the GCE is truly diffuse in nature or made of an exceptionally large number of sources. Quantitatively, for our best fit background model, the excess is essentially consistent with Poisson emission as predicted by dark matter. If due to point sources, our median prediction is $\mathcal{O}(10^5)$ sources, or more than 35,000 at 90\% confidence, both orders of magnitude larger than the hundreds preferred by earlier point-source analyses of the GCE, although variations allowed by background systematics could reduce the required number of sources by roughly an order of magnitude.

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03.
arXiv (CS.CV) 2026-06-18

DreamReg: Belief-Driven World Model for 2D-3D Ultrasound Registration

作者:
Luoyao Kang↗Yuelin Zhang↗Jiwei Shan↗Haifan Gong↗Qingpeng Ding↗Shing Shin Cheng↗

Ultrasound (US) is widely used for surgical navigation, yet real-time registration between intraoperative 2D slices and preoperative 3D volumes remains challenging due to partial observability, speckle noise, and the action-dependent US acquisition. Existing methods are one-shot or short-horizon, making it hard for them to gather evidence over time or capture how surgeons adjust probe motion based on on-screen feedback. We propose DreamReg, a belief-driven world-model framework that formulates 2D-3D registration as belief updating over rigid transformations. DreamReg maintains a latent belief state that summarizes past observations and poses information, and continuously refines the transformation through learned dynamics as new slices arrive. During training, DreamReg is exposed to probe-motion trajectories that mimic clinical scanning behavior and learns to update its belief by conditioning pose refinement on the current US observation. During inference, DreamReg refines registration via internal imagination: it rolls out the learned world model to simulate candidate probe motions and their predicted observations, and integrates these imagined outcomes to converge to an accurate rigid transformation. Experiments on CAMUS and u-RegPro datasets demonstrate improved robustness and competitive registration accuracy for real-time guidance compared with state-of-the-art methods.

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04.
arXiv (CS.CV) 2026-06-12

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

作者:
Jiangtao Kong↗Peijun Zhao↗Chun-Fu Chen↗Youngwook Do↗Shaohan Hu↗Tianyi Zhou↗Huajie Shao↗

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.

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05.
arXiv (math.PR) 2026-06-17

How long does it take to train an Elephant Random Walk

作者:
Zheng Fang↗

arXiv:2509.15049v2 Announce Type: replace Abstract: We study how conditioning on the first $k$ steps, which we think of as training, affects the long-term behavior of the Elephant Random Walk. When the elephant is conditioned to be at position $k$ at time $k$, the first return time to the origin scales as $k^{(4-4p)/(3-4p)}$ in the diffusive regime, and grows exponentially in the critical regime. We loosely interpret this as a measurement of the rate at which the elephant forgets its training.

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

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

作者:
Herbert Woisetschl\"ager↗Arastun Mammadli↗Ryan Zhang↗Shiqiang Wang↗

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.

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

LUCID: Learning Embodiment-Agnostic Intent Models from Unstructured Human Videos for Scalable Dexterous Robot Skill Acquisition

作者:
Harsh Gupta↗Guanya Shi↗Wenzhen Yuan↗

arXiv:2606.11628v1 Announce Type: cross Abstract: The most widely-adopted robot learning pipelines today learn skills from robot demonstrations or structured human data, which are expensive to collect and tied to specific embodiments. In contrast, unstructured human videos provide a scalable alternative. They contain diverse manipulation demonstrations across objects, scenes, and strategies, but are not directly connected to robot action. We propose LUCID, a two-stage framework that learns task intent from unstructured human videos drawn from internet-scale datasets and learns robot control in massively-parallel simulation. The intent model predicts short-horizon intent (what should happen next in the scene) from the current observation in closed loop. An embodiment-specific sensorimotor policy converts this intent into robot actions. The intent interface is shared across controllers, so the same intent model can be applied to different embodiments, from our primary dexterous hand to a parallel-jaw gripper. We evaluate LUCID on five real-world manipulation tasks: stirring, wiping, and binning supervised by only internet video, with zero-shot transfer to novel scenes and object instances; and push-T and cable routing supervised by 1 hr each of self-collected smartphone video. Project page: https://lucid-robot.github.io/.

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08.
PLOS Computational Biology 2026-06-17

Deciphering cell type-specific causal genetic effects on brain imaging-derived phenotypes and disorders with single-cell Mendelian randomization

作者:
Anyi Yang↗

by Anyi Yang, Xingzhong Zhao, Xing-Ming Zhao, Yucheng T. Yang Reconstructing causality routes from genetic effects to complex phenotypes in particular cell types is crucial for understanding biological mechanisms underlying the brain-associated phenotypes including imaging-derived phenotypes (IDPs), and brain disorders and behaviors (DBs). Here, we develop a single-cell Mendelian randomization framework to infer cell type-specific causal relationships between gene expression and diverse brain-associated complex phenotypes by integrating single-cell expression quantitative trait loci (cis-eQTLs) and genome-wide association study findings. We identifiy a set of 254 and 217 cis-eQTL target genes (eGenes) that may have causal effects on 112 IDPs and 26 DBs in eight cell types, respectively. These causal eGenes exhibit strong cell type specificity and varied pleiotropy among different types of brain-associated phenotypes. Further integrative analysis reveals putative causality routes among cell type-specific causal eGenes and brain-associated complex phenotypes. Finally, we characterize the spatiotemporal expression patterns of these causal eGenes, and highlight the coordinated associations of the brain-associated phenotypes based on the expression of their causal eGenes. Overall, our study presents a large-scale analysis of the genetic effects of brain structures, disorders and behaviors, providing a catalog of cell type-specific causal eGenes.

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09.
arXiv (CS.AI) 2026-06-12

Token Complexity Theory for AI-Augmented Computing

作者:
Jie Wang↗

arXiv:2606.12647v1 Announce Type: cross Abstract: AI-augmented computing delegates natural language queries, code generation requests, and other open-ended tasks to a cluster of AI models that processes queries and generates responses. This paradigm introduces a resource dimension that neither classical time nor space complexity captures: the cost of sending queries to and receiving responses from such a cluster. We introduce token complexity, a formal resource measure defined as the minimum expected token cost to achieve a specified level of output quality on a task, and develop a taxonomy classifying AI systems by the strength of their probabilistic properties. We develop token complexity within the framework of AI-Oracle Turing machines, in which a probabilistic Turing machine interacts with a stochastic oracle via dedicated query and response tapes. We prove basic theorems establishing that token complexity behaves as expected: monotonicity (higher quality costs more tokens), convexity (quality improvements become progressively more expensive), price sensitivity (small price changes produce bounded cost changes), and price-relativity of task ordering (the token complexity ordering of tasks can reverse depending on the query-to-response cost ratio). We prove that the complexity frontier, defined as the set of all feasible resource bounds in tokens, time, and space, is non-empty, upward-closed, and convex.

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

The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior

作者:
Laura Gomezjurado Gonzalez↗

arXiv:2604.13082v2 Announce Type: replace-cross Abstract: Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we argue that this delay reflects limited access to already learned structure rather than failure to acquire that structure in the first place. We study one-step Collatz prediction and find that the encoder organizes parity and residue structure within the first few thousand training steps, while output accuracy remains near chance for tens of thousands more. Causal interventions support the decoder bottleneck hypothesis. Transplanting a trained encoder into a fresh model accelerates grokking by 2.75 times, while transplanting a trained decoder actively hurts. Freezing a converged encoder and retraining only the decoder eliminates the plateau entirely and yields 97.6% accuracy, compared to 86.1% for joint training. What makes the decoder's job harder or easier depends on numeral representation. Across 15 bases, those whose factorization aligns with the Collatz map's arithmetic (e.g., base 24) reach 99.8% accuracy, while binary fails completely because its representations collapse and never recover. The choice of base acts as an inductive bias that controls how much local digit structure the decoder can exploit, producing large differences in learnability from the same underlying task.

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12.
arXiv (quant-ph) 2026-06-15

Collision models for open quantum systems coupled to finite environments

作者:
Gyaneswar Bhoi↗Anil Shaji↗

arXiv:2606.14163v1 Announce Type: new Abstract: We study a system qubit repeatedly interacting with the same environmental qubit, with a reservoir acting on the environment between collisions via a completely positive, trace-preserving map. We show that complete suppression of system–environment correlations uniquely requires a full environmental reset, recovering a semi group dynamics with a time-independent Gorini–Kossakowski–Sudarshan–Lindblad generator, whereas a partial reset yields a continuous transition between Markovian and non-Markovian regimes governed by a single dimensionless relaxation parameter. For a resonant excitation-exchange interaction, we obtain exact closed-form expressions for the Bloch-vector dynamics for both a generalized depolarizing channel and a generalized amplitude-damping channel acting as the reservoir-induced map. Using the Breuer–Laine–Piilo measure and a Choi-matrix CP-divisibility witness, we identify three distinct dynamical regimes across the parameter space: CP-divisible Markovian dynamics, CP-indivisible but P-divisible dynamics, and non-P-divisible non-Markovian dynamics. The boundaries between these regimes, and the structural differences between uniform and anisotropic environmental relaxation, are characterized numerically.

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13.
arXiv (CS.AI) 2026-06-11

MLaGA: Multimodal Large Language and Graph Assistant

作者:
Dongzhe Fan↗Yi Fang↗Jiajin Liu↗Djellel Difallah↗Qiaoyu Tan↗

arXiv:2506.02568v2 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated substantial efficacy in advancing graph-structured data analysis. Prevailing LLM-based graph methods excel in adapting LLMs to text-rich graphs, wherein node attributes are text descriptions. However, their applications to multimodal graphs–where nodes are associated with diverse attribute types, such as texts and images–remain underexplored, despite their ubiquity in real-world scenarios. To bridge the gap, we introduce the Multimodal Large Language and Graph Assistant (MLaGA), an innovative model that adeptly extends LLM capabilities to facilitate reasoning over complex graph structures and multimodal attributes. We first design a structure-aware multimodal encoder to align textual and visual attributes within a unified space through a joint graph pre-training objective. Subsequently, we implement a multimodal instruction-tuning approach to seamlessly integrate multimodal features and graph structures into the LLM through lightweight projectors. Extensive experiments across multiple datasets demonstrate the effectiveness of MLaGA compared to leading baseline methods, achieving superior performance in diverse graph learning tasks under both supervised and transfer learning scenarios.

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14.
medRxiv (Medicine) 2026-06-22

Maternal-Fetal immune networks and viral signatures in the healthy amniotic cavity

作者:
Gonzalez-Rovira↗Garcia-Diaz↗Martinez-Pancorbo↗Rodriguez-Herrera↗Sanchez↗Bernardo↗Karatas↗Garcia-Mejido↗J. A↗Sousa↗Mellado↗Sainz-Bueno↗…

The intrauterine environment has traditionally been viewed as a privileged site protected by the placental barrier. However, emerging evidence suggests that early in utero microbial exposure may prime the developing fetal immune system. Here, using target-enriched metagenomics and high-dimensional proteomics, we characterized the intra-amniotic viral landscape and immune networks in 114 healthy pregnancies including both normal and anomalous fetuses. We identify a sparse yet heterogeneous human viral signature in 26% of samples, predominantly composed of Herpesviridae, Polyomaviridae, and Picornaviridae. Although viral reads abundance was associated with fetal abnormalities, viral detection generally did not induce overt inflammatory activation, supporting a state of immune homeostasis within the amniotic cavity. Instead, viral presence was associated with subtle and selective immune modulation, including altered inducible antimicrobial peptide expression (HBD-2 and HBD-3), coupled with an attenuation of regulatory cytokines. Our results further reveal that the amniotic immune environment is primarily governed by gestational age, transitioning from a Th1-predominant "alert" phase to innate-readiness preceding parturition. These findings suggest that fragments of viral genetic material within the amniotic cavity may contribute to fetal immune instruction without triggering overt inflammation, providing a foundational framework for understanding how "silent" viral-exposure during gestation influences the developmental origins of neonatal immunity.

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15.
arXiv (CS.CL) 2026-06-17

Would a Large Language Model Pay Extra for a View? Inferring Willingness to Pay from Subjective Choices

作者:
Manon Reusens↗Sofie Goethals↗Toon Calders↗David Martens↗

As Large Language Models (LLMs) are increasingly deployed in applications such as travel assistance and purchasing support, they are often required to make subjective choices on behalf of users in settings where no objectively correct answer exists. We study LLM decision-making in a travel-assistant context by presenting models with choice dilemmas and analyzing their responses using multinomial logit models to derive implied willingness to pay (WTP) estimates. These WTP values are subsequently compared to human benchmark values from the economics literature. In addition to a baseline setting, we examine how model behavior changes under more realistic conditions, including the provision of information about users' past choices and persona-based prompting. Our results show that while meaningful WTP values can be derived for larger LLMs, they also display systematic deviations at the attribute level. Additionally, they tend to overestimate human WTP overall, particularly when expensive options or business-oriented personas are introduced. Conditioning models on prior preferences for cheaper options yields valuations that are closer to human benchmarks. Overall, our findings highlight both the potential and the limitations of using LLMs for subjective decision support and underscore the importance of careful model selection, prompt design, and user representation when deploying such systems in practice.

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16.
arXiv (CS.LG) 2026-06-11

GLACIER: A Multimodal Student-Teacher Foundation Model for Molecular Property Prediction

作者:
Emily Nguyen↗Yongchan Hong↗Harsh Toshniwal↗Yan Liu↗Andreas Luttens↗

arXiv:2606.11382v1 Announce Type: new Abstract: Deep learning models facilitate the discovery of molecules with tailored properties among billions of candidate compounds. However, the computational burden to develop and deploy state-of-the-art models continuously increases, limiting their scalability. Most large-scale models are unimodal in nature and overlook the potential to leverage complementary molecular data modalities. To address these shortcomings, this paper introduces the Graph-Language Alignment for Chemical Inference and Exploration using Representations (GLACIER) model, a student-teacher framework that integrates molecular graphs, SMILES strings, and physicochemical descriptors to learn rich molecular embeddings. Our framework consists of three stages: (1) we pretrain three student encoders on 100,000 drug-like molecules: a message-passing neural network for molecular graphs, a transformer-based encoder for SMILES strings, and a multilayer perceptron for physicochemical descriptors, (2) we fuse these student modalities using a novel Finsler geometry-aware module, and (3) distill complementary knowledge from large teacher models, including MiniMol and MolFormer, into a single lightweight model via contrastive learning. We demonstrate that GLACIER is a robust framework that delivers high predictive performance and computational efficiency in complex molecular property prediction tasks. Our code is publicly available at https://github.com/eemokey/glacier.

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

Z-Plane Neural Networks: Bounded Geometric Activation Replaces ReLU and LayerNorm

作者:
Sungwoo Goo↗Hwi-yeol Yun↗Sangkeun Jung↗

arXiv:2606.15669v1 Announce Type: cross Abstract: Modern deep neural networks rely on Euclidean scalar activations (e.g., ReLU) and global normalization techniques (e.g., LayerNorm) to prevent gradient instability in deep architectures. However, these mechanisms inherently cause dead neurons, discard critical directional information, and destroy the orthogonality of feature representations. Inspired by the frequency-modulation transmission of biological axons, we propose the Z-Plane Neural Network, which maps hidden states into 2D phasor bundles on a hypersphere. We introduce a novel geometric activation function, Radial Bounding($\mathbf{x} / \max(1, \|\mathbf{x}\|_2)$), which limits the energy magnitude while preserving the phase (direction). We demonstrate mathematically that this isotropic activation maintains 1-Lipschitz continuity and prevents gradient vanishing by preserving tangential gradients. Empirically, a 100-layer Z-Plane Multi-Layer Perceptron (MLP)-entirely devoid of ReLU and LayerNorm-successfully converges on the MNIST dataset with 98.34% accuracy and absolute numerical stability, proving that bounded geometric activation alone is sufficient for stable deep learning.

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18.
arXiv (CS.CV) 2026-06-17

OpenTie: Open-vocabulary Sequential Rebar Tying System

作者:
Sai Fan↗Mingze Liu↗Haozhen Li↗Haobo Liang↗Yixing Yuan↗Yanke Wang↗

Robotic practices on the construction site emerge as an attention-attracting manner owing to their capability of tackling complex challenges, especially in the rebar-involved scenarios. Most of existing products and research are mainly focused on the collection of large amounts of data with model training demands. To fulfill this gap, we propose OpenTie, a 3D training-free rebar tying framework utilizing a RGB-to-point-cloud generation and an open-vocabulary rebar detection on the real-world test. We implement the OpenTie via a robotic arm with a binocular camera and guarantee a high accuracy by applying the prompt-based object detection method on the image filtered by our proposed post-processing procedure for the image-to-point-cloud generation framework. Our pipeline requires no training efforts and outperforms the training-based object detection, i.e., YOLO-based method, with the verification on the real-world sequential rebar tying test. The system is flexible for horizontal and vertical rebar tying tasks and holds the potential application to the real construction site with possibility of commercialization.

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

Assessing Predictive Models for Fairness Based on Movement Patterns

作者:
Francesco Lettich↗Mario A. Nascimento↗Chiara Pugliese↗Chiara Renso↗

arXiv:2605.23234v3 Announce Type: replace Abstract: Assessing the spatial fairness of predictive models involves establishing whether they are statistically penalizing (favoring) individuals associated with certain geographical locations. Literature on this topic makes the fundamental assumption that each individual is assigned to a single geographical location (e.g., place of residence). However, fairness with respect to the set of locations where one has been, i.e., their movement patterns over different regions, also matters when fairness is considered. Consequently, we argue that it is necessary to generalize the notion of spatial fairness to also include movement patterns, leading to the novel problem of assessing predictive models for fairness relative to the movements of individuals. To deal with this problem, we propose an approach that first associates the movements of individuals to certain geographic regions, considering multiple spatial partitions with different resolutions and alignments, and then employs a suitable spatial scan statistic to assess whether a predictive model is fair based on movement patterns. In the experimental evaluation, we study the performance of our approach over thousands of synthetic unfair datasets, showing that it is effective at detecting this new type of unfairness and at retrieving the set of objects treated unfairly, while localization performance exhibits a consistent multi-resolution trade-off.

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

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

作者:
Vijay Kumar↗Gautam Singh↗

arXiv:2606.16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the variational form is implemented using a Petrov-Galerkin formulation. Dirichlet boundary conditions are imposed directly, while the source terms are computed using automatic differentiation. Computational experiments on standard two-dimensional problems demonstrate that the proposed method achieves high accuracy in both the maximum and L_2 norms. These results confirm the efficiency and robustness of the Petrov-Galerkin VPINN approach in accurately capturing the multiscale features of two-dimensional SPPs.

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21.
arXiv (math.PR) 2026-06-19

Power-law hypothesis and (un)fairness of PageRank on undirected multi-type PAMs

作者:
Christian Borgs↗Florian Henning↗Remco van der Hofstad↗Nelly Litvak↗

arXiv:2606.19583v1 Announce Type: new Abstract: The preferential attachment model (PAM) describes the sequential growth of a network based on the "rich-get-richer" principle. Several versions of it have become established for modeling, e.g., citation networks, capturing a power-law degree distribution. Directed versions of the preferential attachment model where the edges are directed from the new to the old vertices have been the subject of extensive research. They have been shown to exhibit remarkable properties such as heavier tails for the limiting graph-normalized PageRank than for the in-degrees. By contrast, for the undirected version, we recently showed that PageRank has similar tails as the degree. In the present paper, we discuss the PageRank asymptotics for a multi-type version of the undirected PAM (here vertices have different colors), complementing previous results of Antunes, Bhamidi, Banerjee and Pipiras on the asymptotics of PageRank on similar directed multi-type or colored PAMs. Our studies are motivated by the aim to go beyond the rigid rule of edge orientation in directed preferential attachment models. As the main result, for the case of a finite set of colors, we show that the power-law hypothesis for PageRank is fulfilled also for the colored undirected PAM, where, by contrast to the directed case, the power-law exponent is color-dependent for some choices of the initial color distribution and the attractiveness function. For the specific case of a two-type model, we discuss implications of our results on fairness in sampling underrepresented nodes from the network.

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22.
arXiv (CS.CL) 2026-06-11

Vector Quantized Latent Concepts: A Scalable Alternative to Clustering-Based Concept Discovery

作者:
Xuemin Yu↗Ankur Garg↗Samira Ebrahimi Kahou↗Hassan Sajjad↗

Large language models (LLMs) encode rich semantic information in their hidden states, yet it remains difficult to understand what information these internal representations capture. Latent concepts extracted from hidden states offer a promising direction for interpreting LLMs, but existing clustering-based methods face a trade-off: hierarchical clustering produces coherent concepts but is limited to small datasets due to its quadratic memory cost, while K-Means scales efficiently but may yield less semantically coherent concepts. We propose Vector Quantized Latent Concept (VQLC), a discrete concept learning framework that learns a codebook of latent concepts on frozen hidden states. Across 12 dataset-model settings, VQLC stays close to K-Means in computational cost, scales better than hierarchical clustering, and remains competitive in faithfulness, with the clearest gains on decoder-only models. LLMs-based evaluation, qualitative analysis, and a Sparse Autoencoder (SAE) comparison demonstrate that the learned concepts are interpretable and task-relevant.

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23.
arXiv (CS.LG) 2026-06-15

High-Frequency Pricing at Scale for E-Commerce

作者:
Stefan Birr↗Tobias Huelden↗Mones Raslan↗Adele Gouttes↗Andreas Schmitt↗Mateusz Koren↗Johannes Stephan↗Robert Streek↗Manuel Kunz↗Tim Januschowski↗

arXiv:2606.13741v1 Announce Type: new Abstract: This paper presents the design, development, and implementation of a specialized forecast-then-optimize algorithmic pricing tool for sales campaigns in fashion e-commerce. Sales events present unique challenges for pricing including volatile demand patterns, rapid pricing decisions, and the need to balance short-term revenue with long-term profitability. We describe our approach combining daily-resolution demand forecasting using gradient-boosted trees with a multi-objective optimization framework that maximizes both long-term profit and net merchandise value for more than 5 million articles. Our solution addresses key limitations of existing weekly-granularity systems by implementing a forecast-then-optimize architecture that reduces pricing decision time from hours to minutes. We validate our approach through 23 A/B tests across 12 markets during 2023-2024 sales campaigns at Zalando, one of Europe's leading online fashion retailers. Experimental results demonstrate that the new pricing system achieves approximately 6% higher profit while maintaining equivalent performance on sales and revenue compared to the previous manual-algorithmic hybrid approach. Based on these results, the algorithm was successfully deployed to production and now handles the majority of algorithmic pricing decisions for sales campaigns at the company.

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

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise

作者:
Jiayu Zhang↗Tianyi Lin↗

arXiv:2605.18528v3 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized. The layerwise input-output structure of neural networks motivates scale-invariant optimizers, such as Muon and Scion, whose updates also support hyperparameter transfer. At the same time, stochastic gradient noise in deep learning is often far from sub-Gaussian and may exhibit heavy tails. These observations have shaped recent algorithmic principles for training neural networks, yet their joint theoretical consequences are underexplored. In particular, it remains unclear what dimension dependence is unavoidable for gradient-based methods given the problem class is defined by input-output norm and under heavy-tailed noise, and whether higher-order smoothness can accelerate training. We study these questions through nonconvex smooth stochastic optimization over $\mathbb R^{m\times n}$ equipped with general norms and under $p^\mathrm{th}$-moment heavy-tailed noise, where the goal is to achieve an $\epsilon$-stationary point in the dual norm. Our first contribution is a dimension-dependent lower bound: when $\frac{\max\{m,n\}}{(\min\{m,n\})^2}$ is large enough, any gradient-based method requires $\Omega(\min\{m, n\}\epsilon^{-\frac{3p-2}{p-1}})$ oracles for the problem class defined by the spectral norm, which is a common input-output norm. We prove that a scale-invariant Scion method with the spectral norm can achieve the matching upper bound of $O(\min\{m, n\}\epsilon^{-\frac{3p-2}{p-1}})$. To exploit higher-order smoothness, we propose a transported Scion method and improve the bound to $O(\min\{m, n\}\epsilon^{-\frac{5p-3}{2p-2}})$ when the Hessian is Lipschitz. Finally, we incorporate heuristics into our transported method and evaluate it across multiple architectures and model sizes, demonstrating its flexibility and compatibility with neural network training.

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

HLS-GPT: A Generative Pretrained Transformer (GPT) for Continental-Scale NASA Harmonized Landsat and Sentinel-2 (HLS) Reflectance Reconstruction Across All Bands on Arbitrary Dates

作者:
Junjie Li↗Hankui K. Zhang↗David P. Roy↗

Recent deep learning methods for Landsat and Sentinel-2 reflectance time series reconstruction remain limited by restricted spectral coverage, limited geographic scalability, or patch-based designs with short temporal contexts. We present HLS-GPT, a large-scale generative pretrained Transformer model for reconstructing NASA Harmonized Landsat Sentinel-2 30 m surface reflectance for all bands, any date, and any pixel location. HLS-GPT uses a hierarchical Transformer architecture to handle the different spectral band configurations of Landsat and Sentinel-2 and operates on single-pixel 12-month time series. To capture geographic and seasonal variability, the model was trained with nine years of HLS time series from more than 0.25 million training pixels across the conterminous United States. A random cropping and masking strategy extracts 12-month periods with varying start dates across epochs, masks 50% of valid observations, and trains the model to reconstruct the masked reflectance values from the remaining observations. Evaluation using more than 62,000 independent test pixels shows robust reconstruction under diverse land surface conditions, including complex crop phenology and sparse, irregular observations. Leave-one-observation-out evaluation achieved reconstruction RMSE below 0.026 for all HLS spectral bands, with relative RMSE below 35% for visible bands and below 13% for other bands. Red-edge band errors were comparable to red and near-infrared errors despite the absence of red-edge bands on Landsat. Sensitivity analyses that randomly masked 10% to 90% of test observations showed only modest degradation when 10% to 50% of observations were masked, with all-band RMSE below 0.028. Image reconstruction over nine independent 109 by 109 km CONUS HLS tiles further demonstrates that HLS-GPT outperforms two conventional methods and the NASA-IBM Prithvi model.

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