OpenRaiser/Intern-Atlas huggingface dataset:
Statistical Learning Theory in Lean 4: Empirical Processes from Scratch
Venue: arXiv cs.LG 2026
Year: 2026

We present the first comprehensive Lean 4 formalization of statistical learning theory (SLT) grounded in empirical process theory. Our end-to-end formal infrastructure implement the missing contents in latest Lean 4 Mathlib library, including a complete development of Gaussian Lipschitz concentration, the first formalization of Dudley's entropy integral theorem for sub-Gaussian processes, and an application to least-squares (sparse) regression with a sharp rate. The project was carried out using a human-AI collaborative workflow, in which humans design proof strategies and AI agents execute tactical proof construction, leading to the human-verified Lean 4 toolbox for SLT. Beyond implementation, the formalization process exposes and resolves implicit assumptions and missing details in standard SLT textbooks, enforcing a granular, line-by-line understanding of the theory. This work establishes a reusable formal foundation and opens the door for future developments in machine learning theory. The code is available at https://github.com/YuanheZ/lean-stat-learning-theory
An Optimization Method for Autoregressive Time Series Forecasting
Venue: arXiv cs.LG 2026
Year: 2026

Current time-series forecasting models are primarily based on transformer-style neural networks. These models achieve long-term forecasting mainly by scaling up the model size rather than through genuinely autoregressive (AR) rollout. From the perspective of large language model training, the traditional training process for time-series forecasting models ignores temporal causality. In this paper, we propose a novel training method for time-series forecasting that enforces two key properties: (1) AR prediction errors should increase with the forecasting horizon. Any violation of this principle is considered random guessing and is explicitly penalized in the loss function, and (2) the method enables models to concatenate short-term AR predictions for forming flexible long-term forecasts. Empirical results demonstrate that our method establishes a new state-of-the-art across multiple benchmarks, achieving an MSE reduction of more than 10% compared to iTransformer and other recent strong baselines. Furthermore, it enables short-horizon forecasting models to perform reliable long-term predictions at horizons over 7.5 times longer. Code is available at https://github.com/LizhengMathAi/AROpt
The SPARSE-Relativization Framework and Applications to Optimal Proof Systems
Venue: arXiv cs.CC 2026
Year: 2026

We investigate the following longstanding open questions raised by Krajíček and Pudlák (J. Symb. L. 1989), Sadowski (FCT 1997), Köbler and Messner (CCC 1998) and Messner (PhD 2000). Q1: Does TAUT have (p-)optimal proof systems? Q2: Does QBF have (p-)optimal proof systems? Q3: Are there arbitrarily complex sets with (p-)optimal proof systems? Recently, Egidy and Glaßer (STOC 2025) contributed to these questions by constructing oracles that show that there are no relativizable proofs for positive answers of these questions, even when assuming well-established conjectures about the separation of complexity classes. We continue this line of research by providing the same proof barrier for negative answers of these questions. For this, we introduce the SPARSE-relativization framework, which is an application of the notion of bounded relativization by Hirahara, Lu, and Ren (CCC 2023). This framework allows the construction of sparse oracles for statements such that additional useful properties (like an infinite polynomial-time hierarchy) hold. By applying the SPARSE-relativization framework, we show that the oracle construction of Egidy and Glaßer also yields the following new oracle. O1: No set in PSPACE\NP has optimal proof systems, $\mathrm{NP} \subsetneq \mathrm{PH} \subsetneq \mathrm{PSPACE}$, and PH collapses We use techniques of Cook and Krajíček (J. Symb. L. 2007) and Beyersdorff, Köbler, and Müller (Inf. Comp. 2011) and apply our SPARSE-relativization framework to obtain the following new oracle. O2: All sets in PSPACE have p-optimal proof systems, there are arbitrarily complex sets with p-optimal proof systems, and PH is infinite Together with previous results, our oracles show that questions Q1 and Q2 are independent of an infinite or collapsing polynomial-time hierarchy.
TTT-Parkour: Rapid Test-Time Training for Perceptive Robot Parkour
Venue: arXiv cs.RO 2026
Year: 2026

Achieving highly dynamic humanoid parkour on unseen, complex terrains remains a challenge in robotics. Although general locomotion policies demonstrate capabilities across broad terrain distributions, they often struggle with arbitrary and highly challenging environments. To overcome this limitation, we propose a real-to-sim-to-real framework that leverages rapid test-time training (TTT) on novel terrains, significantly enhancing the robot's capability to traverse extremely difficult geometries. We adopt a two-stage end-to-end learning paradigm: a policy is first pre-trained on diverse procedurally generated terrains, followed by rapid fine-tuning on high-fidelity meshes reconstructed from real-world captures. Specifically, we develop a feed-forward, efficient, and high-fidelity geometry reconstruction pipeline using RGB-D inputs, ensuring both speed and quality during test-time training. We demonstrate that TTT-Parkour empowers humanoid robots to master complex obstacles, including wedges, stakes, boxes, trapezoids, and narrow beams. The whole pipeline of capturing, reconstructing, and test-time training requires less than 10 minutes on most tested terrains. Extensive experiments show that the policy after test-time training exhibits robust zero-shot sim-to-real transfer capability.
LCLs Beyond Bounded Degrees
Venue: arXiv cs.DC 2026
Year: 2026

The study of Locally Checkable Labelings (LCLs) has led to a remarkably precise characterization of the distributed time complexities that can occur on bounded-degree trees. A central feature of this complexity landscape is the existence of gap results, which rule out large ranges of intermediate complexities. While it was initially hoped that these gaps might extend to more general graph classes, this has turned out not to be the case. In this work, we investigate a different direction: we remain in the class of trees, but allow arbitrarily large degrees. We focus on the \emph{polynomial regime} ($Θ(n^{1/k} \mid k \in \mathbb{N})$) and show that whether polynomial gap results persist in the unbounded-degree setting depends on how LCLs are generalized beyond bounded degrees. There already exists a complex construction that shows that the polynomial gaps also vanish for LCLs on unbounded degree trees. Rather than stopping at this negative result, we give a much simpler set of problems that already contradicts the existence of any polynomial gaps. The insight obtained from this cleaner construction is that for gap results to exist, we cannot allow problems to distinguish infinitely many cases. This guides us to a natural class of problems for which polynomial gap results can still be recovered. We introduce \emph{Locally Finite Labelings} (LFLs), which formalize the intuition that \emph{every node must fall into one of finitely many local cases}. Our main result shows that this restriction is sufficient to restore the polynomial gaps: for any LFL $Π$ on trees with unbounded degrees, the deterministic LOCAL complexity of $Π$ is either - $Θ(n^{1/k})$ for some integer $k \geq 1$, or - $O(\log n)$. Moreover, which case applies, and the corresponding value of $k$, can be determined solely from the description of $Π$.
NAB: Neural Adaptive Binning for Sparse-View CT reconstruction
Venue: arXiv cs.CV 2026
Year: 2026

Computed Tomography (CT) plays a vital role in inspecting the internal structures of industrial objects. Furthermore, achieving high-quality CT reconstruction from sparse views is essential for reducing production costs. While classic implicit neural networks have shown promising results for sparse reconstruction, they are unable to leverage shape priors of objects. Motivated by the observation that numerous industrial objects exhibit rectangular structures, we propose a novel Neural Adaptive Binning (NAB) method that effectively integrates rectangular priors into the reconstruction process. Specifically, our approach first maps coordinate space into a binned vector space. This mapping relies on an innovative binning mechanism based on differences between shifted hyperbolic tangent functions, with our extension enabling rotations around the input-plane normal vector. The resulting representations are then processed by a neural network to predict CT attenuation coefficients. This design enables end-to-end optimization of the encoding parameters -- including position, size, steepness, and rotation -- via gradient flow from the projection data, thus enhancing reconstruction accuracy. By adjusting the smoothness of the binning function, NAB can generalize to objects with more complex geometries. This research provides a new perspective on integrating shape priors into neural network-based reconstruction. Extensive experiments demonstrate that NAB achieves superior performance on two industrial datasets. It also maintains robust on medical datasets when the binning function is extended to more general expression. The code is available at https://github.com/Wangduo-Xie/NAB_CT_reconstruction.
SWE-Universe: Scale Real-World Verifiable Environments to Millions
Venue: arXiv cs.SE 2026
Year: 2026

We propose SWE-Universe, a scalable and efficient framework for automatically constructing real-world software engineering (SWE) verifiable environments from GitHub pull requests (PRs). To overcome the prevalent challenges of automatic building, such as low production yield, weak verifiers, and prohibitive cost, our framework utilizes a building agent powered by an efficient custom-trained model. This agent employs iterative self-verification and in-loop hacking detection to ensure the reliable generation of high-fidelity, verifiable tasks. Using this method, we scale the number of real-world multilingual SWE environments to a million scale (807,693). We demonstrate the profound value of our environments through large-scale agentic mid-training and reinforcement learning. Finally, we applied this technique to Qwen3-Max-Thinking and achieved a score of 75.3% on SWE-Bench Verified. Our work provides both a critical resource and a robust methodology to advance the next generation of coding agents.
ReasonCACHE: Teaching LLMs To Reason Without Weight Updates
Venue: arXiv cs.LG 2026
Year: 2026

Can Large language models (LLMs) learn to reason without any weight update and only through in-context learning (ICL)? ICL is strikingly sample-efficient, often learning from only a handful of demonstrations, but complex reasoning tasks typically demand many training examples to learn from. However, naively scaling ICL by adding more demonstrations breaks down at this scale: attention costs grow quadratically, performance saturates or degrades with longer contexts, and the approach remains a shallow form of learning. Due to these limitations, practitioners predominantly rely on in-weight learning (IWL) to induce reasoning. In this work, we show that by using Prefix Tuning, LLMs can learn to reason without overloading the context window and without any weight updates. We introduce $\textbf{ReasonCACHE}$, an instantiation of this mechanism that distills demonstrations into a fixed key-value cache. Empirically, across challenging reasoning benchmarks, including GPQA-Diamond, ReasonCACHE outperforms standard ICL and matches or surpasses IWL approaches. Further, it achieves this all while being more efficient across three key axes: data, inference cost, and trainable parameters. We also theoretically prove that ReasonCACHE can be strictly more expressive than low-rank weight update since the latter ties expressivity to input rank, whereas ReasonCACHE bypasses this constraint by directly injecting key-values into the attention mechanism. Together, our findings identify ReasonCACHE as a middle path between in-context and in-weight learning, providing a scalable algorithm for learning reasoning skills beyond the context window without modifying parameters. Our project page: https://reasoncache.github.io/
Uncertainty-Aware Image Classification In Biomedical Imaging Using Spectral-normalized Neural Gaussian Processes
Venue: arXiv cs.CV 2026
Year: 2026

Accurate histopathologic interpretation is key for clinical decision-making; however, current deep learning models for digital pathology are often overconfident and poorly calibrated in out-of-distribution (OOD) settings, which limit trust and clinical adoption. Safety-critical medical imaging workflows benefit from intrinsic uncertainty-aware properties that can accurately reject OOD input. We implement the Spectral-normalized Neural Gaussian Process (SNGP), a set of lightweight modifications that apply spectral normalization and replace the final dense layer with a Gaussian process layer to improve single-model uncertainty estimation and OOD detection. We evaluate SNGP vs. deterministic and MonteCarlo dropout on six datasets across three biomedical classification tasks: white blood cells, amyloid plaques, and colorectal histopathology. SNGP has comparable in-distribution performance while significantly improving uncertainty estimation and OOD detection. Thus, SNGP or related models offer a useful framework for uncertainty-aware classification in digital pathology, supporting safe deployment and building trust with pathologists.
The hybrid confirmation tree: A robust strategy for hybrid intelligence
Venue: arXiv cs.HC 2026
Year: 2026

Combining human and artificial intelligence (AI) is a potentially powerful approach to boost decision accuracy. However, few such approaches exist that effectively integrate both types of intelligence while maintaining human agency. Here, we introduce and evaluate the hybrid confirmation tree, a simple aggregation strategy that compares the independent decisions of both a human and AI, with disagreements triggering a second human tiebreaker. Through analytical derivations, we show that the hybrid confirmation tree can match and exceed the accuracy of a three-person human majority vote while requiring fewer human inputs, particularly when AI accuracy is comparable to or exceeds human accuracy. We analytically demonstrate that the hybrid confirmation tree's ability to achieve complementarity -- outperforming individual humans, AI, and the majority vote -- is maximized when human and AI accuracies are similar and their decisions are not overly correlated. Empirical reanalysis of six real-world datasets (covering skin cancer diagnosis, deepfake detection, geopolitical forecasting, and criminal rearrest) validates these findings, showing that the hybrid confirmation tree improves accuracy over the majority vote by up to 10 percentage points while reducing the cost of decision making by 28--44$\%$. Furthermore, the hybrid confirmation tree provides greater flexibility in navigating true and false positive trade-offs compared to fixed human-only heuristics like hierarchies and polyarchies. The hybrid confirmation tree emerges as a practical, efficient, and robust strategy for hybrid collective intelligence that maintains human agency.
An Empirical Study on Noisy Data and LLM Pretraining Loss Divergence
Venue: arXiv cs.LG 2026
Year: 2026

Large-scale pretraining datasets drive the success of large language models (LLMs). However, these web-scale corpora inevitably contain large amounts of noisy data due to unregulated web content or randomness inherent in data. Although LLM pretrainers often speculate that such noise contributes to instabilities in large-scale LLM pretraining and, in the worst cases, loss divergence, this phenomenon remains poorly understood.In this work, we present a systematic empirical study of whether noisy data causes LLM pretraining divergences and how it does so. By injecting controlled synthetic uniformly random noise into otherwise clean datasets, we analyze training dynamics across model sizes ranging from 480M to 5.2B parameters. We show that noisy data indeed induces training loss divergence, and that the probability of divergence depends strongly on the noise type, amount of noise, and model scale. We further find that noise-induced divergences exhibit activation patterns distinct from those caused by high learning rates, and we provide diagnostics that differentiate these two failure modes. Together, these results provide a large-scale, controlled characterization of how noisy data affects loss divergence in LLM pretraining.
Trust Region Continual Learning as an Implicit Meta-Learner
Venue: arXiv cs.LG 2026
Year: 2026

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: \emph{trust region continual learning} that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly \emph{re-converges} to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.
SafeGround: Know When to Trust GUI Grounding Models via Uncertainty Calibration
Venue: arXiv cs.AI 2026
Year: 2026

Graphical User Interface (GUI) grounding aims to translate natural language instructions into executable screen coordinates, enabling automated GUI interaction. Nevertheless, incorrect grounding can result in costly, hard-to-reverse actions (e.g., erroneous payment approvals), raising concerns about model reliability. In this paper, we introduce SafeGround, an uncertainty-aware framework for GUI grounding models that enables risk-aware predictions through calibrations before testing. SafeGround leverages a distribution-aware uncertainty quantification method to capture the spatial dispersion of stochastic samples from outputs of any given model. Then, through the calibration process, SafeGround derives a test-time decision threshold with statistically guaranteed false discovery rate (FDR) control. We apply SafeGround on multiple GUI grounding models for the challenging ScreenSpot-Pro benchmark. Experimental results show that our uncertainty measure consistently outperforms existing baselines in distinguishing correct from incorrect predictions, while the calibrated threshold reliably enables rigorous risk control and potentials of substantial system-level accuracy improvements. Across multiple GUI grounding models, SafeGround improves system-level accuracy by up to 5.38% percentage points over Gemini-only inference.
Energy-Efficient Neuromorphic Computing for Edge AI: A Framework with Adaptive Spiking Neural Networks and Hardware-Aware Optimization
Venue: arXiv cs.NE 2026
Year: 2026

Edge AI applications increasingly require ultra-low-power, low-latency inference. Neuromorphic computing based on event-driven spiking neural networks (SNNs) offers an attractive path, but practical deployment on resource-constrained devices is limited by training difficulty, hardware-mapping overheads, and sensitivity to temporal dynamics. We present NeuEdge, a framework that combines adaptive SNN models with hardware-aware optimization for edge deployment. NeuEdge uses a temporal coding scheme that blends rate and spike-timing patterns to reduce spike activity while preserving accuracy, and a hardware-aware training procedure that co-optimizes network structure and on-chip placement to improve utilization on neuromorphic processors. An adaptive threshold mechanism adjusts neuron excitability from input statistics, reducing energy consumption without degrading performance. Across standard vision and audio benchmarks, NeuEdge achieves 91-96% accuracy with up to 2.3 ms inference latency on edge hardware and an estimated 847 GOp/s/W energy efficiency. A case study on an autonomous-drone workload shows up to 312x energy savings relative to conventional deep neural networks while maintaining real-time operation.
Drift-Bench: Diagnosing Cooperative Breakdowns in LLM Agents under Input Faults via Multi-Turn Interaction
Venue: arXiv cs.AI 2026
Year: 2026

As Large Language Models transition to autonomous agents, user inputs frequently violate cooperative assumptions (e.g., implicit intent, missing parameters, false presuppositions, or ambiguous expressions), creating execution risks that text-only evaluations do not capture. Existing benchmarks typically assume well-specified instructions or restrict evaluation to text-only, single-turn clarification, and thus do not measure multi-turn disambiguation under grounded execution risk. We introduce \textbf{Drift-Bench}, the first diagnostic benchmark that evaluates agentic pragmatics under input faults through multi-turn clarification across state-oriented and service-oriented execution environments. Grounded in classical theories of communication, \textbf{Drift-Bench} provides a unified taxonomy of cooperative breakdowns and employs a persona-driven user simulator with the \textbf{Rise} evaluation protocol. Experiments show substantial performance drops under these faults, with clarification effectiveness varying across user personas and fault types. \MethodName bridges clarification research and agent safety evaluation, enabling systematic diagnosis of failures that can lead to unsafe executions.
Conflict-Aware Client Selection for Multi-Server Federated Learning
Venue: arXiv cs.LG 2026
Year: 2026

Federated learning (FL) has emerged as a promising distributed machine learning (ML) that enables collaborative model training across clients without exposing raw data, thereby preserving user privacy and reducing communication costs. Despite these benefits, traditional single-server FL suffers from high communication latency due to the aggregation of models from a large number of clients. While multi-server FL distributes workloads across edge servers, overlapping client coverage and uncoordinated selection often lead to resource contention, causing bandwidth conflicts and training failures. To address these limitations, we propose a decentralized reinforcement learning with conflict risk prediction, named RL CRP, to optimize client selection in multi-server FL systems. Specifically, each server estimates the likelihood of client selection conflicts using a categorical hidden Markov model based on its sparse historical client selection sequence. Then, a fairness-aware reward mechanism is incorporated to promote long-term client participation for minimizing training latency and resource contention. Extensive experiments demonstrate that the proposed RL-CRP framework effectively reduces inter-server conflicts and significantly improves training efficiency in terms of convergence speed and communication cost.