Sequential Scaling

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11 papers in the last four weeks, up 120% on the four weeks before. 0.1% of all new papers.

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Latest papers 74

Oct 1, 2026cs.LG

In-context Learning of Single-index Targets: Comparing Kernel and Feature Learners

In-context learning (ICL) enables a pretrained model to infer a task from demonstrations without updating its parameters. While much of the existing theory focuses on linear target functions, in this paper we study nonlinear cases by comparing two one-layer attention architectures on the same family of single-index tasks. A kernel learner first maps inputs through a fixed nonlinear feature map and then applies linear attention, whereas a feature learner applies attention to the original input, followed by a learned nonlinear readout. We derive predictions for their memorization and generalization errors using the replica method, retaining the effects of pretraining size, task-pool diversity, and training and inference context lengths. The resulting predictions closely match numerical experiments across a broad range of regimes. Our analysis yields phase diagrams that characterize when each architecture is advantageous as the amount of pretraining data, task diversity, and context lengths vary. We further identify qualitatively different context-length scalings for the two learners. Together, these results clarify how architectural choices interact with the dataset and govern nonlinear in-context learning.

Haotian Gu, Yizhou Xu, Lenka Zdeborová

Statistical Physics of Computation Laboratory, École Polytechnique Fédérale de Lausanne (EPFL) · University of Chinese Academy of Sciences · Information, Learning and Physics Laboratory, École Polytechnique Fédérale de Lausanne (EPFL)

In-Context Learning Linear Attention Memorization Sequential Scaling

Oct 1, 2026cs.LG

Looping Beyond Twice: A Scalable Recipe for Looped Mixture-of-Experts

Looped Transformers introduce recurrent depth as a new scaling axis for LLMs: by repeatedly applying shared Transformer blocks, they increase effective depth without increasing parameter count. However, the benefits of looping remain unclear for large MoE LLMs under FLOPs-matched comparisons. The main reason is that the gains from additional iterations diminish quickly and can even turn into degradation, so the extra FLOPs spent on looping yield little substantial improvement. Consequently, prior work typically settles on two loops. We identify two main obstacles to scaling looped MoE. First, looping inherits and amplifies the curse of depth: hidden-state variance grows with each iteration as residual updates accumulate, which destabilizes deep recurrence and causes representations to drift. Second, looped MoE suffers from expert selection collapse: routers repeatedly select the same experts across loops, so extra iterations add computation without adding computational diversity. Guided by this diagnosis, we propose LOOM, built on a single principle: each loop should contribute new computation while keeping the recurrent state stable. LOOM stabilizes recurrence by scaling residual updates to bound variance growth and re-injecting the input embedding at every loop, and diversifies it through per-loop routers that engage different experts and a Looping Residual that carries earlier outputs forward. Experiments across 100M-1.7B models show stable scaling to 9-12 loops. Under near-iso-FLOP, the 700M model performs best at 5 loops, reducing perplexity from 18.36 to 16.54 and improving average zero-shot accuracy from 38.84% to 39.53% over the non-looped baseline. Without FLOP matching, the 1.7B model trained on 60B tokens peaks at 9 loops, reducing perplexity from 9.62 to 7.77 and improving average zero-shot accuracy from 42.4% to 47.7%. Code is available https://github.com/hed-ucas/LOOM.

Di He, Pengxiang Li, Da Chang +3

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences · Peng Cheng Laboratory · University of Chinese Academy of Sciences +5

Mixture-Of-Experts Large Language Models Mixture-Of-Experts Transformer Architectures Hidden States Sequential Scaling Recipe

Oct 1, 2026cs.LG

Does Scaling Reinforcement Learning Really Require More Training?

Scaling reasoning typically spends more compute on reinforcement learning (RL) or on inference. We show that a completed RL training history can yield policies stronger than the checkpoints visited by its optimizer. We call this policy-space scaling: expanding the deployable policy set accessible from a fixed RL history, without extending training or increasing per-query inference computation. We instantiate it with SURGE (Scaling Up RL Gradient-free via Eigenspace fusion). SURGE combines two checkpoints from the same RL run: a high-accuracy anchor and a competitive donor that generates shorter responses. It expresses both checkpoints as changes from their shared initialization, then spectrally decomposes the anchor's update to retain its dominant component and incorporate the donor's complementary component. With a fixed target for how much of the anchor update to retain, SURGE determines the block size from the weights without testing candidate policies. We evaluate two 1.5B mathematical-reasoning histories, DeepSeek and Nemotron, and one 7B coding history, OLMo. SURGE improves benchmark-average accuracy over both input checkpoints while using fewer reasoning tokens than the anchor. It reaches 54.17% on DeepSeek AIME24 against a measured native maximum of 50.83%, and 83.7% on OLMo HumanEval+ against 82.8%. These gains exceed the observed training curves. Geometric controls support the importance of RL-update structure beyond weight displacement or token reduction alone. Each constructed model runs as a single policy. Our findings identify stored RL history as a reusable scaling resource: the capability available from a training run need not end at its best checkpoint.

Bangji Yang, Jiajun Fan, Hongba Ma +2

University of Illinois at Urbana-Champaign · Tsinghua University

Offline Reinforcement Learning Sequential Scaling Scaling Intermediate Checkpoints Mathematical Reasoning

Oct 1, 2026cs.CV

Overcoming Kernel Redundancy for Scaling Logic Gate Networks

Differentiable logic gate networks, which operate using only logic gates, have recently attracted attention as an efficient alternative to conventional neural networks. However, despite their efficiency, the scaling behavior of logic gate networks remains underexplored. By contrast, scaling model capacity is a central design principle in deep neural networks and typically leads to improved performance. This discrepancy raises a key question: Can similar scaling benefits also be achieved in logic gate networks? In this work, we focus on width as a primary scaling axis and conduct a systematic analysis of its behavior in logic gate networks. We observe that naive width scaling often introduces redundancy among logic kernels, limiting the effective use of additional kernels and leading to performance saturation. To address this limitation, we propose a dynamic logic kernel framework that reorganizes kernel utilization by promoting specialization across kernel groups. This enables the network to better utilize increased width via input-dependent kernel routing, while ensuring that both routing and computation are implemented entirely with gate-level Boolean operations at inference time. We further find that kernel redundancy is most pronounced at the first gate level, motivating an early-stage dynamic logic kernel strategy that concentrates adaptation at this level. Experimental results demonstrate that our approach improves kernel utilization and increases kernel diversity, leading to higher accuracy with improved parameter efficiency.

Sejin Park, Hongjae Lee, Changwoo Han +1

Department of Electrical Engineering Korea University

Differentiable Logic Gate Networks Sequential Scaling Capacity Scaling Redundancy

Sep 30, 2026cs.CL

Mid-Harness: Scaling Actions Between Model and Harness for Terminal Agents

Terminal agents act through stochastic model generations, yet the ability to generate a useful action does not ensure its reliable execution. A poor command (e.g., wrong package install) can change the environment in ways that hinder subsequent progress, even when the model could generate a better alternative. We investigate whether allocating test-time compute at the model-harness boundary can improve action reliability and trajectory success, and what makes this allocation effective. To study these questions, we introduce Mid-Harness, which samples and verifies candidate actions before forwarding one for execution, while keeping the generator and harness unchanged. With a TMAX-9B generator, more action sampling yields little benefit under weak verification, whereas a capable verifier can exploit useful alternatives from the same generator. On TerminalBench-Lite, a GPT-5.6 Sol verifier raises Pass@1 from 50.00% for the base agent to 68.03% with 8 sampled actions. When the same TMAX-9B model serves as the verifier, pairwise verification performs best among the evaluated verification mechanisms. Distilling responses from the stronger verifier into TMAX-9B further improves Pass@1, while leaving the action generator unchanged. With TMAX-9B on TerminalBench-Lite, combining action and trajectory scaling reaches higher success at lower estimated token cost than generating more trajectories alone. Mid-Harness also improves performance across additional models, benchmarks, and harnesses. These findings identify action scaling as a promising target for test-time compute scaling in terminal agents.

Minki Kang, Ryo Hachiuma, Shaokun Zhang +8

NVIDIA · KAIST

Test-Time Scaling Agent Harness Sequential Scaling

Sep 30, 2026cs.LG

TRACE: Trajectory Selection for Parallel Scaling of Search Agents

Parallel search may generate a correct answer that final-answer voting fails to select. We formulate this consolidation stage as trajectory selection and introduce TRACE (Trajectory Ranking with Aggregated Cross-Rollout Evidence), a lightweight learned selector that ranks completed trajectories using the search evidence behind their answers. TRACE preserves individual query and evidence occurrences, connects rollouts through shared content or document identity, and propagates information across these relations. Each candidate answer then reads the updated states of its own trajectory, preserving retrieval provenance while incorporating evidence from related rollouts. Trained with answer-level supervision over frozen text embeddings, TRACE returns an existing answer without additional search or autoregressive aggregation. One selector per search setting transfers across rollout policies and agent backbones without agent-specific fine-tuning, improving over voting across six WebQA policies and six long-horizon dataset-backbone combinations at

K=16

. On Qwen2.5-14B Base/SFT WebQA pools, TRACE achieves 45.2/49.2% EM, compared with 43.9/48.0% for the strongest Qwen3-32B generative aggregators. On long-horizon FRAMES, GAIA, and BrowseComp, it reaches 78.6% average accuracy, exceeding majority voting by 3.1 percentage points. On Base WebQA pools, TRACE with only 8 rollouts comes within 0.4 points of majority voting over 64. TRACE also achieves at least

10\times

higher processing throughput than SolAgg, SummAgg, and AggAgent across all seven WebQA benchmarks. These results show that reusing cross-rollout search evidence provides an effective and efficient alternative to heavyweight generative aggregation for parallel search. Code is available at https://github.com/Jaasssoooonnnnn/TRACE.

Qisheng Zhou, Zhen Xiong, Qiaoyu Tan

New York University Shanghai · New York University

Search Agents Traces Trajectory Generation Sequential Scaling

Sep 30, 2026cs.LG

Towards Better Exploration in Sequential Test-Time Scaling

Test-time scaling improves language model reasoning by spending additional compute at inference. However, both classes of existing methods often fail to continue improving over long timescales. Parallel methods repeatedly sample independent answers from the model, scaling poorly on problems the model is unlikely to solve in a single attempt. In contrast, sequential methods build on previous answers to access new ideas, yet so far have not been shown to reach answers beyond those found by parallel scaling. First, we show that sequential scaling often stops improving because it becomes prematurely trapped in an attractor: a set of answers that prevents exploration of different answers once entered. Across 27 combinations of scaling methods, models, and benchmarks, we find that 53.8% of sequential scaling trajectories enter an attractor within four iterations. Second, we show that a simple model-mixing intervention helps escape attractors. This reduces the attractor hit rate by 21.2 percentage points on average, expands solution coverage beyond a compute-matched parallel baseline, and improves accuracy of recursive self-aggregation by at least 2.2 percentage points. Our results motivate refocusing long-horizon test-time scaling from parallel methods to sequential methods that improve previous answers.

Joseph Rance, Fabio Pizzati, Juil Sock +4

University of Oxford · MBZUAI · BBC R&D

Test-Time Scaling Sequential Scaling Scaling Attractors Exploration

Sep 30, 2026cs.RO

SteerQuant: Steering Quantization Error with Action-Guided Scaling in World-Action Models

World-action models (WAMs) jointly generate future world states and actions through iterative denoising, using shared weights to process heterogeneous semantic streams of video, proprioceptive, and action tokens. Quantization reduces inference cost, but comparable numerical errors in different streams can have markedly different effects on final actions, making numerical accuracy alone insufficient for reliable control. We introduce SteerQuant, a 4-bit quantization framework for WAMs that steers errors toward computations with less influence on final actions. It maps how each stream's quantization errors affect final actions and uses this map to guide shared channel scaling. Activation scaling is further calibrated for each stream and denoising step to accommodate changes in activation ranges and action impact. This adapts quantization to different stream requirements without duplicating weights or increasing bit-widths for selected streams. To reduce the extra kernel launches and memory traffic introduced by scaling, we develop Rudder, a 4-bit inference engine for WAMs that fuses scaling and output compensation into low-bit kernels. Under W4A8 and W4A4, SteerQuant maintains mean LIBERO success within 0.8 percentage points of full precision, while delivering up to

2.23\times

denoising speedup over BF16 across three WAMs with reduced peak GPU memory usage. On a real dual-arm robot, W4A8 deployment achieves a

1.35\times

end-to-end inference speedup while maintaining average task success relative to BF16.

Yunhan Wang, Haodong Wang, Zhiming Liu +7

Tongji · HKUST · HIT +1

Steering Sequential Scaling Rate Scaling

Sep 30, 2026cs.LG

Mitigating the Length-Scaling Tax with Online Distillation

Length scaling during reinforcement-learning (RL) post-training is often viewed as a sign of improved reasoning ability, especially on difficult problems, but may also make responses to already-solved problems unnecessarily verbose. We quantify this side effect as the length-scaling tax (LST): excess response length on already-solved queries without a commensurate accuracy gain. To mitigate LST, we propose Length Self-Distillation (LSD), which routes solved prompts to on-policy distillation and retains the original RL objective for unsolved prompts. LSD uses an exponential moving average of the online policy as its teacher, requiring no external model. We find that LSD achieves comparable or better performance than RL across multiple variants, while substantially curbing response-length growth on easy queries. LSD reduces LST from 19.0% to -3.7% on single-turn reasoning and from 31.4% to 13.7% on multi-turn agentic tasks, demonstrating that LSD effectively preserves concise response patterns on easy queries while supporting efficient exploration on difficult queries during RL post-training.

Xu Wan, Wenyue Xu, Shengjie Zhao +1

ByteDance Seed · Tongji University · Peking University

Sequential Scaling Symbolic Distillation

Sep 29, 2026cs.SD

Pruning for Efficiency, Paying in Fairness: Demographic Disparities in Pruned Speech-LLMs

Speech-LLMs are expensive to run, making compression important for real-world deployment. However, compressed models are usually selected using aggregate word error rate (WER), which can hide how pruning affects different demographic groups. In this work, we systematically study the effect of audio encoder pruning on SLAM-ASR for different demographic groups. Using the Fair-Speech and Common Voice datasets, we found that the pruning does not affect all demographic groups equally; the gap between best- and worst-performing groups increases in fold. These disparities appear across all three encoder scales, but only the largest model initially hides them behind aggregate WER. LoRA adaptation improves WER for every group, but benefits groups already performing well more strongly and widens for certain groups. On Common Voice English, Danish, and Dutch, accent gaps persist but do not clearly widen, showing that the fairness effects of pruning vary across datasets and must be measured directly. Our findings suggest that for pruned models, deployment decisions should include per-group WER, with the worst-performing group's error rate as an explicit criterion.

Ganesh Pavan Kartikeya Bharadwaj Kolluri, Michael Kampouridis, Ravi Shekhar

School of Computer Science and Electronic Engineering, University of Essex, UK

Character Error Rate Disparities Algorithmic Fairness Sequential Scaling Efficiency Orb-Slam2

Sep 29, 2026cs.LG

Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling

Test-time compute scaling has emerged as a cornerstone of advanced machine reasoning, yet performing iterative deliberation directly within continuous latent representation spaces reveals a catastrophic pathology: the Deliberation Drift Cliff. While unconstrained recurrent latent models achieve initial reasoning gains at short horizons (K <= 4), their reasoning collapses when extrapolated to deeper thinking steps (K >= 16), dropping by 22% to 62% across standard logical benchmarks. We resolve the trilemma among expressivity, Lyapunov stability, and computational efficiency in test-time latent reasoning through a 22-round empirical and theoretical investigation. We demonstrate that strictly conservative scalar potential gradient flows suppress long-range drift (cliff 3.40%) but bottleneck peak reasoning accuracy at 32.73%, whereas unconstrained rotational flows achieve high symbolic expressivity (82.33%) but suffer a severe 36.87% drift cliff. To resolve this geometric duality, we establish Port-Hamiltonian Latent Deliberation (PH-LD) and propose the Direct-Gradient Pure-Tensor Helmholtz-Hodge Decomposition (DG-HHD). DG-HHD parameterizes the attracting flow as a tangent projection tensor network while orthogonally decoupling non-zero circulation (Hodge machine error 1.65e-17, contraction error 5.55e-17), eliminating runtime autograd dependencies to achieve 1.84x vector field and 2.09x RK45 rollout speedups. In a 15-arm symmetrical Pareto benchmark, DG-HHD achieves 58.67% peak accuracy (+25.94% absolute gain over conservative HHD) and retains 35.27% at K=32. Transferred to small language model (SLM) multi-hop causal reasoning, DG-HHD delivers monotonic compute scaling (49.33% to 51.56%) and suppresses out-of-distribution drift (cliff -0.66%). All 30 Level 0 deterministic invariants are certified.

Zeyu Jia

School of Biomedical Engineering and Technology, Tianjin Medical University, Medical School, Tianjin University

Test-Time Scaling Efficient Latent Reasoning Test Time Deliberation Sequential Scaling Scaling

Sep 29, 2026cs.LG

Longer Records, Broader Invariance: The Hidden Scaling Problem in Longitudinal Contrastive Learning

Longitudinal data are valuable because people change. Yet the objectives used to learn from these data can inadvertently erase that change. In person-level contrastive learning, observations from the same person are treated as positives; as records grow, those positives can span increasingly distant---and increasingly different---behavioral states. More history can therefore produce not only more data, but broader invariance. We show that this distinction is fundamental. We separate \emph{record span}, how much history the learner sees, from \emph{supervision span}, how far across that history positive-pair supervision reaches. Across in-home sensing records spanning up to 2.7 years, broader supervision systematically suppresses recoverable changing-state information, even when the available history is held fixed. At the broadest span, less than 10% of the information recoverable from an untrained encoder remains. Yet keeping positives local is not sufficient: as records grow, even distant states that are never paired become increasingly similar. Explicitly contrasting other observations from the same person reverses this loss without shortening the record, revealing a second route by which longitudinal scale can broaden invariance. Finally, we prospectively reproduce the supervision-span effect in 199 GLOBEM participants. Longitudinal scale therefore presents a choice: more history need not mean more invariance. By controlling what is held invariant as records grow, we can preserve the change that made the longitudinal data valuable in the first place.

Rameen Mahmood, Xuhai "Orson" Xu, Zachary Beattie +2

New York University · Columbia University · Oregon Health & Science University

Longitudinal Data Contrastive Learning Equivariant Learning Sequential Scaling

Sep 28, 2026cs.AI

From Search to Research: Exploring Search Scaling in Autonomous Quantitative Factor Mining

Inference scaling has been shown to improve large language model (LLM) performance, and this principle naturally extends to autonomous LLM agents through increased search budgets, which we refer to as search scaling. Although prior work has characterized the mechanisms, scaling behavior, and performance limits of LLM inference scaling, much less is known about these questions in autonomous research. Therefore, we investigate how search scaling affects research performance and what mechanisms drive these gains using 50 quantitative factor-mining tasks grounded in financial research reports. Each task requires an agent to carry out an end-to-end research loop, from interpreting a hypothesis and implementing it in code to evaluating and iteratively refining the resulting factor. Across nine models, we examine how model capability, search depth, and search organization shape factor quality by tracing performance across varying budgets, transferring intermediate research states between models, and comparing different search strategies. We find that (1) initial performance is more strongly associated with model capability, while deeper search can narrow cross-model gaps; (2) model grafting shows that the early research state materially shapes final performance; and (3) parallel search outperforms sequential search under the same iteration budget, consistent with benefits from broader coverage of the search space. Further trajectory analysis shows that higher-performing models more effectively diagnose failures, revise search directions, and preserve the intended economic hypothesis when selecting candidates. These findings suggest that future progress in autonomous research will require stronger models together with adaptive policies for deploying test-time computation throughout the research process.

Kangcheng Deng, Hui Cai, Jiacheng Lu +6

StepFun · Shanghai Jiao Tong University · University of California, Los Angeles +1

Research Automation Sequential Scaling LLM Inference Optimization Factor

Sep 27, 2026cs.CL

DISCO: Distributed Long Context Scaling with Grounding-Reasoning Disaggregation

While Large Language Models (LLMs) advertise million-token context windows, reasoning quality often collapses as inputs grow -- a phenomenon termed context rot. This failure stems from a structural entanglement in monolithic architectures, where the massive search burden of contextual grounding exhausts the representational capacity needed for complex reasoning. To resolve this, we propose Grounding-Reasoning Disaggregation via DIStributed long COntext scaling (DISCO). Inspired by distributed computing frameworks like Apache Spark, DISCO partitions long context across a fleet of Worker LLMs dedicated exclusively to parallel, localized grounding. A central Driver LLM, trained via Reinforcement Learning (GRPO) to optimize planning, orchestrates execution by dynamically mapping queries into atomic extraction tasks and reducing the gathered evidence to synthesize a final answer. By isolating reasoning from raw context noise, DISCO effectively eliminates context rot. On RULER-QA (1M tokens), it maintains 78.4% accuracy where standard baselines collapse. Furthermore, it outperforms full-context models by up to 9.8 points on LongBench v2 and matches frontier models like Gemini-3-Pro-Preview while reducing inference costs by over 80%, establishing a highly efficient paradigm for robust long-context inference.

Guanzheng Chen, Viet Dac Lai, Subhojyoti Mukherjee +5

National University of Singapore · Adobe Research

Efficient Long-Context Inference LLM Reasoning Strategies Sequential Scaling

Sep 23, 2026cs.LG

KITE: KV-Invariant Transformer Expansion for Efficient Agentic LLM Scaling

Scaling a language model is not only a question of final quality: the architectural choice determines how much computation is spent during training, prompt processing, and autoregressive decoding to achieve certain model quality. An ideal model architecture should lower all above computation costs to facilitate scaling to a larger model, while ensure the larger model indeed outperforms smaller baselines. We introduce KV-Invariant Transformer Expansion (KITE), a scaling paradigm that achieves this goal. It trains the model from a smaller size to a larger size (i.e., saving training costs via upcycling), while places newly added parameters in regions that do not affect attention KV. Consequently, during inference, prefilling KV only relies on the smaller part of the model, so the inference costs are saved. As a concrete instantiation, we present Step Scale Transformer (SST), a two-tower decoder in which one tower produces KV and the other reads them. At comparable cumulative training compute, SST, a 67B MoE model with 2.15B active body parameters per decode token, achieves lower training loss than 47B and 63B MoE Transformers with 1.48B and 2.02B active body parameters, respectively, while reducing estimated inference cost by 6.7% and 31.6%.

Zhiheng Hu, Yixun Wei, Jian Zhou +8

StepFun

LLM Inference Optimization Sequential Scaling Scaling Inference Cost

Sep 23, 2026cs.RO

NaviScale: Generating Large-Scale Semantic Map Datasets for Object Navigation

Embodied navigation requires spatial representations that generalize across unseen environments, yet collecting large amounts of annotated data from real 3D environments is difficult. We propose NaviScale for semantic-map-based object navigation (ObjectNav), whose predictor can be trained on pairs of partial and complete semantic maps without reconstructing a complete 3D environment for every training sample. The framework generates large-scale semantic map training data by composing floorplans of real homes with room-level semantic and obstacle maps extracted from MP3D and HM3DSem. NaviScale increases data diversity in two ways: inter-room scaling increases floorplan-level structural diversity, while intra-room scaling fills each fixed floorplan with different combinations of room maps matched by room category. Visibility through Ray Casting (VisRC) converts the composed maps into partial observations that account for field of view, sensing range, and occlusion. The resulting dataset contains 192,000 semantic maps generated from 24,000 floorplans associated with 12,794 properties. With 300k training iterations and the training and inference settings described in this paper, the system reaches 64.3% SR and 34.8% SPL on HM3D, together with 43.1% SR and 16.8% SPL on MP3D, without changing the prediction architecture. Additional experiments evaluate the quality of the composed maps, the effects of semantic-segmentation errors, and deployment on a physical robot.

Chuanlin Lan, Yanwei Zheng, Yuxi Jing +6

School of Computer Science and Technology, Shandong University, Qingdao, China

Object Goal Navigation Navigation Sequential Scaling

Sep 21, 2026cs.LG

Taking a Second Look: Correcting Sea Ice Forecasts with Sparse Observations

Sea ice forecasts are issued several days ahead, allowing errors to accumulate while new, often sparse sea ice concentration (SIC) observations become available. We find that fixed-propagation errors concentrate near structured, high-gradient ice edges, whereas homogeneous interiors require limited propagation, suggesting that propagation distance should be state dependent. We therefore introduce ECHO (Evidence-guided Correction with Heterogeneous prOpagation), where ECHO-Scale adapts propagation distance while preserving correction geometry, and ECHO-Delta learns a bounded residual around fixed propagation. Across all 96 standard evaluation settings spanning diverse priors, observation times, sparsity levels, geometries, and noise conditions, both outperform fixed propagation. ECHO-Delta achieves the best average accuracy, while ECHO-Scale is more robust to geometry shifts. Code is available at https://github.com/yingtian22/TAKING-A-SECOND-LOOK.

Tianshuo Zhang, Xianglei Xing, Aowen Yang +4

College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China

Sea-Surface Temperature Data Forecast Sparsity Sequential Scaling

Sep 14, 2026cs.SD

Rethinking Procedural Audio Pre-training: Source Scaling and Objective Adaptation

Procedural audio has emerged as a viable source for transferable audio representation learning, but its design principles remain unclear.We revisit two questions: how a procedural source should be scaled, and whether training choices developed on natural audio should transfer unchanged to procedural data.Using a controlled source, we separate scale into formula-class coverage C and within-class rendering diversity I.Experiments with FDSL and AudioMAE show that these two forms of scale provide different benefits and depend on the learning formulation and downstream task. A matched AudioMAE study further shows that procedural audio favors low mask ratios (10%--25%), whereas AudioSet-28K favors 50%--75%. Shared-codebook analysis reveals lower patch diversity and stronger temporal predictability in procedural audio. These results motivate source-aware procedural pre-training, where source scaling and learning configuration are considered jointly.Code is available at https://github.com/Cross-Innovation-Lab/Formula-Bank.

Jiajun Peng, Fengrui Liu, Xinyu Liu +1

School of Data Science, University of Science and Technology of China, Hefei 230026, China · School of Computer Science and Technology, East China Normal University, Shanghai 200062, China · School of Psychology, Shanghai Jiao Tong University, Shanghai 200030, China

Neural Audio Procedural Audio Understanding Sequential Scaling

Sep 14, 2026stat.ML

Inference for Newton Methods with Accelerated Sketch-and-Project via Random Scaling

We study an online sketched Newton method that approximates the Newton direction at each step via a state-of-the-art sketching solver, called the generalized accelerated sketch-and-project solver (GAS), thereby mitigating the computational bottleneck of classical second-order methods. The GAS solver improves upon vanilla, unaccelerated sketch-and-project solvers by achieving accelerated convergence through Nesterov momentum updates, and accommodates a flexible projection metric whose proper choice further reduces computational cost. Building on this design, we establish asymptotic normality of the averaged sketched Newton iterates and characterize their limiting covariance matrix. The resulting covariance recovers that of the unaccelerated sketched Newton method under a specific choice of acceleration parameters, converges more rapidly (in the number of sketching steps) to the minimax-optimal covariance in general, and is smaller than that of the last iterate produced by the accelerated method. Finally, we strengthen these results by establishing a functional central limit theorem for the Newton iterates, which allows us to bypass explicit covariance estimation and develop an online inference procedure based on random scaling. Specifically, we construct a pivotal test statistic by appropriately rescaling the averaged iterates, so that its limiting distribution is free of any unknown parameters, enabling asymptotically valid online inference. Numerical experiments demonstrate superior performance of the proposed inference procedure.

Xinchen Du, Elizaveta Rebrova, Micha\l Dereziński +1

School of Industrial and Systems Engineering, Georgia Institute of Technology · Department of Operations Research and Financial Engineering, Princeton University · Computer Science and Engineering, University of Michigan

Newton Covariance Sequential Scaling Sketches

Sep 7, 2026cs.DC

Scalability Analysis of Distributed Kolmogorov-Arnold Network Training on High-Performance Computing Systems

Kolmogorov-Arnold Networks (KANs) replace the fixed activation functions and linear weights of Multi-Layer Perceptrons (MLPs) with learnable univariate functions on network edges, offering improved interpretability and, in some settings, competitive parameter efficiency. While the approximation properties of KANs have received considerable attention, their behavior under distributed, multi-GPU training has not been systematically characterized. This paper presents an empirical scalability study of data-parallel KAN training on multi-node, multi-GPU high-performance computing (HPC) infrastructure, evaluated along four dimensions: strong scaling, weak scaling, communication overhead, and model-size scaling. Experiments were conducted on the FinisTerrae III supercomputer using up to 8 NVIDIA A100 GPUs across 4 nodes with PyTorch Distributed Data Parallel (DDP). KAN training reaches 74.7% parallel efficiency at 8 GPUs with a 5.97x speedup, consistent with conventional deep learning workloads. Weak scaling shows an initial single-to-multi-GPU throughput drop followed by strong stability. Communication overhead follows a non-monotonic pattern (1.3%-6.1%), driven primarily by All-Reduce algorithm selection and inter-node latency rather than KAN's edge-wise gradient structure. The parameter-to-memory ratio improves with model size even as training time scales unfavorably. These results indicate that operator-level and data-parallel optimizations for KAN are complementary. We provide deployment guidelines for GPU topology and model-size selection, and discuss the limitations of a synthetic-regression evaluation.

Guangneng Chen, David Garcia Selfa, Pablo Quesada Barriuso

University of Santiago de Compostela, 15782 Santiago de Compostela, Spain · Galicia Supercomputing Center (CESGA), 15705 Santiago de Compostela, Spain

Kolmogorov-Arnold Networks High-Performance Computing Scalability Sequential Scaling

Sep 3, 2026math.PR

Correlated initialization of deep residual networks

We study the large-depth behavior of residual networks whose weights are correlated across layers at initialization. Our results confirm and extend a conjecture of Marion et al. [2025], according to which correlated initializations should interpolate continuously between the Brownian stochastic differential equation arising from independent initialization and the ordinary differential equation arising from perfectly correlated initialization. When the initialization is obtained from the application of a feature function to a stationary Gaussian sequence with regularly varying correlation, we prove that there exists a unique critical scaling such that the infinite-depth limit is the solution of a Young differential equation driven by a Hermite process. Hermite processes reduce to the fractional Brownian motion if the feature function generating the initialization has Hermite rank one, which is the case for the identity function, for example. We show that the critical scaling and asymptotic limit are uniquely determined by the decay of correlations together with the Hermite rank of the feature function. Consequently, the correlation structure and Hermite rank of the initialization represent meaningful hyperparameters in the asymptotic regime. By contrast, under finite-variance iid initialization, the asymptotic driver is universally Brownian up to normalization regardless of the choice of distribution. Our proofs rely on a collection of novel results establishing a robust stability theory for Young differential equations in Banach spaces.

Felix Benning, Ivan Nourdin, Giovanni Peccati

Residual Networks Infinities Stochastic Differential Equations Sequential Scaling

Sep 1, 2026cs.IR

From Language to Behavior: Scaling Sequence Transformers for Industrial Recommendation Ranking with Rec-Native Designs

Scaling Transformers has driven large gains in language modeling, but transplanting this to behavior-sequence modeling in production ranking is challenging: recommendation differs in signal quality, where behavior sequences are noisy, temporally irregular, and sparsely supervised, and in computation asymmetry, where each request scores many candidates against one shared user history under tight latency budgets. We propose ReST, a recommendation-native Transformer scaling framework. For signal quality, it introduces a sequence encoder with dual-gated attention, rotary positional and temporal embedding, stabilized residual normalization, and training-only auxiliary objectives. For computation asymmetry, it factorizes ranking into a heavy reusable encoder and a lightweight cross decoder with projection-free KV attention and token-specific parameterization, coupling user-level shared-prefix training with shared-prefix serving for compute-once, decode-many-times ranking. Across industrial and public benchmarks, ReST achieves higher accuracy and scales more consistently along sequence length, depth, and width, where LLM-style Transformer blocks saturate. A one-week online A/B test on a production advertising platform improves online AUC by 1.31% and lifts a core revenue metric by 11.93% within a 50 ms P99 budget; ReST has since been fully deployed in production, showing that behavior-sequence scaling remains a promising, under-exploited axis for production ranking.

Jie Chen, Xiangqian Yu, Yanchao Lian +9

ByteDance

Recommendation Sequential Scaling Sequence Modeling Language Modeling

Aug 31, 2026cs.LG

HBQ: Hierarchical Scaling Block Quantization with Hardware-Efficiency-Aware Design for Accurate LLM Inference

Block Quantization (BQ) enables efficient LLM inference by quantizing both weights and activations, but its design space remains underexplored. Through hardware-accuracy design space exploration, we identify block size as a key trade-off: larger blocks improve hardware efficiency by amortizing dequantization and accumulation costs, but degrade accuracy. Motivated by this insight, we propose Hierarchical Block Quantization (HBQ), which combines large blocks with low-overhead significand (SIG) scaling for second-level quantization. SIG scaling effectively compensates for large-block quantization errors while accounting for distinct weight and activation distributions. HBQ-A achieves W4A16-level accuracy with W4A5 and lower area than NVFP4, while HBQ-E further reduces hardware cost by 17% while outperforming existing BQ methods in accuracy. We implement HBQ for weights, activations, and KV cache in a 28nm ASIC accelerator and introduce partial-sum BQ to reduce EMA energy. At comparable accuracy, HBQ achieves 2.3x/4.6x higher area/energy efficiency than state-of-the-art weight-only quantization and 1.6-3.3x lower system energy with 1.5-3x speedup over prior BQ methods. Our implementation is publicly available at: https://github.com/SeoLabCornell/HBQ.git.

Chun-Ting Chen, Dongmin Han, Hangyeol Mun +6

Cornell University New York, NY, USA · Intel Corporation Santa Clara, CA, USA · Intel Corporation Hillsboro, OR, USA

Gradient Quantization LLM Inference Optimization Sequential Scaling

Aug 31, 2026cs.LG

RSLM: Training-Free Vector Quantization for Approximate Nearest Neighbor Search

By introducing RSLM (Rotated Scaled Lloyd-Max), a family of training-free vector quantization codecs compressing embeddings to 1--4 bits per dimension, we reduce memory cost and memory bandwidth of a typical large-scale Approximate Nearest Neighbor (ANN) search system, while reducing its complexity and keeping or improving recall across multiple benchmark datasets. State-of-the-art systems filter candidates using coarse partitions, approximately score them to narrow the set, and then rescore the best with higher precision representations (often >=8 bits per dimension). Our relativized codecs can bring this down to 2--4 bits per dimension. We use the properties of the ANN system to encode residual vectors instead of full vectors, both for the approximate scoring phase and the rescoring phase. Since Maximum Inner Product Search (MIPS) is very sensitive to vector norms, we correct the

L_2

norms of quantized vectors. Our major innovation is that we correct the

L_2

norm of the final reconstructed vector rather than just the residual. Our rescaling replaces more complicated schemes, such as Anisotropic loss. The residualization scheme gives us a more favorable quality vs size trade-off than generic quantization methods. Our high-performance implementation leverages a block-wise cascaded Fast Walsh-Hadamard Transform (FWHT) with linear-like complexity, AVX SIMD-optimized codebooks, and a steganographic encoding of scaling factors for perfect cache-line alignment.

Rastislav Lenhardt, Teodora Dobos, Thomas Vecchiato +2

Google Zurich, Switzerland · Technical University of Munich Munich, Germany · University of Copenhagen Copenhagen, Denmark +1

Residual Vector Quantization Approximate Nearest-Neighbor Search Vector Database Randomized Hadamard Transforms Behavioral Embeddings Affectcodec+1

Aug 28, 2026cs.CL

Ladders in Chaos: When, How, (and Perhaps Why) Does Test-Time Scaling Improve LLM Machine Translation

Two forms of test-time scaling for Large Language Models (LLMs) have emerged as effective and widely adopted paradigms: sequential, in which later answer attempts depend on earlier ones, and parallel, such as i.i.d. sampling with reranking. In this study, we investigate their properties in translation. First, our study shows that sequential sampling has a higher performance ceiling, providing a more diverse and effective pool of samples, particularly under smaller sampling budgets. Second, we interrogate the nature of test-time scaling through a multidimensional manual analysis. Human analysis of the Best-of-N translations demonstrates that sequential sampling substantially improves translation fluency and naturalness, but can degrade accuracy when inference budgets are large. Finally, we suggest an explanation of the mechanism through which sequential scaling improves machine translation. Our controlled analysis partially attributes the success of sequential self-improvement to the model's access to a larger target-side context. Ablation experiments on sequential sampling demonstrate its robustness across different sampling temperatures, while also revealing sensitivity to context construction, suggesting directions for future improvement.

Di Wu, Sergey Troshin, Christof Monz +2

University of Amsterdam · Vrije Universiteit Amsterdam

Test-Time Scaling Machine Translation Sequential Scaling Fluency Chaos

Aug 12, 2026cs.CV

XYZFlow:Scaling Multi dimensional Shortcut Flows for Efficient Generative Modeling

High-fidelity image generation faces a trade-off between speed and quality. Diffusion models produce strong visuals but require costly iterative sampling. Existing efficient methods mainly distill pretrained models into few-step samplers, a challenging process that depends heavily on teacher-model quality. In this paper, we introduce XYZFlow, a framework that rethinks efficient generation through multidimensional scaling of flow matching. Unlike single-step mappings, XYZFlow enhances expressivity by making probability paths more identifiable and learnable through structured multidimensional conditioning. We view autoregressive modeling as implicit flow straightening, where richer context reduces trajectory ambiguity. XYZFlow realizes this idea through two orthogonal dimensions: temporal scaling, which uses non-Markovian conditioning on the full denoising history; and spatial scaling, enabled by Next Shortcut Prediction, which sequentially generates patches using preceding patches' denoising trajectories as priors. Experiments show that XYZFlow achieves state-of-the-art performance, with 7.2-8.5X teacher speedups and competitive FID, while Next Shortcut Prediction delivers superior quality-latency trade-offs over model scaling or step reduction.

Jinxiu Liu, Xuanming Liu, Kangfu Mei +2

1CUHK · 2Westlake University · 3Johns Hopkins University

Generative Flow Networks Diffusion Models Generative Models Sequential Scaling Scaling

Aug 10, 2026cs.LG

Online Learning of Scale Parameters in Score-Driven Filters

A score-driven filter multiplies its scaled log-likelihood score by a scale parameter. We call this coefficient the gain and learn it online. Given the current state and realised scaled score, each admissible gain selects a reachable next state and predictive density. A scalar gain moves along a line; diagonal gains control coordinatewise transmission and may change direction. We evaluate gain selection using a one-step predictive Kullback-Leibler objective. In the scalar unscaled case, the negative consecutive-score product is a stochastic gradient; the positive product used in accelerated recursions is a descent direction. Positive scalar score scaling changes only the effective learning rate. Strictly increasing, continuously differentiable gain links with positive derivative induce mirror-descent geometry, while persistence adds a Bregman pull towards a reference gain. Under convexity, compactness, integrability, and schedule conditions, projected and discounted mirror updates satisfy dynamic-regret bounds relative to time-varying, current-information comparators. Simulations isolate score scaling, link geometry, persistence, and coordinatewise gains. Across twelve equity indices, the bounded discounted-logistic gain records a lower out-of-sample mean negative log score than the constant gain in eleven markets, although market-level evidence is mixed. It also avoids the extreme transients of the numerically capped exponential-link benchmark.

Fabrizio Lillo, Giulia Livieri, Gianluca Palmari

Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italy · Department of Statistics, London School of Economics and Political Science, Columbia House, 69 Aldwych, London, United Kingdom

Mirror Descent Sequential Scaling Monotonicity

Aug 8, 2026cs.RO

Spatiotemporal Context-dependent Personalized Movement Compensation in Delayed Telemanipulation

Communication delay remains a central challenge in telerobotics, where it disrupts visuomotor coordination and reduces task precision. Motion scaling is an effective countermeasure to delay-induced overshoot, yet typical deployments rely on uniform gains that neglect individual and contextual variability. We propose a human-centered method that fits personalized delay-, direction-, and distance-specific scaling parameters for each participant. We conducted experiments with twenty participants who performed delayed reaching tasks in a virtual simulator. Scaling gains were computed to minimize mean overshoot in simulation in each combination of experimental conditions. Evaluation was done in simulation and on a telesurgical robot to evaluate assistance benefits. Performance was assessed across multiple delays, distances, and movement directions using overshoot, endpoint error, trajectory smoothness, economy of motion, and a composite error-time metric. Motion scaling consistently improved performance relative to unassisted trials, yielding up to 20-25% performance gains in key metrics. Effects were most pronounced at longer delays. Personalization demonstrated additional accuracy benefits for inward reaching at a short distance under moderate delay. The results highlight the potential of personalized scaling as a foundation for more adaptive frameworks that integrate contextual information to improve the safety and precision of teleoperated procedures.

Sai Jiang, Zonghe Chua

Department of ECSE, Case Western Reserve University, Cleveland, OH 44106 USA

Teleoperation Sequential Scaling Robot Systems

Aug 4, 2026cs.CV

ParVL: Parallel Scaling and Expandable Compute Allocation for Multimodal LLMs

Existing scaling strategies for Multimodal Large Language Models (MLLMs) typically expand either model parameters or sequential inference computation, incurring substantial memory or latency overhead. More importantly, most existing methods fail to alter the rigid, fixed computation allocation between the Vision Transformer and the Large Language Model components, limiting task-specific optimization. To address this, we introduce the Parallel Vision-Language (ParVL) scaling framework for MLLMs, which scales parallel computation by reusing the existing ViT and LLM backbone parameters across multiple vision and language branches. This framework raises a central question: given a fixed backbone parameter budget, how should additional shared-backbone computation be allocated between the vision and language modalities? We instantiate each parallel computational stream with branch-specific prefix parameters over a shared backbone, and train the entire model end-to-end via full-parameter supervised fine-tuning on roughly 13B tokens. We systematically study the computation-allocation trade-off between the ViT encoder and LLM decoder. ParVL improves overall multimodal performance over same-recipe single-branch baselines, and the best evaluated vision--language allocation varies across tasks. Code is available at https://github.com/YangYangGirl/ParVL.

Yang Yang, Qinyu Zhao, Mouxiang Chen +5

1The Australian National University · 2Shanghai AI Laboratory · 3Zhejiang University +2

Multimodal Large Language Models Vision Transformer Sequential Scaling

Aug 2, 2026stat.ML

How fine a change can moments see? A scale law for detecting distribution shift, with a kernel calibration rule

Detecting that a stream of high-dimensional embeddings has changed is usually framed as a choice of statistic. We give a scale law that constrains any moment-based choice and test it against topological alternatives. The law: certifying a feature of spatial scale eps carrying mass fraction f requires polynomial tests of degree N* >= log(1/f)/(2 eps), proved via the Chebyshev extremal problem; a Gauss-quadrature construction gives N* >= 4b-1 for a b-scale topology, so cost is set by feature fineness, not feature count. The law is one-sided: we exhibit an annulus whose mean, covariance and all fourth-order moments equal those of a filled disk, yet H_1 is nonzero. Its practical content is a calibration rule. The upper bound is attained by Gaussian test functions, the RKHS witness of an RBF kernel, so the law predicts which bandwidth an MMD test should use: the feature scale. On real embedding streams we measure sigma*/eps with median 1.12 (IQR 1.01-1.52, n=26) over three settings and three scales, and a data-driven bandwidth reaches AUC >= 0.95. Against an adversary optimised against the defender's statistics (mean, covariance, k-NN, kurtosis), only a bandwidth-matched kernel test still detects. For persistent homology the verdict is mixed and depends on choices usually left implicit. The summary matters more than the filtration: total persistence attains recall 0.75 at FPR 1% where the first persistence landscape attains 0.00. What survives is a cost gap, not a power gap: where persistence works it costs 116x kurtosis, which works at least as well. We conclude not that topological summaries are useless, but that on this task a kernel test whose bandwidth the law sets dominates them.

Adel Kaleche

Independent researcher, France

Persistent Homology Two-Sample Testing Skewness Distribution Shifts Sequential Scaling Scaling Laws+1

Jul 30, 2026cs.LG

KAISEN: Reproducible Subgroup Fairness Auditing for Clinical Risk Models

Clinical risk models routinely achieve strong aggregate performance while producing materially different error rates across patient subgroups. Audit pipelines have been proposed to catch this, but their components are rarely stress-tested, so it is unclear which parts of an audit can be trusted and under what conditions. We present KAISEN, a five-phase audit pipeline covering subgroup stratification, disparity measurement, mechanism diagnostics, post-hoc mitigation, and drift monitoring, evaluated to the point of failure on a synthetic benchmark of 16 disease tasks, 15 social-determinant axes from Healthy People 2030, and three prespecified intersections. Four findings follow. (i) Significance tracks each axis's gap against its own minimum detectable effect: rank correlation between significance count and raw equalized-odds difference (EOD) across the 15 axes is rho = 0.56, rising to rho = 0.78 once EOD is standardized by that floor. (ii) Per-group threshold optimization reduces EOD in 48 of 48 held-out runs (paired delta = -0.285, 95% CI [-0.313, -0.252]), while group-wise Platt scaling -- the better calibrator -- behaves as a coin flip on EOD (19 of 48 runs improved, 95% CI [0.26, 0.55]) with mean effect near zero, so what an audit should report is the variance, not the average. (iii) The mechanism diagnostic classifies 144 of 144 controlled cases correctly but recovers none of 48 model-driven cases under proxy misspecification, with no signal that it failed. (iv) CUSUM failures and false alarms track cohort realization far more than disease: at the reference threshold, all 27 false alarms and 7 of 8 missed shifts come from different seeds (chi-squared p = 0.002), so a threshold tuned on one cohort fails to transfer. All results are synthetic with known ground truth and do not establish clinical validity. Code, artifacts, and scripts reproducing every number are released.

Sparsh Roy, Samuel Girmachew, Nishita Chavan

Massachusetts Institute of Technology · Hopewell Valley Central High School · East Brunswick High School

Fairness Audits Risk Stratification Subgroups Model Auditing Algorithmic Fairness Risk+2

Jul 27, 2026cs.LG

MXAttention: Data-Free Optimal Scaling and Pre-Normalization Quantization for MXFP4 Attention

The quadratic cost of attention is a major bottleneck in diffusion-based video generation models. MXFP4 attention provides a promising path toward efficient inference, but direct MXFP4 quantization often degrades generation quality due to two numerical issues: the clipping-underflow trade-off from power-of-two scaling and the row-wise normalization error introduced in the softmax loop. We propose MXAttention, a data-free post-training quantization framework for MXFP4 attention. MXAttention introduces two components: Universal Optimal Scaling (UOS), which exploits the periodic structure of power-of-two microscaling to derive a distribution-independent optimal scaling boundary Qmax=7.25 without calibration or search, and Pre-Normalization Quantization (PNQ), which quantizes unnormalized softmax exponentials before row-wise summation to preserve normalization by construction. Experiments on Wan2.2 and HunyuanVideo show that MXAttention closes at least 95% of the VBench Imaging Quality gap between OCP MXFP4 and FP16, substantially improves frame-level similarity, and preserves FP16-level generation quality with less than 0.01 absolute degradation on all reported VBench metrics. MXAttention also achieves performance competitive with strong NVFP4-based baselines with negligible overhead when fused into the attention pipeline. The implementation is publicly available in MindIE-SD.

Jianlin Yu, Jing Lin, Linghui Kong +13

Huawei Technologies Co., Ltd.

Text-To-Video Diffusion Models Attention Layers Sequential Scaling

Jul 14, 2026cs.CL

Ring-Zero: Scaling Zero RL to a Trillion Parameters for Emergent Reasoning

Reinforcement learning with verifiable rewards without human-annotated data, often referred to as zero RL, has emerged as a powerful paradigm for eliciting chain-of-thought reasoning. However, due to computational constraints, existing studies are largely restricted to small models, leaving the training dynamics and emergent capabilities at a large scale unexplored. To meaningfully explore this frontier, we aim to elicit high-quality reasoning behaviors from the model. However, we find that naive scaling often suffers from poor readability, token redundancy, and a lack of adaptive reasoning depth. To address these challenges, we present a stable and efficient training pipeline, incorporating algorithmic and system optimizations such as clipped importance sampling, training-inference ratio correction, and mixed-precision control. Our experiments offer three key findings that validate the "bitter lesson" of scaling: (1) scaling to 1T parameters significantly enhances sample efficiency and performance ceilings; (2) the training process progresses sequentially through an initial discovery phase followed by a sharpening phase; and (3) the model spontaneously develops advanced cognitive behaviors, including anthropomorphism, structured formatting, self-verification, parallel reasoning, and context anxiety, rendering hand-crafted heuristics redundant. Evaluated on seven mathematical benchmarks, Ring-2.5-1T-Zero achieves competitive performance. Additionally, to assess CoT quality beyond final-answer correctness, we propose a structured evaluation framework across three dimensions: comprehensibility, reproducibility, and efficiency, where our model demonstrates clear advantages in producing structured and concise reasoning traces. By sharing our observed emergent phenomena, we hope to provide the community with deeper insights into scaling behaviors, particularly at the 1-trillion scale.

Xinyu Tang, Qianggang Cao, Yurou Liu +13

1Gaoling School of Artificial Intelligence, Renmin University of China · 2Ant Group · 3Tsinghua University +1

Reinforcement Learning With Verifiable Reward Test-Time Scaling Offline Reinforcement Learning Sequential Scaling Chain-of-Thought Reasoning

Jul 10, 2026quant-ph

An End-to-End Hybrid Quantum--Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study

Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where

2^n

target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples (

τ\approx 1

). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are

16.35

,

7.29

,

1.82

, and

1.79

, showing modern classical samplers substantially close this gap. Amortizing

O(2^n)

preprocessing into wall-clock time, exact inverse-CDF sampling yields

17.7\text{M}

ESS/s versus

488\text{K}

ESS/s for the quantum sampler (

36\times

mean rate,

153\times

per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at

n \in \{8,10,12\}

. An MPS scaling study (

n \le 40

) shows bond dimension

χ=32

achieves

F=0.721\pm0.059

at

n=40

. Finally, a matched-budget VQC vs. MPS comparison at

n \in \{8,10,12\}

shows VQC fidelities fall far below MPS:

(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)

at compressions

10.7\times

,

34.1\times

, and

113.8\times

.

Arul Rhik Mazumder

School of Computer Science

Markov Chain Monte Carlo Hybrid Quantum-Classical Pipeline Markov Reproducibility Sequential Scaling

Jul 8, 2026cs.LG

Optimal Learning Rate Scaling Depends on Data in Deep Scalar Linear Networks

In this short note we consider the gradient descent dynamics of deep scalar linear networks,

f(x) = \prod_{l=1}^L w_l x

, which enjoy exact time-course solutions for any integer depth. We show that even in this minimal model, the optimal depth-wise learning rate scaling depends on data, whereas data-agnostic scaling rules fail to transfer across depths. Under the data-dependent optimal scaling, the learning dynamics is independent of data and weakly dependent on depth, resulting in a constant linear convergence rate across all depths including infinity. We further show similar data-dependent effects in deep scalar linear networks with residual connections.

Yedi Zhang, Peter E. Latham, Leena Chennuru Vankadara +1

Gatsby Computational Neuroscience Unit, University College London · Sainsbury Wellcome Centre, University College London

Batch Sequential Scaling Convergence Rate Scaling

Jul 2, 2026cs.CL

Will Scaling Improve Social Simulation with LLMs?

Large Language Model (LLM) social simulations are a promising research method, but they are not yet faithful enough to be adopted widely. In this work, we investigate whether the current scaling paradigm in language modeling is likely to close these gaps, or whether simulation fidelity is orthogonal to general capabilities and therefore deserving of more research attention. We use scaling laws to study the relationship between LLMs' compute scale, general capability benchmarks, and the fidelity of social simulation in three representative sub-domains: opinion modeling, behavioral simulation, and longitudinal forecasting. Surprisingly, we discover strong compute scaling in all three settings, using a suite of 85 transformer LLMs with the Qwen3 architecture pre-trained on the DCLM web text corpus under fixed-compute budgets from

10^{18}

to

10^{20}

FLOPs. Then we evaluate 35 larger and more capable open-weight models up to 70B parameters, allowing us to predict downstream accuracy from loss. This reveals that the majority of behavioral and opinion simulation tasks will rapidly improve with scale, particularly when they involve populations that are well-represented in English web corpora. Longitudinal forecasting and underrepresented opinions scale more slowly, especially when they are less correlated with general knowledge and reasoning benchmarks like MMLU. In behavior simulation, scaling fails to improve model calibration with human cognitive biases like risk aversion, as well as human heuristics like learning correlated rewards from related tasks. On these tasks, even fine-tuned models fail to noticeably scale up performance from 0.5B to 8B parameters. Taken together, we conclude that scale will improve social simulations in most settings, but outliers exist, and improvements will be less reliable in low-resource domains.

Caleb Ziems, William Held, Su Doga Karaca +3

Stanford University · Open Athena

Scaling Improve Social Simulation Sequential Scaling Reasoning Benchmark

Jul 1, 2026stat.CO

Optimal scaling of MCMC algorithms: the Hamiltonian approach

We present a simple, yet general approach to study the scaling properties as the dimensionality of Metropolised MCMC sampling algorithms increases. The study relies on the symmetries of the Hamiltonian formalism and ultimately on the symmetry of the Metropolis-Hastings formula. Our findings contain, as particular cases, many known results for the Random Walk Metropolis, MALA and other algorithms. In addition, they provide, in an easy way, new optimal scaling results for a variety of proposal mechanisms, including implicit proposals and proposals generated with the help of differential equation integrators. The analysis applies to targets that are products of a given, not necessarily univariate distribution, and also to cases where the different terms in the product are scaled differently. We show how to construct gradient-based MALA-like proposals where the variance of the proposal as the dimension

d

increases may be taken as

O(1/d^μ)

, with

μ>0

arbitrarily small, to be compared with the values

μ= 1

for Random Walk Metropolis and

μ=1/3

for MALA.

P. Dobson, J. M. Sanz-Serna, K. C. Zygalakis

Maxwell Institute for Mathematical Sciences and Mathematics Department Heriot-Watt University, Edinburgh, EH14 4AS, UK · Departamento de Matem´aticas, Universidad Carlos III de Madrid Avenida Universidad 30, 28911 Legan´es, Madrid · Maxwell Institute for Mathematical Sciences and School of Mathematics University of Edinburgh, Peter Guthrie Tait Rd, EH9 3FD, Edinburgh

Markov Chain Monte Carlo Sequential Scaling Symmetry Diffusion Models

Jun 30, 2026cs.RO

ELASTIC: Efficiently Learning to Adaptively Scale Test-Time Compute for Generative Control Policies

Generative control policies (GCPs), such as diffusion policies and flow-based vision-language-action models, enable test-time scaling in robot control. Test-time compute can be allocated along two axes: sequential scaling, which increases denoising steps to refine actions, and parallel scaling, which samples multiple candidate actions to search across modes of the policy distribution. However, the optimal allocation of sequential and parallel compute is hard to know a priori as it is state-, task-, and policy-dependent. For example, early stages of a grasp may benefit from broader parallel exploration, while near-contact phases may require more sequential refinement for precision. We present ELASTIC, an algorithm that learns state-dependent test-time compute schedules for GCPs. We formulate compute allocation as a meta-Markov Decision Process in which a meta-policy interacts with a frozen pretrained robot policy and selects sequential steps and parallel samples at each denoising iteration to maximize task success while minimizing compute. Using reinforcement learning, this meta-policy also learns adaptive compute schedules without access to the GCP's training data. Across simulated manipulation benchmarks with diffusion policies, ELASTIC Pareto-dominates fixed and single-axis scaling baselines at matched compute budgets. On real-world robot manipulation with the

π_{0.5}

vision-language-action model, ELASTIC matches best-of-

10

success while reducing wall-clock latency by 34%.

Andrew Zou Li, Gokul Swamy, Yonatan Bisk +1

Carnegie Mellon University

Generative Control Policies Test-Time Scaling Sequential Scaling Test Time

Jun 26, 2026cs.LG

MixTTA: Low-Rank Cross-Channel Mixing for Reliable Test-Time Adaptation

Test-Time Adaptation (TTA) methods commonly update the affine parameters of normalization layers to adapt deployed models under distribution shifts. However, per-channel affine parameters perform axis-aligned scaling and shifting, making them geometrically incapable of correcting cross-channel structural changes induced by distribution shift. To address this limitation, we propose MixTTA, a lightweight plug-in module that equips normalization layers with a low-rank cross-channel transformation, enabling inter-channel mixing at each layer. To ensure that the low-rank branch captures only cross-channel interactions, we also propose Decoupling Projection that enforces strict separation from the diagonal affine path, along with Spectral Projection that prevents rank-1 collapse under non-stationary test streams. MixTTA can be seamlessly integrated into any existing normalization-based TTA method. Experiments in both standard and wild TTA settings show consistent improvements over strong baselines while mitigating adaptation failure under challenging conditions. The source code is publicly available at https://github.com/delta6189/MixTTA.

Mansoo Jung, Youngwook Kim, Jungwoo Lee

Seoul National University, Seoul, Republic of Korea · Kookmin University, Seoul, Republic of Korea · HodooAI Labs, Seoul, Republic of Korea

Stable Test-Time Adaptation Test-Time Adaptation Training-Side Stage-Aware Low-Rank Adaptation Mix Low-Rank Structure Sequential Scaling

Jun 24, 2026cs.SD

Sarashina2.2-TTS: Tackling Kanji Polyphony in Japanese Speech Generation via Data Scaling and Targeted Data Synthesis

While large language model (LLM)-based text-to-speech (TTS) systems have achieved high-quality speech synthesis, most existing systems focus on English and Chinese. Japanese, however, remains under-explored, and its unique linguistic challenges, such as widespread context-dependent kanji polyphony, have yet to be adequately tackled. Here we introduce Sarashina2.2-TTS (https://github.com/sbintuitions/sarashina2.2-tts), a Japanese-centric LLM-TTS system that tackles these challenges through a dual approach: data strategy and evaluation methodology. First, we scale training to approximately 361k hours of speech, incorporating a balanced mix of Japanese and English data. Furthermore, we design a targeted data augmentation pipeline covering all 2,136 Joyo (regular-use) kanji designated by Japan's Agency for Cultural Affairs to efficiently address kanji polyphony disambiguation. Second, we introduce the Joyo Kanji Yomi Benchmark (https://github.com/sbintuitions/JoyoKanji-Yomi-Benchmark), covering all 2,136 Joyo kanji and their 4,378 readings. Alongside this benchmark, we propose Kana-CER, a metric that compares synthesized speech against reference readings in the kana space, eliminating orthographic variations to directly measure pronunciation correctness. Experiments demonstrate that our targeted data augmentation significantly improves reading accuracy. Overall, Sarashina2.2-TTS achieves state-of-the-art kanji-level reading accuracy and matches top baselines on general sentence-level pronunciation, while delivering the highest speaker similarity in zero-shot Japanese speech synthesis. Furthermore, cross-lingual evaluation reveals that Sarashina2.2-TTS is the only system that maintains stable Japanese pronunciation regardless of the prompt language, confirming that our balanced training approach improves cross-lingual robustness.

Lianbo Liu, Shiao Zhu, Kai Washizaki +10

SB Intuitions

Flow-Matching Text-To-Speech Speaker Similarity Synthetic Data Sequential Scaling

Jun 23, 2026stat.ML

Model selection with proper scoring rules on data sets of time series: prefer the mean scaled score

We study the problem of model selection among probabilistic forecasting models evaluated on datasets of multiple time series. The performance of a model on a single time series is quantified by the average value (score) of a proper scoring rule over a test set, but extending model selection to data sets of time series requires aggregating these scores. Common approaches either rely on scaling scores and averaging them (mean scaled score) or avoid scaling by using alternative statistics such as mean ranks or win rates. However, these approaches can yield conflicting conclusions. We show that such discrepancies arise from the skewness of the distribution of the scores, which is particularly pronounced when test sets are short. The skewness can cause non-mean criteria (e.g., mean rank, median, win rate) to select misspecified models. In contrast, the mean score is immune from this problem. We further show that, as the size of the test sets increases, all aggregation criteria converge to the same model selection decision, mitigating these discrepancies. Our experiments on intermittent demand time series, including data from the M5 competition, highlight the importance of sufficiently large test sets; the mean scaled score appears to be the more reliable approach, also because empirically we found its decision to remain consistent when different scaling factors are adopted.

Giorgio Corani, Stefano Damato, Dario Azzimonti +1

SUPSI, Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Lugano, Switzerland

Model Selection Probabilistic Forecasting Time Series Skewness Sequential Scaling

Jun 18, 2026cs.LG

Self-Adaptive Scale Handling for Forecasting Time Series with Scale Heterogeneity

Current time series forecasting (TSF) research predominantly focuses on scale-homogeneous data, where different time series share similar numerical magnitude ranges. However, in real-world industrial scenarios such as financial product sales, different time series often differ by orders of magnitude (scale heterogeneity). Since these series share similar temporal patterns, joint modeling is desirable for better data utilization, yet existing scaling methods either compress low-scale signals (global normalization) or destroy semantic discriminability and amplify inverse-scaling errors (window-based scaling). This paper proposes a self-Adaptive Scale-handling (AS) module that learns adaptive scale factors tailored to each input, preserving semantic discriminability while reducing inverse-scaling errors. AS consists of Scale Calibrating (SC), which calibrates prior mean scaling factors through neural networks, and Scaling Selection (SS), which decides whether to apply calibration or retain the original factor, avoiding over-calibration. Experiments on real-world fund sales datasets from Ant Fortune and Alipay show that AS seamlessly integrates into popular TSF models and consistently improves their performance. The code and dataset are available at the link https://github.com/Meteor-Stars/ASTSF.

Xu Zhang, Zhengang Huang, Yunzhi Wu +6

College of Computer Science and Artificial Intelligence, Fudan University, Shanghai, China · Ant Group, Shanghai, China

Time Series Forecasting Time Series Sequential Scaling Heterogeneity Normalization

Jun 16, 2026cs.LG

Recursive Scaling in Masked Diffusion Models

Masked diffusion models (MDMs) generate sequences by iteratively refining a partially masked state and committing tokens in parallel. We introduce recursion in MDMs and propose new Recursive Masked Diffusion Models (R-MDMs), which apply a shared denoising transformer

L

times within each denoising step, adding recursive depth as an additional compute axis without increasing parameter count. Across structured generation tasks, recursive depth improves quality at fixed parameter budget, matches substantially larger non-recursive models at matched FLOPs, and can reduce the number of denoising steps needed to reach a target quality. We interpret these gains with a dependence--fidelity decomposition of parallel decoding error: recursion refines model marginals at a fixed masked state, whereas denoising steps change that state by committing tokens. Building on this analysis, we propose to treat decoding as a two-axis decision (how many loops to run and which tokens to commit) and show that entropy-guided adaptive rules improve the quality--compute frontier over fixed schedules, transferring across various tasks on Sudoku, Countdown, RNA, and executable math generation. Together, these results establish recursive depth as a practical, complementary test-time scaling mechanism for MDMs.

Alba Carballo-Castro, Julianna Piskorz, Paulius Rauba +2

LTS4, EPFL, Lausanne, Switzerland · University of Cambridge, Cambridge, UK.

Masked Diffusion Language Models Diffusion Models Recursive Models Sequential Scaling Scaling

Jun 15, 2026cs.RO

Training and Evaluating Diffusion Policies with Long Context Lengths

Imitation learning has enabled highly-dexterous robotic manipulation from RGB observations. Policies trained with these methods, however, typically condition robot actions on only a short history of observations. These policies cannot solve tasks that require memory and can get stuck repeatedly executing the same failing motions. In this work, we first benchmark policy performance as context length is incrementally increased from short to long, across a spectrum of tasks with varying local stability and memory requirements, and in multiple data regimes. To our knowledge, this is the first study to investigate context length for Diffusion Policies at this level of detail. Our results challenge prior claims: naively scaling context length is not as brittle as advertised in literature. With an appropriate conditioning method and denoising backbone (UNet+Cross-Attention), single-task policies achieve high success rates on many tasks in the usual data regime even with naive scaling. Next, we propose a training algorithm to jointly train policies at multiple context lengths, further reducing the sample complexity of long-context learning. Finally, we apply our findings to re-evaluate some previously proposed solutions to long-context imitation learning.

Abhinav Agarwal, Adam Wei, Taylan Kargin +6

Massachusetts Institute of Technology

Imitation Learning Diffusion Policies Context Length Sequential Scaling

Jun 11, 2026cs.AI

The Hidden Power of Scaling Factor in LoRA Optimization

In Low-Rank Adaptation (LoRA), the scaling factor

α

is often treated as a mere complement to the learning rate, yet its role in optimization remains poorly understood. In this paper, we reveal that the scaling factor

α

and the learning rate function differently, with

α

emerging as the dominant driver of effective optimization, delivering gains that cannot be replicated by learning rate scaling alone. Through the synergy of extensive empirical analysis and a theoretical Signal-Drift framework, we uncover three findings into LoRA's scaling mechanism: First, LoRA's spectral suppression smooths the optimization landscape, rendering standard hyperparameters overly conservative and creating an optimization gap. Second, when leveraging this smoothness to accelerate convergence,

α

outperforms the learning rate by amplifying the task signal without increasing the drift ratio. Third, the optimal scaling factor follows a sublinear relationship with the rank, well characterized by a square-root law with an unexpectedly large coefficient, revealing the insufficient scaling of existing rank-tied heuristics. Based on these insights, we propose LoRA-

α

, a minimalist framework that restores

α

to its principled regime, making LoRA compatible with standard small learning rates. Extensive evaluations across diverse tasks demonstrate that LoRA-

α

consistently improves performance while streamlining hyperparameter search, unleashing the learning potential of LoRA.

Zicheng Zhang, Haoran Li, Jiaxing Wang +10

JD · School of Mathematical Sciences, UCAS · School of Mathematical Sciences, NKU +1

Batch Multi-Lora Sequential Scaling

Jun 10, 2026cs.LG

A Riemannian Approach to Low-Rank Optimal Transport

Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature. To address these limitations, we propose a unified Riemannian geometric framework for low-rank OT, modeling balanced and unbalanced rank-

r

positive factored couplings as novel smooth embedded submanifolds of the positive orthant. By equipping these manifolds with the Fisher-Rao product metric, we derive tractable formulations for Riemannian projectors, retractions, and Hessian-vector products. Our cost-agnostic framework seamlessly extends to linear OT, Gromov-Wasserstein (GW), fused GW, and their unbalanced counterparts. For balanced OT, our geometric ingredients are computed via efficient conjugate-gradient and iterative Bregman updates. For the unbalanced OT, our operations elegantly reduce to closed-form scalings, completely eliminating inner iterative loops. In both regimes, per-iteration complexity scales linearly with dataset size, and we provide a rank-sufficiency certificate for global optimality verification. Extensive experiments across a range of problem sizes demonstrate that our regularization-free first- and second-order solvers achieve faster convergence and superior performance over existing state-of-the-art low-rank OT solvers.

Pratik Jawanpuria, Bamdev Mishra

Centre for Machine Intelligence and Data Science, IIT Bombay · Microsoft India

Low-Rank Structure Riemannian Optimization Riemannian Manifolds Mirror Descent Sequential Scaling

Jun 10, 2026cs.CV

AVIS: Adaptive Test-Time Scaling for Vision-Language Models

Modern Vision-Language Models (VLMs) benefit from chain-of-thought prompting and test-time scaling, but these gains often come with prohibitive inference cost due to large visual contexts and long decoding chains. We view this cost through two coupled axes: Visual Context Scaling (VCS), which controls how much visual evidence is passed to the language model, and Visual Reasoning Scaling (VRS), which controls how much inference-time reasoning search is performed. Existing methods typically optimize one axis at a time, leaving the joint allocation of compute across these axes underexplored. We introduce Adaptive Visual Inference Scaling (AVIS), a lightweight policy that adapts both VCS and VRS per query. AVIS realizes VCS through Key Diversity Visual (KDV) pruning, a training-free

O(N)

key-based rule for removing redundant visual tokens before prefilling, and realizes VRS through adaptive self-consistency, using a learned difficulty predictor to select the number of reasoning rollouts. AVIS is deployment-friendly and compatible with shared-prefill inference, where all rollouts reuse a single prefilling pass and KV cache. Across diverse image and video reasoning benchmarks, AVIS improves the accuracy--compute trade-off relative to VCS-only and VRS-only baselines, and remains effective on top of RL post-trained VLMs while keeping compute and latency low.

Ahmadreza Jeddi, Minh Ngoc Le, Amirhossein Kazerouni +8

AI Center-Toronto, Samsung Electronics · University of Toronto · Vector Institute +1

Fast Inference Efficient Inference Test-Time Scaling Sequential Scaling

Jun 6, 2026cs.SD

Exploring the Scale and Diversity of Speech Anti-spoofing Datasets: Experiments and Analysis

The scale of speech anti-spoofing datasets has grown exponentially over the past decade, driven by the assumption that larger data leads to better performance. However, it remains unclear whether indiscriminate scaling commensurately improves model generalization. This study challenges the "scale-first" paradigm by decoupling the impacts of training data scale versus diversity. Through experiments on representative datasets, we report two key findings: (1) Larger is not always better. Expanding data scale excessively under fixed generation methods yields negligible returns and may even degrade cross-domain generalization due to overfitting.(2) Diversity outweighs scale. A smaller composite training set featuring diverse attacks significantly outperforms larger-scale datasets with limited diversity in cross-dataset evaluations. We conclude that future dataset construction should prioritize the diversity of generation methods over scale to effectively enhance model generalization.

Zhuolin Yi, Jun Xue, Yanzhen Ren +5

School of Cyber Science and Engineering, Wuhan University, China

Cross-Dataset Benchmark Sequential Scaling Diversity Diverse Attacks

Jun 4, 2026cs.CV

Synthetic Benchmarks Overstate Forward-Forward Scaling: Real-Data Limits of Layer-Local Training

Forward-Forward (FF) learning [Hinton, 2022] replaces backpropagation with strictly layer-local goodness updates. Recent FF-CNN work has narrowed the gap to BP on 32x32 benchmarks, raising the question of whether layer-local training is becoming a viable alternative at realistic scale. To probe this rigorously, we develop DTG-FF -- dynamic temperature goodness, decoupled normalization, and multi-layer fusion -- as an instrument that sets FF-family state of the art across nine real-data benchmarks (91.8% CIFAR-10 and the first FF baseline at ImageNet-100 224x224), and use it to audit how far layer-local training actually scales. (1) Real-data scaling. Under identical recipe and backbone, an architecture-matched BP-DeepSup baseline beats DTG-FF by 2.40/5.93 pp on CIFAR-10/CIFAR-100, and the gap widens with class count. At 224x224 the same instrument reaches only 49.4% -- the first FF baseline at this scale, versus typical BP above 75% [Tian et al., 2020] -- exposing a real-data ceiling invisible at 32x32. (2) Synthetic vs. real K-conflict. DTG-FF increasingly outperforms BP as class count K grows on synthetic teacher-student tasks, yet on real images the FF-BP gap reverses sign and widens with K. A within-dataset CIFAR-100 coarse vs. fine probe isolates label-hierarchy from image distribution: synthetic K-sweeps confound output dimensionality with fine-grained discrimination difficulty and thereby overstate FF transferability. (3) Systems audit. FF can be implemented without storing depth-wide activations, but on commodity 8 GB hardware standard BP+gradient-accumulation reaches 4.18 GB / 157 imgs/s versus DTG-FF's 7.90 GB / 138 imgs/s, so a memory-based justification for FF at this scale is not supported under fair baselines.

Yucheng Chen

Amplimit Toronto, ON, Canada

Forward Propagation Singular Learning Theory Sequential Scaling Synthetic Benchmark Scaling Scale Gap

Jun 3, 2026cs.RO

HORIZON: Recoverability-Governed Curriculum for Physical-Domain Scaling

Scaling robust robot policies requires more than broader randomization, because physical-domain experience must remain organized and learnable throughout training. We study when a policy can benefit from harder physics and identify recoverability as a central constraint in on-policy physical-domain scaling. In on-policy training, new dynamics are useful only insofar as they remain close enough to the current policy to generate corrective on-policy data, rather than collapsing rollouts into unrecoverable failures. Using quadruped locomotion as a physically demanding benchmark for embodied generalization, we introduce HORIZON, a checkpointed frontier curriculum that expands physical domains only within the current policy's recoverable boundary. HORIZON uses rollback and boundary refinement to govern each expansion step, turning fixed randomization into a continual process of physical-domain growth. Experiments reveal three regularities of physical-domain expansion. First, direct domain widening is uneven across physical axes and often unlearnable without staged ordering. Second, domain composition is non-monotonic, and adding more domains beyond a compact core can dilute recoverable joint samples and reduce overall robustness. Third, offline distillation of isolated experts cannot substitute for the joint interaction generated by on-policy curriculum. Together, these results frame physical-domain generalization as a continual growth problem for embodied control, with recoverability as the organizing principle for on-policy expansion.

Chenhao Bai, Liqin Lu, Kaijun Wang +5

1Zhejiang University, State Key Lab of CAD & CG · 2Zhejiang University of Technology

Robot Policies Curriculum Horizon Rate Scaling Sequential Scaling

Jun 3, 2026cs.LG

Test-Time Compute Scaling for ASR with Depth-Conditioned Looped Transformers

End-to-end ASR systems typically use fixed-depth acoustic encoders at inference, making it difficult to trade additional test-time computation for improved recognition without training a larger model. A natural approach is to reuse a shared Transformer block recurrently, but we find that naive looping does not fully exploit additional recurrent compute. We introduce LARM, a depth-conditioned looped Transformer that turns recurrent encoder depth into a controllable test-time compute axis. LARM combines sparse CTC checkpoints, supervision-clock embeddings, FiLM depth conditioning, and delayed soft-posterior feedback. These components structure the loop into recognition checkpoints separated by latent refinement phases and allow shared weights to specialize across recurrent steps. On LibriSpeech, LARM improves WER as the number of inference loops increases and achieves performance competitive with deeper unshared-parameter baselines. Our results show that test-time compute scaling can extend beyond autoregressive language-model reasoning to continuous non-autoregressive speech recognition.

Yacouba Kaloga, Shashi Kumar, Shakeel A. Sheikh +3

Idiap Research Institute, Switzerland · EPFL, Switzerland · BUT, Czech Republic

Automatic Speech Recognition Transformer Architectures Test-Time Scaling Sequential Scaling LLM Reasoning Strategies

Jun 2, 2026cs.RO

Humanoid-GPT: Scaling Data and Structure for Zero-Shot Motion Tracking

We introduce Humanoid-GPT, a GPT-style Transformer with causal attention trained on a billion-scale motion corpus for whole-body control. Unlike prior shallow MLP trackers constrained by scarce data and an agility-generalization trade-off, Humanoid-GPT is pre-trained on a 2B-frame retargeted corpus that unifies all major mocap datasets with large-scale in-house recordings. Scaling both data and model capacity yields a single generative Transformer that tracks highly dynamic behaviors while achieving unprecedented zero-shot generalization to unseen motions and control tasks. Extensive experiments and scaling analyses show that our model establishes a new performance frontier, demonstrating robust zero-shot generalization to unseen tasks while simultaneously tracking highly dynamic and complex motions.

Zekun Qi, Xuchuan Chen, Dairu Liu +10

Tsinghua University · Galbot Inc. · Shanghai Jiao Tong University +2

Generative Pretrained Transformers Sequential Scaling Text Corpora

Jun 1, 2026stat.ML

Provable Data Scaling Law for Meta Learning via Complexity Minimization

Pre-training has become a fundamental paradigm in modern machine learning, with one of its key empirical benefits being reduced downstream sample complexity as the scale of pre-training data increases. However, existing theoretical frameworks for pre-training do not fully explain this phenomenon. In this paper, we introduce complexity minimization, a novel meta-representation learning framework designed to enable theoretical analysis of this scaling behavior, which learns representations by evaluating the downstream model complexity best suited to each domain and minimizing the worst-case such complexity across source domains. Our end-to-end theoretical analysis, spanning pre-training through downstream regression, shows that this framework provably captures this scaling behavior; in particular, we show that the error rate of few-shot adaptation improves as the amount of meta-training data grows. Empirically, we demonstrate that incorporating complexity regularization into existing meta-learning methods consistently improves downstream sample efficiency.

Kazuto Fukuchi, Ryuichiro Hataya, Kota Matsui

University of Tsukuba, Japan · RIKEN AIP, Japan · SB Intuitions Corp., Japan +3

Meta-Learning Pretraining Optimal Sample Complexity Few-Shot Learning Downstream Fine-Tuning Scaling Laws+2

Jun 1, 2026cs.CV

Conditional Collapse in Sign Language Production: A Diagnostic and a Scaling Argument

Sign Language Production (SLP) is the task of generating avatar sign language motion from natural language text. The quality of the generated motion is typically evaluated by a motion-space Fréchet distance (FID) and back-translation (BT) BLEU score on benchmarks such as How2Sign. Both metrics can improve substantially while the underlying generator fails to faithfully represent the sign language gestures. In this work we propose to evaluate the generated motion at three independent levels: (

\tau1

) initial-pose conditioning, (

\tau2

) output diversity, and (

\tau3

) target faithfulness. We compute these as pairwise-distance ratios using latent representations of a frozen motion autoencoder (MoAE). We evaluate 14 SLP model checkpoints on the How2Sign dataset, including a re-implemented Neural Sign Actors (NSA), and show that

\tau3

faithfulness is never attained, while FID varies by nearly two orders of magnitude and is uncorrelated with faithfulness. We show that on the isolated gloss dataset ASL3DWord favorable

\tau3

can be attained, hence isolating the size of the sentence-level paired-dataset as the bottleneck.

Rui Hong, Jana Košecká

George Mason University

Sign Language Translation Speech Language Models Collapse Sequential Scaling

May 30, 2026cs.LG

Memory-Efficient LLM Training with Dynamic Sparsity: From Stability to Practical Scaling

Dynamic Sparse Training (DST) offers a promising paradigm for improving the training and inference efficiency of deep neural networks; however, we find that in large language model training, DST can suffer from optimization instability, manifested as loss spikes after topology updates. In this work, we show that the naive use of standard Adam-based optimizers leads to a cold-start issue for newly regrown parameters, resulting in excessively large updates and disrupted training dynamics. To address this issue, we propose Sparse Memory-Efficient Training (SMET), which stabilizes DST with optimizer warm-up and improves training progress through density-aware learning-rate scaling. SMET further reduces memory consumption by storing gradients and optimizer states only for active parameters. We provide a theoretical analysis of the update behaviors under SMET, showing improved optimization stability. Extensive experiments demonstrate that SMET enables stable, scalable, and memory-efficient sparse pre-training of LLMs, paving the way for sparse training as a practical alternative to dense training. Our code is publicly available at: https://github.com/QiaoXiao7282/SMET.

Qiao Xiao, Boqian Wu, Patrik Okanovic +6

Eindhoven University of Technology · University of Luxembourg · University of Twente +1

Large Language Model Training Sparsity Adam Sequential Scaling

May 29, 2026cs.LG

Balancing Learning Rates Across Layers: Exact Two-Step Dynamics and Optimal Scaling in Linear Neural Networks

We study optimal learning-rate selection in two-layer and three-layer linear neural networks trained to learn linear target functions. In particular, we derive the exact closed-form expressions for the gradients and test loss after one and two steps of gradient descent, enabling a precise characterization of early training dynamics. We characterize how learning rates should scale under the gradient approximation in the first two steps, and prove that performing updates with this approximation yields a tractable surrogate loss with a tight, small approximation error. This formulation enables the theoretical analysis of layer-wise learning rates and reveals a distinct early-training regime: test loss can be minimized by unequal learning rates at the initial step, while equal learning rates become optimal in subsequent steps. Our numerical experiments validate the theory and demonstrate the importance of balancing layer-wise learning rates early during training. The code is available at: https://github.com/TDCSZ327/Layer-Balancing.

Tianyu Pang, Vignesh Kothapalli, Shenyang Deng +3

Dartmouth College · Stanford University · Virginia Tech

Batch Two-Layer Neural Networks Gradient Descent Sequential Scaling

May 27, 2026cs.SI

Snippet-Driven Supply Chain Discovery with LLMs: Scaling Visibility in China

Financial and economic research often relies on structured supply-chain disclosures and commercial databases. In China, supplier--customer disclosure is typically limited to major partners of listed firms, leaving unlisted firms and long-tail inter-firm links poorly captured in structured data. Public web evidence can partly complement this gap through corporate, government, and trade-media disclosures; however, full-text web mining at scale is costly because pages are often inaccessible or expensive to process with large language models (LLMs). We propose a snippet-driven method for constructing a supply chain knowledge graph (SCKG), with firms as nodes and inter-firm relationships as edges. Web search snippets are query-biased summaries returned with search results. We use them as a scalable first-pass evidence layer for LLM-based relationship extraction. We evaluate the pipeline in terms of extraction efficiency and coverage. For extraction efficiency, exhaustive full-text chunking discovers 19.8

\times

more unique relationships than snippets, but requires 251.2

\times

more input tokens and yields higher redundancy. For coverage, we use 130,685 Chinese firms as search seeds, covering Shanghai/Shenzhen-listed firms and large unlisted firms as of 2024. In the listed-firm subset, the resulting SCKG covers 7.2

\times

more firms and 9.3

\times

more relationships than the CSMAR disclosure-based benchmark, while revealing heavy-tailed degree patterns. Retained provenance metadata make the SCKG an auditable complement to disclosure-based databases.

Hiroto Fukada, Takayuki Mizuno

Graduate Institute for Advanced Studies (SOKENDAI) · National Institute of Informatics · Tokyo, Japan

Supply Chain Optimization Knowledge Graphs Sequential Scaling

May 26, 2026cs.CL

FAB-Bench: A Framework for Adaptive RAG Benchmarking in Semiconductor Manufacturing

Retrieval-Augmented Generation (RAG) has become critical for knowledge-intensive applications, yet evaluating its performance in vertical domains remains difficult due to domain complexity, diverse context scales, and heavy reliance on expert assessments that are costly, inconsistent, and non-scalable. We introduce FAB-Bench, an end-to-end framework for adaptive benchmarking of RAG systems in semiconductor manufacturing. FAB-Bench defines six diagnostic metrics measuring factual accuracy, contextual utilization, completeness, retrieval relevance, technical depth, and reasoning consistency. The framework couples retriever diagnostics with generator-level reasoning analysis across context windows of 4K-32K tokens, quantifying how retrieval precision and generative fidelity co-evolve as contextual scope expands. From over 1,300 generated candidates, we curated a high-quality benchmark of 200 query-answer pairs spanning three synthesis strategies: needle-in-haystack, intra-document multi-topic, and cross-document multi-hop. Systematic evaluation across four LLMs and four RAG frameworks reveals three distinct context-scaling behaviors: logarithmic growth, early saturation, and cold-start dynamics, and identifies attention dilution as the primary mechanism behind performance degradation at extreme context lengths. Cross-framework validation on three additional production RAG systems confirms evaluation portability.

Jingbin Qian, Congwen Yi, Min Xia +3

FutureFab.AI

Semiconductor Manufacturing Multi-Hop Reasoning Sequential Scaling

May 21, 2026cs.CL

RAS: Reflection-Augmented Scaling with In-Context Learning for Executable Cypher Query Generation

Inference-time scaling can reduce errors in structured query generation, but methods to allocate the compute for query code generation remains underexplored. We study Text2Cypher, where language models generate Cypher queries that execute against property graph databases. Non-executable queries constitute a distinct syntactic failure separate from semantic inaccuracy: a syntax error triggers a system-generated error message from the database. These error messages are typically discarded at inference time rather than leveraged through in-context learning (ICL). We compare two inference methods: Independent Scaling (IS), which performs memoryless resampling, and Reflection-Augmented Scaling (RAS), which conditions each new attempt on prior execution feedback via ICL. Across three Neo4j datasets and five code-specialized language models, RAS reduces the Query Execution Error Rate by 41--50% at n{=}5, outperforming IS at 32--38%. Execution errors are not merely failures to discard but actionable feedback, and structuring inference-time compute around them is a more efficient path to executability than scaling independent samples.

Minseok Jung, Abhas Ricky, Muhammad Rameez Chatni

Cloudera 6220 America Center Dr. San Jose, CA 95002

Inference-Time Text2Cypher Sequential Scaling Code Generation In-Context Learning

May 19, 2026cs.AI

Position: The Turing-Completeness of Autoregressive Transformers Relies Heavily on Context Management

Many works make the eye-catching claim that Transformers are Turing-complete. However, the literature often conflates two distinct settings: (i) a fixed Transformer system setting, in which a fixed autoregressive Transformer is coupled with a fixed context-management method to process inputs of different lengths step by step, and (ii) a scaling-family setting, in which a family of different models (with increasing context-window length or numerical precision) is used to handle different input lengths. Existing proofs of Transformer Turing-completeness are frequently established in setting (ii), whereas real-world LLM deployment and the standard notion of Turing-completeness correspond more naturally to setting (i). In this paper, we first formalize the fixed-system setting, thereby providing a concrete characterization of how real-world LLMs operate. We then argue that results proved in the scaling-family setting provide theoretically meaningful resource bounds but do not establish Turing-completeness, thereby clarifying a common misinterpretation of existing results. Finally, we show that different context-management methods can yield sharply different computational power, and we advocate the position that context management is a central component that critically determines the computational power of real-world autoregressive Transformers.

Guanyu Cui, Zhewei Wei, Kun He

Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · DEKE Lab, Renmin University of China, Beijing, China

Autoregressive Transformers Transformer Architectures Sequential Scaling Position