#01Oct 26, 2026
cs.LG
Quantitative Generalization Bounds for Multi-Layer Transformers: A Few Long Strings can Beat Many Short Ones
Marius Henry, Michael Rizvi-Martel, Michael Hahn
Transformer-based language models exhibit an astonishing capacity to generalize to longer and more difficult problem instances than those seen in training. However, theoretical understanding of this phenomenon still lags behind. Unlike most machine learning models, the generalisation abilities of transformers inherently require considering two axes. On one hand, one must examine in-distribution statistical generalisation, which concerns the ability of a model to broaden a function from training samples to novel samples of the same distribution. On the other hand, given the sequential nature of language data, one must also consider length generalisation, which reflects whether a model trained on inputs of a given length can extrapolate to longer ones.These two notions have mostly been studied separately, leaving open how they interact. In this work, we give a joint treatment of both axes for fixed-precision transformers. We give generalisation guarantees in terms of the parameter sizes of the involved models, as well as the quantization space and the alphabet size that supply the sequences. Finally, we illustrate how the requirements in the sample count and training length trade off. In particular, we find that increasing training length can be exponentially more efficient than increasing the sample size. Experiments support predictions of the theory.
#02Oct 26, 2026
cs.LG
Improving Signals, Declining Encoder: A Known-Answer Test of Label-Free Monitoring in Self-Supervised Learning
Nilotpal Kakati
Self-supervised training is monitored without labels, through the loss and statistics of the learned features. We report a case where we know the encoders lost part of what they had learned, so we can check whether these signals noticed. We trained LeJEPA encoders on synthetic images with known generating factors. In nine of ten seeds, the readability of those factors fell abruptly and stayed down, nearly always along the same direction in factor space. Meanwhile the loss kept falling, and most of the eleven label-free signals we tracked kept improving and rated the declining runs better than runs that did not decline. Standard change-point detection rarely flagged the decline near its onset, and selecting checkpoints by these signals mostly chose ones after it.
#03Oct 26, 2026
cs.IT
Information-Theoretic Secure Aggregation With Heterogeneous Client Quantization
Shreya Meel, Sennur Ulukus, Itzhak Tamo
In federated learning (FL), secure aggregation enables a server to compute the sum of local model updates of $N$ clients, without revealing any information on the individual model updates to the server, beyond their sum. Different clients may be subject to heterogeneous bandwidth constraints, and consequently may choose different numbers of quantization levels to represent the information they send. Most secure aggregation works require the clients to project the values of their update parameters to a common finite group (or field), which does not directly accommodate heterogeneous precision constraints on their transmitted masked updates. Existing approaches of secure aggregation with heterogeneous quantization levels reveal partial aggregates of model-updates, and can reveal segments of individual model updates, under certain dropout and client-server collusion patterns. To prevent this privacy breach, we propose an information-theoretic secure aggregation scheme that tolerates client drop-outs, and up to $T$ semi-honest clients that collude with each other and with the server, under heterogeneous quantization at clients. Our protocol utilizes the $(T+1, N)$ threshold black-box secret sharing construction, where secret shares of the client updates, despite belonging to distinct algebraic groups owing to different quantization, are generated from identical linear integer systems.
#04Oct 26, 2026
cs.LG
FOCUS: Active Critic Learning for Long-Horizon Language Model Agents
Zhengping Jiang, William Jurayj, Liaoyaqi Wang and 3 more
Sparse outcome rewards make it difficult for long-horizon language-model agents to assign credit to earlier actions. Learned critics provide value estimates for intermediate states, but these estimates can be inaccurate, while estimating intermediate values with repetitive continuation samples from points within a trajectory incurs substantial costs. To mitigate these issues, we introduce FOCUS, an RL method that uses selective branching to help the critic network learn its value estimator. The rollout controller facilitates active learning for the critic by sampling continuations from states that are expected to most reduce the critic's estimation error. These refined value estimates then score the segment between consecutive states with a TD($λ$) advantage, while the sampled evidence supplies training targets for the critic. FOCUS supports long-horizon agentic reinforcement learning through a modular context-management interface that decouples context management from rollout allocation. Our experiments show that using compaction-induced segment boundaries for value estimation and credit assignment, FOCUS outperforms GRPO and VinePPO with matched per-step generation budgets on legal reasoning, deep search, and code localization benchmarks, improving held-out accuracy at Qwen3.5-9B scale by 7.2 points over the strongest baseline on BrowseComp-Plus (55.4 vs. 48.2) and by 4.1 points on DeonticBench (56.5 vs. 52.4).
#05Oct 26, 2026
cs.CL
Learning When to Commit: Schedule Distillation for Fast Diffusion Language Models
Aidar Myrzakhan, Zhiqiang Shen
Diffusion large language models (dLLMs) can generate multiple tokens in parallel, but often require many decoding rounds to complete a response. Efficient generation depends not only on which tokens are easy to predict, but also on how committing to them helps predict the remaining positions. A highly predictable token may provide little useful context, while revealing a less predictable token can help several other positions become predictable sooner. We propose dSpark, a new schedule distillation-based framework for learning when to commit tokens for faster diffusion language generation. To achieve this, we construct unmasking schedules that prioritize tokens whose reveal makes other positions easier to predict, reducing uncertainty earlier in decoding. We then distill these schedules into the model to enable faster parallel sampling, with a KL-divergence regularizer to help preserve generation quality. We extensively evaluate our approach across mathematical reasoning and code generation tasks. On GSM8K, our method achieves remarkable 10.12$\times$ and 5.12$\times$ speedups over the various baselines on LLaDA-8B-Instruct and Dream-7B-Instruct, respectively, while maintaining superior task performance. Our code is available at https://github.com/VILA-Lab/dSpark.