We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law). Fitting the proposed law on a large set of training runs, we find that it correctly recovers the scaling of the optimal batch size. Moreover, because it makes use of training runs with suboptimal batch size, our proposed law can be robustly fit with a significantly smaller amount of training runs. We further show that the three-term law can be used to derive scaling laws for suboptimal batch sizes, and that it matches previous empirical findings related to the critical batch size.

However, most existing optimizers stop searching the parameter space once they reach a local minimum. Given the complex geometric properties of the loss landscape, it is difficult to guarantee that such a point is the lowest or provides the best generalization. To address this, we propose an adaptor "E" for gradient-based optimizers. The adapted optimizer tends to continue exploring along landscape 5.0 valleys (areas with low and nearly identical losses) in order to search for potentially1.0

Large Language Models (LLMs) are now integral across various domains and have demonstrated impressive performance. Progress, however, rests on the premise that benchmark scores are both accurate and reproducible. We demonstrate that the reproducibility of LLM performance is fragile: changing system configuration, such as evaluation batch size, GPU count, and GPU version, can introduce significant differences in the generated responses. This issue is especially pronounced in reasoning models, where minor rounding differences in early tokens can cascade into divergent chains of thought, ultimately affecting accuracy. For instance, under bfloat16 precision with greedy decoding, a reasoning model like DeepSeek-R1-Distill-Qwen-7B can exhibit up to 9% variation in accuracy and 9,000 tokens difference in response length due to differences in GPU count, type, and evaluation batch size.

As models grow larger and training them becomes expensive, it becomes increasingly important to scale training recipes not just to larger models and more data, but to do so in a compute-optimal manner that extracts maximal performance per unit of compute. While such scaling has been well studied for language modeling, reinforcement learning (RL) has received less attention in this regard. In this paper, we investigate compute scaling for online, value-based deep RL. These methods present two primary axes for compute allocation: model capacity and the updateto-data (UTD) ratio. Given a fixed compute budget, we ask: how should resources be partitioned across these axes to maximize data efficiency? Our analysis reveals a nuanced interplay between model size, batch size, and UTD. In particular, we identify a phenomenon we call TD-overfitting: increasing the batch quickly harms Q-function accuracy for small models, but this effect is absent in large models, enabling effective use of large batch size at scale. We provide a mental model for understanding this phenomenon and build guidelines for choosing batch size and UTD to optimize compute usage. Our findings provide a grounded starting point for compute-optimal scaling in deep RL, mirroring studies in supervised learning but adapted to TD learning.

Conventional wisdom dictates that small batch sizes make language model pretraining and fine-tuning unstable, motivating gradient accumulation, which trades off the number of optimizer steps for a proportional increase in batch size. While it is common to decrease the learning rate for smaller batch sizes, other hyperparameters are often held fixed. In this work, we revisit small batch sizes all the way down to batch size one, and we propose a rule for scaling Adam hyperparameters to small batch sizes. In particular, rather than holding the decay rate of the second moment fixed across batch sizes, we propose to hold its half-life fixed in terms of tokens. We find that small batch sizes (1) train stably, (2) are consistently more robust to hyperparameter choices, (3) achieve equal or better per-FLOP performance than larger batch sizes, and (4) notably enable stable language model training with vanilla SGD, even without momentum, despite storing no optimizer state. Building on these results, we provide practical recommendations for selecting a batch size and setting optimizer hyperparameters. We further recommend against gradient accumulation unless training on multiple devices with multiple model replicas. Finally, we show that a small batch size combined with an optimizer with a small state size can provide the performance benefits of full fine-tuning while maintaining a similar memory footprint to LoRA.

Multimodal Sentiment Analysis (MSA) aims to infer human emotions by integrating complementary signals from diverse modalities. However, in real-world scenarios, missing modalities are common due to data corruption, sensor failure, or privacy concerns, which can significantly degrade model performance. To tackle this challenge, we propose Hyper-Modality Enhancement (HME), a novel framework that avoids explicit modality reconstruction by enriching each observed modality with semantically relevant cues retrieved from other samples. This cross-sample enhancement reduces reliance on fully observed data during training, making the method better suited to scenarios with inherently incomplete inputs. In addition, we introduce an uncertainty-aware fusion mechanism that adaptively balances original and enriched representations to improve robustness. Extensive experiments on three public benchmarks show that HME consistently outperforms state-of-the-art methods under various missing modality conditions, demonstrating its practicality in real-world MSA applications.

In recent advancements in Test Time Adaptation (TTA), most existing methodologies focus on updating normalization layers to adapt to the test domain. However, the reliance on normalization-based adaptation presents key challenges. First, normalization layers such as Batch Normalization (BN) are highly sensitive to small batch sizes, leading to unstable and inaccurate statistics. Moreover, normalizationbased adaptation is inherently constrained by the structure of the pre-trained model, as it relies on training-time statistics that may not generalize well to unseen domains. These issues limit the effectiveness of normalization-based TTA approaches, especially under significant domain shift.

Despite progress, deep neural networks still suffer performance declines under distribution shifts between training and test domains, leading to a substantial decrease in Quality of Experience (QoE) for applications. Existing test-time adaptation (TTA) methods are challenged by dynamic, multiple test distributions within batches. We observe that feature distributions across different domains inherently cluster into distinct groups with varying means and variances. This divergence reveals a critical limitation of previous global normalization strategies in TTA, which inevitably distort the original data characteristics. Based on this insight, we propose Feature-based Instance Neighbor Discovery (FIND), which comprises three key components: Layer-Wise Feature Disentanglement (LFD), Feature-Aware Batch Normalization (FABN) and Selective FABN (S-FABN). LFD stably captures features with similar distributions at each layer by constructing graph structures; while FABN optimally combines source statistics with test-time distribution-specific statistics for robust feature representation. Finally, S-FABN determines which layers require feature partitioning and which can remain unified, thus enhancing the efficiency of inference. Extensive experiments demonstrate that FIND significantly outperforms existing methods, achieving up to approximately 30% accuracy improvement in dynamic scenarios while maintaining computational efficiency. The source code is available at https://github.com/Peanut-255/

Self-Supervised Learning (SSL) has become a powerful solution to extract rich representations from unlabeled data. Yet, SSL research is mostly focused on clean, curated and high-quality datasets. As a result, applying SSL on noisy data remains a challenge, despite being crucial to applications such as astrophysics, medical imaging, geophysics or finance. In this work, we present a fully selfsupervised framework that enables noise-robust representation learning without requiring a denoiser at inference or downstream fine-tuning. Our method first trains an SSL denoiser on noisy data, then uses it to construct a denoised-tonoisy data curriculum (i.e., training first on denoised, then noisy samples) for pretraining a SSL backbone (e.g., DINOv2), combined with a teacher-guided regularization that anchors noisy embeddings to their denoised counterparts. This process encourages the model to internalize noise robustness. Notably, the denoiser can be discarded after pretraining, simplifying deployment. On ImageNet-1k with ViT-B under extreme Gaussian noise (σ = 255, SNR = 0.72 dB), our method improves linear probing accuracy by 4.8% over DINOv2, demonstrating that denoiser-free robustness can emerge from noise-aware pretraining.

Several recently introduced deep learning optimizers utilizing matrix-level preconditioning have shown promising speedups relative to the current dominant optimizer AdamW, particularly in relatively small-scale experiments. However, efforts to validate and replicate their successes have reported mixed results. To better understand the effectiveness of these optimizers at scale, in this work we investigate how to scale preconditioned optimizers via hyperparameter transfer, building on prior works such as µP. We study how the optimal learning rate and weight decay should scale with model width and depth for a wide range of optimizers, including Shampoo, SOAP, and Muon, accounting for the impact of commonly used techniques such as blocking and grafting. We find that scaling the learning rate according to µP improves transfer, but can still suffer from significant finite-width deviations that cause drifting optimal learning rates, which we show can be mitigated by blocking and explicit spectral normalization. For compute-optimal scaling, we find scaling independent weight decay as 1/width is nearly optimal across optimizers. Applying these scaling rules, we show Muon, SOAP and Shampoo consistently achieve near 1.4 speedup over AdamW for training Llama-architecture language models of sizes ranging from 190M to 1.4B, whereas the speedup vanishes rapidly with scale under incorrect scaling. Based on these results and further ablations, we argue that studying optimal hyperparameter transfer is essential for reliably comparing optimizers at scale given a realistic tuning budget.