Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention
Authors: Jing Huang, Daniel Wurgaft, Rachit Bansal, Laura Ruis, Naomi Saphra, David Alvarez-Melis, Andrew Kyle Lampinen, Christopher Potts, +1 more
Abstract
Larger models learn tasks smaller models do not. What drives this phenomenon? We develop a simple phenomenological argument that power-law scaling already suggests that a larger model will be able to learn a part of the data distribution that a smaller model fails to learn, even with infinite training data. To validate this claim and identify its causes, we study the effects of model scaling on a synthetic setup consisting of a mixture of tasks that show monotonic scaling curves. The results point to a data-induced competition over resources (neurons). Specifically, smaller models allocate their neurons to high frequency or low complexity tasks, and so they learn solutions that perform poorly on rare and complex tasks. Moreover, this happens even when solutions capable of expressing the desired task exist. We then assess how a larger model circumvents this data-centric bottleneck, finding that it traces to a reduced interference mechanism: larger models can allocate enough resources to common tasks that the gradient updates for those tasks become weak, which means that they do not overwrite rare-task features as they slowly accumulate. Finally, to further validate these claims, we pretrain OLMo models (4M to 4B parameters) on novel tasks of varying frequency and complexity. The results mirror those from our synthetic data experiments: only the larger OLMo models learn the infrequent and complex tasks, and these larger models embed more task features in their representations and show less gradient interference between tasks. Overall, we offer a data-centric account of why larger models learn tasks that smaller models fail to. This helps explain why larger models are better in practice, and it can inform practical questions concerning model sizing and training data mixtures.
This work investigates the ``small-vs-large gap'', where repeating on fewer samples can lead to compute saving during training compared to using a larger dataset. This is observed across algorithmic tasks, architectures and optimizers and cannot be explained using prior theory. We argue that the speedup comes from appropriate layer-wise growth enabled by sampling biases, which is more pronounced when the dataset size is smaller. We provide both theoretical analysis and empirical evidence from various interventions. Our results suggest that using a smaller dataset with more repetitions is not just a fallback strategy under data scarcity, but can be proactively leveraged as a favorable inductive biases for optimization, particularly in reasoning tasks.
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn serves as a stepping stone to efficiently learn rare long-tailed skills. Our results offer an alternative perspective on what constitutes an effective data distribution for training models.
Existing scaling laws for Large Language Models (LLMs), predominantly monotonic power laws, fail to explain emerging non-monotonic phenomena such as catastrophic overtraining and quantization-induced degradation, where performance deteriorates despite increased compute. We propose the Shannon Scaling Law, a unified theoretical framework that models LLM training as information transmission over a noisy channel, grounded in the Shannon-Hartley theorem. By mapping model parameters to channel bandwidth and training tokens to signal power, our formulation explicitly captures the interaction between learning signal and intrinsic noise. This perspective reveals a fundamental Shannon capacity for LLMs: scaling model size or data without preserving a sufficient signal-to-noise ratio (SNR) inevitably amplifies noise, inducing a transition from monotonic improvement to U-shaped performance degradation. We validate our theory through experiments on Pythia and OLMo2 under perturbations, including Gaussian noise, quantization and supervised fine-tuning on math, QA and code tasks. The Shannon Scaling Law consistently outperforms classical scaling laws and recent perturbation-aware laws, achieving strong R2 scores and accurately capturing loss basins missed by prior approaches. It also extrapolates: fitted on ≤6.9B Pythia models with ≤180B tokens, it predicts the unseen 12B model up to 307B tokens at pooled R2=0.847, while monotonic baselines collapse.