32 accepted papers
Post-training (via supervised fine-tuning) improves instruction-following, but often induces semantic mode collapse by biasing models toward low-entropy fine-tuning data at the expense of the high-entropy pre-training distribution. Crucially, we find this trade-off worsens with scale. To close this …
Recent advances in reasoning domains with neural networks have primarily been enabled by a training recipe that optimizes Large Language Models, previously trained to predict the next-token in a sequence, with reinforcement learning algorithms. We introduce a framework to study the success of this p…
We study program-learning methods that are efficient in both samples and computation. Classical learning theory suggests that when the target admits a short program description (for example, a short piece of ``Python code''), it can be learned from relatively few examples by performing ERM over the …
Reinforcement Learning with Verifiable Rewards (RLVR) is a leading approach for tuning language models on mathematical reasoning tasks. However, it remains unclear whether RLVR's gains stem from genuine reasoning improvements or simply from steering the model toward answer formats that already appea…
Video Joint Embedding Predictive Architectures (V‑JEPA) learn generalizable off-the-shelf video representations by predicting masked regions in latent space with an exponential moving average (EMA)‑updated teacher. While EMA prevents representation collapse, it complicates scalable model selection a…
State Space Models (SSMs) have become the leading alternative to Transformers for sequence modeling tasks. Their primary advantage is efficiency in long-context and long-form generation, enabled by fixed-size memory and linear scaling of computational complexity. We begin this work by showing a simp…
Shampoo, a second-order optimization algorithm that uses a Kronecker product preconditioner, has recently received increasing attention from the machine learning community. Despite the increasing popularity of Shampoo, the theoretical foundations of its effectiveness are not well understood. The pre…
Efficient scheduling is crucial for interactive Large Language Model (LLM) applications, where low request completion time directly impacts user engagement. Size-based scheduling algorithms like Shortest Remaining Process Time (SRPT) aim to reduce average request completion time by leveraging known…
Inference-time computation has emerged as a promising scaling axis for improving large language model reasoning. However, despite yielding impressive performance, the optimal allocation of inference-time computation remains poorly understood. A central question is whether to prioritize sequential sc…
Low-Rank Adaptation (LoRA) is a popular technique for parameter-efficient fine-tuning of Large Language Models (LLMs). We study how different LoRA modules can be merged to achieve skill composition—testing the performance of the merged model on a target task that involves combining multiple skills,…
The Mixture-of-Experts (MoE) architecture enables a significant increase in the total number of model parameters with minimal computational overhead. However, it is not clear what performance tradeoffs, if any, exist between MoEs and standard dense transformers. In this paper, we show that as we i…
We study the relationship between gradient-based optimization of parametric models (e.g., neural networks) and optimization of linear combinations of random features. Our main result shows that if a parametric model can be learned using mini-batch stochastic gradient descent (bSGD) without making as…
Training large language models to predict beyond their training context lengths has drawn much attention in recent years, yet the principles driving such behavior of length generalization remain underexplored. We propose a new theoretical framework to study length generalization for the next-token p…
Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to achieve length generalization, these proposals typically app…
Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto…
Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context. We theoretically demonstrate that ARDTs can compute complex…
Transformers are the dominant architecture for sequence modeling, but there is growing interest in models that use a fixed-size latent state that does not depend on the sequence length, which we refer to as ''generalized state space models'' (GSSMs). In this paper we show that while GSSMs are promis…
Large language models have the ability to generate text that mimics patterns in their inputs. We introduce a simple Markov Chain sequence modeling task in order to study how this in-context learning capability emerges. In our setting, each example is sampled from a Markov chain drawn from a prior di…
Generative models are trained with the simple objective of imitating the conditional probability distribution induced by the data they are trained on. Therefore, when trained on data generated by humans, we may not expect the artificial model to outperform the humans on their original objectives. In…
In modern deep learning, algorithmic choices (such as width, depth, and learning rate) are known to modulate nuanced resource tradeoffs. This work investigates how these complexities necessarily arise for feature learning in the presence of computational-statistical gaps. We begin by considering off…
Recent work has demonstrated the effectiveness of using patch based representations when learning from image data. Here we provide theoretical support for this observation, by showing that a simple semi-supervised algorithm that uses patch statistics can efficiently learn labels produced by a one-hi…
There is mounting evidence of emergent phenomena in the capabilities of deep learning methods as we scale up datasets, model sizes, and training times. While there are some accounts of how these resources modulate statistical capacity, far less is known about their effect on the computational proble…
Large neural networks trained in the overparameterized regime are able to fit noise to zero train error. Recent work of Nakkiran and Bansal has empirically observed that such networks behave as “conditional samplers” from the noisy distribution. That is, they replicate the noise in the train data to…
Convolutional neural networks (CNN) exhibit unmatched performance in a multitude of computer vision tasks. However, the advantage of using convolutional networks over fully-connected networks is not understood from a theoretical perspective. In this work, we show how convolutional networks can lever…
We study the power of learning via mini-batch stochastic gradient descent (SGD) on the loss of a differentiable model or neural network, and ask what learning problems can be learnt using this paradigm. We show that SGD can always simulate learning with statistical queries (SQ), but its ability to g…
We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial…
In recent years we see a rapidly growing line of research which shows learnability of various models via common neural network algorithms. Yet, besides a very few outliers, these results show learnability of models that can be learned using linear methods. Namely, such results show that learning neu…
The lottery ticket hypothesis (Frankle and Carbin, 2018), states that a randomly-initialized network contains a small subnetwork such that, when trained in isolation, can compete with the performance of the original network. We prove an even stronger hypothesis (as was also conjectured in Ramanujan…
It is known that learning deep neural-networks is computationally hard in the worst-case. In fact, the proofs of such hardness results show that even weakly learning deep networks is hard. In other words, no efficient algorithm can find a predictor that is slightly better than a random guess. Howeve…
Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during…
Neural networks exhibit good generalization behavior in the over-parameterized regime, where the number of network parameters exceeds the number of observations. Nonetheless, current generalization bounds for neural networks fail to explain this phenomenon. In an attempt to bridge this gap, we study…
Deep learning requires data. A useful approach to obtain data is to be creative and mine data from various sources, that were created for different purposes. Unfortunately, this approach often leads to noisy labels. In this paper, we propose a meta algorithm for tackling the noisy labels problem. T…