Related papers: Gradient Flow Polarizes Softmax Outputs towards Lo…
Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…
Large language models (LLMs) have made transformed changes for human society. One of the key computation in LLMs is the softmax unit. This operation is important in LLMs because it allows the model to generate a distribution over possible…
This paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the…
Attention mechanism is a central component of the transformer architecture which led to the phenomenal success of large language models. However, the theoretical principles underlying the attention mechanism are poorly understood,…
We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns:…
The softmax function is crucial in Transformer attention, which normalizes each row of the attention scores with summation to one, achieving superior performances over other alternative functions. However, the softmax function can face a…
Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. The self-attention mechanism underpinning the strength of ViTs has a quadratic complexity in both computation and memory usage. This motivates the…
Projected policy gradient under the simplex parameterization, policy gradient and natural policy gradient under the softmax parameterization, are fundamental algorithms in reinforcement learning. There have been a flurry of recent…
In this work, we present a new approach to analyze the gradient flow for a positive semi-definite matrix denoising problem in an extensive-rank and high-dimensional regime. We use recent linear pencil techniques of random matrix theory to…
Various forms of sparse attention have been explored to mitigate the quadratic computational and memory cost of the attention mechanism in transformers. We study sparse transformers not through a lens of efficiency but rather in terms of…
The last layer of neural language models (LMs) projects output features of dimension $D$ to logits in dimension $V$, the size of the vocabulary, where usually $D \ll V$. This mismatch is known to raise risks of limited expressivity in…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
Multi-head attention enables transformer models to represent multiple attention patterns simultaneously. Empirically, head specialization emerges in distinct stages during training, while many heads remain redundant and learn similar…
The training of neural networks by gradient descent methods is a cornerstone of the deep learning revolution. Yet, despite some recent progress, a complete theory explaining its success is still missing. This article presents, for…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to…
Despite their empirical success, the internal mechanism by which transformer models align tokens during language processing remains poorly understood. This paper provides a mechanistic and theoretical explanation of token alignment in LLMs.…
Many theoretical studies on neural networks attribute their excellent empirical performance to the implicit bias or regularization induced by first-order optimization algorithms when training networks under certain initialization…
Policy-gradient approaches to reinforcement learning have two common and undesirable overhead procedures, namely warm-start training and sample variance reduction. In this paper, we describe a reinforcement learning method based on a…
Softmax attention maps every query--key interaction into a probability distribution, but the underlying structure remains largely unexplored. We define the \emph{energy field}, the row-centered attention logit, and show that it exhibits…