Lawrence Stewart

Lawrence Stewart, Francis Bach, Quentin Berthet et al.

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on the cross entropy loss results in better performance. By focusing on two-layer ReLU networks, which can be fully characterized by measures over their feature space, we explore how the implicit bias induced by gradient-based optimization could partly explain the above phenomenon. We provide theoretical evidence that the regression formulation yields a measure whose support can differ greatly from that for classification, in the case of one-dimensional data. Our proposed optimal supports correspond directly to the features learned by the input layer of the network. The different nature of these supports sheds light on possible optimization difficulties the square loss could encounter during training, and we present empirical results illustrating this phenomenon.

Lawrence Stewart, Matthew Trager, Sujan Kumar Gonugondla et al. · amazon-science

Speculative decoding aims to speed up autoregressive generation of a language model by verifying in parallel the tokens generated by a smaller draft model.In this work, we explore the effectiveness of learning-free, negligible-cost draft strategies, namely $N$-grams obtained from the model weights and the context. While the predicted next token of the base model is rarely the top prediction of these simple strategies, we observe that it is often within their top-$k$ predictions for small $k$. Based on this, we show that combinations of simple strategies can achieve significant inference speedups over different tasks. The overall performance is comparable to more complex methods, yet does not require expensive preprocessing or modification of the base model, and allows for seamless `plug-and-play' integration into pipelines.

Lawrence Stewart, Francis Bach, Quentin Berthet

Regression, the task of predicting a continuous scalar target y based on some features x is one of the most fundamental tasks in machine learning and statistics. It has been observed and theoretically analyzed that the classical approach, meansquared error minimization, can lead to suboptimal results when training neural networks. In this work, we propose a new method to improve the training of these models on regression tasks, with continuous scalar targets. Our method is based on casting this task in a different fashion, using a target encoder, and a prediction decoder, inspired by approaches in classification and clustering. We showcase the performance of our method on a wide range of real-world datasets.

Lawrence Stewart, Francis S Bach, Felipe Llinares López et al.

We introduce a differentiable clustering method based on stochastic perturbations of minimum-weight spanning forests. This allows us to include clustering in end-to-end trainable pipelines, with efficient gradients. We show that our method performs well even in difficult settings, such as data sets with high noise and challenging geometries. We also formulate an ad hoc loss to efficiently learn from partial clustering data using this operation. We demonstrate its performance on several data sets for supervised and semi-supervised tasks.

Lawrence Stewart, Mark Stalzer

When applying Machine Learning techniques to problems, one must select model parameters to ensure that the system converges but also does not become stuck at the objective function's local minimum. Tuning these parameters becomes a non-trivial task for large models and it is not always apparent if the user has found the optimal parameters. We aim to automate the process of tuning a Neural Network, (where only a limited number of parameter search attempts are available) by implementing Bayesian Optimization. In particular, by assigning Gaussian Process Priors to the parameter space, we utilize Bayesian Optimization to tune an Artificial Neural Network used to learn the XOR function, with the result of achieving higher prediction accuracy.