Wilson Wu

Wilson Wu

We discuss the problem of learning a deterministic finite automaton (DFA) from a confidence oracle. That is, we are given access to an oracle $Q$ with incomplete knowledge of some target language $L$ over an alphabet $Σ$; the oracle maps a string $x\inΣ^*$ to a score in the interval $[-1,1]$ indicating its confidence that the string is in the language. The interpretation is that the sign of the score signifies whether $x\in L$, while the magnitude $|Q(x)|$ represents the oracle's confidence. Our goal is to learn a DFA representation of the oracle that preserves the information that it is confident in. The learned DFA should closely match the oracle wherever it is highly confident, but it need not do this when the oracle is less sure of itself.

Wilson Wu, Victor Lecomte, Michael Winer et al.

By far the most common way to estimate an expected loss in machine learning is to draw samples, compute the loss on each one, and take the empirical average. However, sampling is not necessarily optimal. Given an MLP at initialization, we show how to estimate its expected output over Gaussian inputs without running samples through the network at all. Instead, we produce approximate representations of the distributions of activations at each layer, leveraging tools such as cumulants and Hermite expansions. We show both theoretically and empirically that for sufficiently wide networks, our estimator achieves a target mean squared error using substantially fewer FLOPs than Monte Carlo sampling. We find moreover that our methods perform particularly well at estimating the probabilities of rare events, and additionally demonstrate how they can be used for model training. Together, these findings suggest a path to producing models with a greatly reduced probability of catastrophic tail risks.

Wilson Wu, John X. Morris, Lionel Levine

Do transformers "think ahead" during inference at a given position? It is known transformers prepare information in the hidden states of the forward pass at time step $t$ that is then used in future forward passes $t+τ$. We posit two explanations for this phenomenon: pre-caching, in which off-diagonal gradient terms present during training result in the model computing features at $t$ irrelevant to the present inference task but useful for the future, and breadcrumbs, in which features most relevant to time step $t$ are already the same as those that would most benefit inference at time $t+τ$. We test these hypotheses by training language models without propagating gradients to past timesteps, a scheme we formalize as myopic training. In a constructed synthetic data setting, we find clear evidence for pre-caching. In the autoregressive language modeling setting, our experiments are more suggestive of the breadcrumbs hypothesis, though pre-caching increases with model scale.

Philipp Alexander Kreer, Wilson Wu, Maxwell Adam et al.

Classical influence functions face significant challenges when applied to deep neural networks, primarily due to non-invertible Hessians and high-dimensional parameter spaces. We propose the local Bayesian influence function (BIF), an extension of classical influence functions that replaces Hessian inversion with loss landscape statistics that can be estimated via stochastic-gradient MCMC sampling. This Hessian-free approach captures higher-order interactions among parameters and scales efficiently to neural networks with billions of parameters. We demonstrate state-of-the-art results on predicting retraining experiments.

Lakshya Jain, Varun Chandrasekaran, Uyeong Jang et al.

Even as deep neural networks (DNNs) have achieved remarkable success on vision-related tasks, their performance is brittle to transformations in the input. Of particular interest are semantic transformations that model changes that have a basis in the physical world, such as rotations, translations, changes in lighting or camera pose. In this paper, we show how differentiable rendering can be utilized to generate images that are informative, yet realistic, and which can be used to analyze DNN performance and improve its robustness through data augmentation. Given a differentiable renderer and a DNN, we show how to use off-the-shelf attacks from adversarial machine learning to generate semantic counterexamples -- images where semantic features are changed as to produce misclassifications or misdetections. We validate our approach on DNNs for image classification and object detection. For classification, we show that semantic counterexamples, when used to augment the dataset, (i) improve generalization performance (ii) enhance robustness to semantic transformations, and (iii) transfer between models. Additionally, in comparison to sampling-based semantic augmentation, our technique generates more informative data in a sample efficient manner.