Empirical scaling laws have shown that scaling model capacity, data, and compute improves language modeling performance. However, the relationship between model parameters and compute (FLOPs) per example, and their combined contribution to model capacity, is not well-understood. We explore this relationship through sparse Mixture-of-Experts (MoE) models, which allow scaling the total number of parameters without proportionally increasing the FLOPs per example at inference time. Specifically, we conduct a large-scale empirical study to investigate how varying the sparsity level, i.e., the ratio of non-active to total parameters, affects model performance in terms of both pretraining and downstream objectives. Our results demonstrate that under constraints such as total parameters and training budget, there is an optimal level of sparsity that improves both training efficiency and model performance. More broadly, our work (a) sheds light on the joint effect of model size and compute per example on model capacity in the context of MoEs and (b) provides insights on MoE design choices for efficient scaling.

How do language models actually use information provided as context when generating a response? Can we infer whether a particular generated statement is actually grounded in the context, a misinterpretation, or fabricated? To help answer these questions, we introduce the problem of context attribution: pinpointing the parts of the context (if any) that led a model to generate a particular statement. We then present ContextCite, a simple and scalable method for context attribution that can be applied on top of any existing language model. Finally, we showcase the utility of ContextCite through two case studies: (1) automatically verifying statements based on the attributed parts of the context and (2) improving response quality by extracting query-relevant information from the context.

How does the internal computation of a machine learning model transform inputs into predictions? In this paper, we introduce a task called component modeling that aims to address this question. The goal of component modeling is to decompose an ML model's prediction in terms of its components -- simple functions (e.g., convolution filters, attention heads) that are the "building blocks" of model computation. We focus on a special case of this task, component attribution, where the goal is to estimate the counterfactual impact of individual components on a given prediction. We then present COAR, a scalable algorithm for estimating component attributions; we demonstrate its effectiveness across models, datasets, and modalities. Finally, we show that component attributions estimated with COAR directly enable model editing across five tasks, namely: fixing model errors, ``forgetting'' specific classes, boosting subpopulation robustness, localizing backdoor attacks, and improving robustness to typographic attacks. We provide code for COAR at github.com/MadryLab/modelcomponents

We study the problem of (learning) algorithm comparison, where the goal is to find differences between models trained with two different learning algorithms. We begin by formalizing this goal as one of finding distinguishing feature transformations, i.e., input transformations that change the predictions of models trained with one learning algorithm but not the other. We then present ModelDiff, a method that leverages the datamodels framework (Ilyas et al., 2022) to compare learning algorithms based on how they use their training data. We demonstrate ModelDiff through three case studies, comparing models trained with/without data augmentation, with/without pre-training, and with different SGD hyperparameters. Our code is available at github.com/MadryLab/modeldiff

Post-hoc gradient-based interpretability methods [Simonyan et al., 2013, Smilkov et al., 2017] that provide instance-specific explanations of model predictions are often based on assumption (A): magnitude of input gradients -- gradients of logits with respect to input -- noisily highlight discriminative task-relevant features. In this work, we test the validity of assumption (A) using a three-pronged approach. First, we develop an evaluation framework, DiffROAR, to test assumption (A) on four image classification benchmarks. Our results suggest that (i) input gradients of standard models (i.e., trained on original data) may grossly violate (A), whereas (ii) input gradients of adversarially robust models satisfy (A). Second, we introduce BlockMNIST, an MNIST-based semi-real dataset, that by design encodes a priori knowledge of discriminative features. Our analysis on BlockMNIST leverages this information to validate as well as characterize differences between input gradient attributions of standard and robust models. Finally, we theoretically prove that our empirical findings hold on a simplified version of the BlockMNIST dataset. Specifically, we prove that input gradients of standard one-hidden-layer MLPs trained on this dataset do not highlight instance-specific signal coordinates, thus grossly violating assumption (A). Our findings motivate the need to formalize and test common assumptions in interpretability in a falsifiable manner [Leavitt and Morcos, 2020]. We believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at github.com/harshays/inputgradients.

Several works have proposed Simplicity Bias (SB)—the tendency of standard training procedures such as Stochastic Gradient Descent (SGD) to find simple models—to justify why neural networks generalize well [Arpit et al. 2017, Nakkiran et al. 2019, Soudry et al. 2018]. However, the precise notion of simplicity remains vague. Furthermore, previous settings that use SB to theoretically justify why neural networks generalize well do not simultaneously capture the non-robustness of neural networks—a widely observed phenomenon in practice [Goodfellow et al. 2014, Jo and Bengio 2017]. We attempt to reconcile SB and the superior standard generalization of neural networks with the non-robustness observed in practice by designing datasets that (a) incorporate a precise notion of simplicity, (b) comprise multiple predictive features with varying levels of simplicity, and (c) capture the non-robustness of neural networks trained on real data. Through theory and empirics on these datasets, we make four observations: (i) SB of SGD and variants can be extreme: neural networks can exclusively rely on the simplest feature and remain invariant to all predictive complex features. (ii) The extreme aspect of SB could explain why seemingly benign distribution shifts and small adversarial perturbations significantly degrade model performance. (iii) Contrary to conventional wisdom, SB can also hurt generalization on the same data distribution, as SB persists even when the simplest feature has less predictive power than the more complex features. (iv) Common approaches to improve generalization and robustness—ensembles and adversarial training—can fail in mitigating SB and its pitfalls. Given the role of SB in training neural networks, we hope that the proposed datasets and methods serve as an effective testbed to evaluate novel algorithmic approaches aimed at avoiding the pitfalls of SB; code and data available at github.com/harshays/simplicitybiaspitfalls.

This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain the emergence of rich structural properties found in real-world networks. We make three contributions. First, we propose a parsimonious and accurate model of attributed network growth that jointly explains the emergence of in-degree distributions, local clustering, clustering-degree relationship and attribute mixing patterns. Second, our model is based on biased random walks and uses local processes to form edges without recourse to global network information. Third, we account for multiple sociological phenomena: bounded rationality, structural constraints, triadic closure, attribute homophily, and preferential attachment. Our experiments indicate that the proposed Attributed Random Walk (ARW) model accurately preserves network structure and attribute mixing patterns of six real-world networks; it improves upon the performance of eight state-of-the-art models by a statistically significant margin of 2.5-10x.

Due to resource constraints and restricted access to large-scale graph datasets, it is often necessary to work with a sampled subgraph of a larger original graph. The task of inferring a global property of the original graph from the sampled subgraph is of fundamental interest. In this work, we focus on estimating the number of connected components. Due to the inherent difficulty of the problem for general graphs, little is known about the connection between the number of connected components in the observed subgraph and the original graph. To make this connection, we propose a highly redundant motif-based representation of the observed subgraph, which, at first glance, may seem counter-intuitive. However, the proposed representation is crucial in introducing a novel estimator for the number of connected components in general graphs. The connection is made precise via the Schatten \(k\)-norms of the graph Laplacian and the spectral representation of the number of connected components. We provide a guarantee on the resulting mean squared error that characterizes the bias-variance trade-off. Furthermore, our experiments on synthetic and real-world graphs show that we improve upon competing algorithms for graphs with spectral gaps bounded away from zero.