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Avi Schwarzschild, Zhili Feng, Pratyush Maini, Zachary C. Lipton, J. Zico Kolter

Large language models (LLMs) trained on web-scale datasets raise substantial concerns regarding permissible data usage. One major question is whether these models "memorize" all their training data or they integrate many data sources in some way more akin to how a human would learn and synthesize information. The answer hinges, to a large degree, on $\textit{how we define memorization}$. In this work, we propose the Adversarial Compression Ratio (ACR) as a metric for assessing memorization in LLMs -- a given string from the training data is considered memorized if it can be elicited by a prompt shorter than the string itself. In other words, these strings can be "compressed" with the model by computing adversarial prompts of fewer tokens. We outline the limitations of existing notions of memorization and show how the ACR overcomes these challenges by (i) offering an adversarial view to measuring memorization, especially for monitoring unlearning and compliance; and (ii) allowing for the flexibility to measure memorization for arbitrary strings at a reasonably low compute. Our definition serves as a valuable and practical tool for determining when model owners may be violating terms around data usage, providing a potential legal tool and a critical lens through which to address such scenarios. Project page: https://locuslab.github.io/acr-memorization.

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Yiming Zhang, Zhuokai Zhao, Zhaorun Chen, Zhili Feng, Zenghui Ding, Yining Sun

Among the ever-evolving development of vision-language models, contrastive language-image pretraining (CLIP) has set new benchmarks in many downstream tasks such as zero-shot classifications by leveraging self-supervised contrastive learning on large amounts of text-image pairs. However, its dependency on rigid one-to-one mappings overlooks the complex and often multifaceted relationships between and within texts and images. To this end, we introduce RankCLIP, a novel pretraining method that extends beyond the rigid one-to-one matching framework of CLIP and its variants. By leveraging both in-modal and cross-modal ranking consistency, RankCLIP improves the alignment process, enabling it to capture the nuanced many-to-many relationships between and within each modality. Through comprehensive experiments, we demonstrate the enhanced capability of RankCLIP to effectively improve performance across various downstream tasks, notably achieving significant gains in zero-shot classifications over state-of-the-art methods, underscoring the potential of RankCLIP in further advancing vision-language pretraining.

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Zhili Feng, Michal Moshkovitz, Dotan Di Castro, J. Zico Kolter

Concept explanation is a popular approach for examining how human-interpretable concepts impact the predictions of a model. However, most existing methods for concept explanations are tailored to specific models. To address this issue, this paper focuses on model-agnostic measures. Specifically, we propose an approach to concept explanations that satisfy three natural axioms: linearity, recursivity, and similarity. We then establish connections with previous concept explanation methods, offering insight into their varying semantic meanings. Experimentally, we demonstrate the utility of the new method by applying it in different scenarios: for model selection, optimizer selection, and model improvement using a kind of prompt editing for zero-shot vision language models.

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Pratyush Maini, Zhili Feng, Avi Schwarzschild, Zachary C. Lipton, J. Zico Kolter

Large language models trained on massive corpora of data from the web can memorize and reproduce sensitive or private data raising both legal and ethical concerns. Unlearning, or tuning models to forget information present in their training data, provides us with a way to protect private data after training. Although several methods exist for such unlearning, it is unclear to what extent they result in models equivalent to those where the data to be forgotten was never learned in the first place. To address this challenge, we present TOFU, a Task of Fictitious Unlearning, as a benchmark aimed at helping deepen our understanding of unlearning. We offer a dataset of 200 diverse synthetic author profiles, each consisting of 20 question-answer pairs, and a subset of these profiles called the forget set that serves as the target for unlearning. We compile a suite of metrics that work together to provide a holistic picture of unlearning efficacy. Finally, we provide a set of baseline results from existing unlearning algorithms. Importantly, none of the baselines we consider show effective unlearning motivating continued efforts to develop approaches for unlearning that effectively tune models so that they truly behave as if they were never trained on the forget data at all.

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Zhili Feng, J. Zico Kolter

This work studies the neural tangent kernel (NTK) of the deep equilibrium (DEQ) model, a practical ``infinite-depth'' architecture which directly computes the infinite-depth limit of a weight-tied network via root-finding. Even though the NTK of a fully-connected neural network can be stochastic if its width and depth both tend to infinity simultaneously, we show that contrarily a DEQ model still enjoys a deterministic NTK despite its width and depth going to infinity at the same time under mild conditions. Moreover, this deterministic NTK can be found efficiently via root-finding.

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Zhili Feng, Ezra Winston, J. Zico Kolter

Deep Boltzmann machines (DBMs), one of the first ``deep'' learning methods ever studied, are multi-layered probabilistic models governed by a pairwise energy function that describes the likelihood of all variables/nodes in the network. In practice, DBMs are often constrained, i.e., via the \emph{restricted} Boltzmann machine (RBM) architecture (which does not permit intra-layer connections), in order to allow for more efficient inference. In this work, we revisit the generic DBM approach, and ask the question: are there other possible restrictions to their design that would enable efficient (approximate) inference? In particular, we develop a new class of restricted model, the monotone DBM, which allows for arbitrary self-connection in each layer, but restricts the \emph{weights} in a manner that guarantees the existence and global uniqueness of a mean-field fixed point. To do this, we leverage tools from the recently-proposed monotone Deep Equilibrium model and show that a particular choice of activation results in a fixed-point iteration that gives a variational mean-field solution. While this approach is still largely conceptual, it is the first architecture that allows for efficient approximate inference in fully-general weight structures for DBMs. We apply this approach to simple deep convolutional Boltzmann architectures and demonstrate that it allows for tasks such as the joint completion and classification of images, within a single deep probabilistic setting, while avoiding the pitfalls of mean-field inference in traditional RBMs.

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Zhili Feng, Anna Bair, J. Zico Kolter

Modern image classification is based upon directly predicting model classes via large discriminative networks, making it difficult to assess the intuitive visual ``features'' that may constitute a classification decision. At the same time, recent works in joint visual language models such as CLIP provide ways to specify natural language descriptions of image classes but typically focus on providing single descriptions for each class. In this work, we demonstrate that an alternative approach, arguably more akin to our understanding of multiple ``visual features'' per class, can also provide compelling performance in the robust few-shot learning setting. In particular, we automatically enumerate multiple visual descriptions of each class -- via a large language model (LLM) -- then use a vision-image model to translate these descriptions to a set of multiple visual features of each image; we finally use sparse logistic regression to select a relevant subset of these features to classify each image. This both provides an ``intuitive'' set of relevant features for each class, and in the few-shot learning setting, outperforms standard approaches such as linear probing. When combined with finetuning, we also show that the method is able to outperform existing state-of-the-art finetuning approaches on both in-distribution and out-of-distribution performance.

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Jon Ergun, Zhili Feng, Sandeep Silwal, David P. Woodruff, Samson Zhou

$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier, we consider a scenario where "advice" is provided to help perform clustering. Specifically, we consider the $k$-means problem augmented with a predictor that, given any point, returns its cluster label in an approximately optimal clustering up to some, possibly adversarial, error. We present an algorithm whose performance improves along with the accuracy of the predictor, even though na\"{i}vely following the accurate predictor can still lead to a high clustering cost. Thus if the predictor is sufficiently accurate, we can retrieve a close to optimal clustering with nearly optimal runtime, breaking known computational barriers for algorithms that do not have access to such advice. We evaluate our algorithms on real datasets and show significant improvements in the quality of clustering.

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Zhili Feng, Fred Roosta, David P. Woodruff

A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As a result, much of the expensive computation can be performed on the small matrix. The sketching of positive semidefinite (PSD) matrices is well understood, but there are many applications where the related matrices are not PSD, including Hessian matrices in non-convex optimization and covariance matrices in regression applications involving complex numbers. In this paper, we present novel dimensionality reduction methods for non-PSD matrices, as well as their ``square-roots", which involve matrices with complex entries. We show how these techniques can be used for multiple downstream tasks. In particular, we show how to use the proposed matrix sketching techniques for both convex and non-convex optimization, $\ell_p$-regression for every $1 \leq p \leq \infty$, and vector-matrix-vector queries.

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Zhili Feng, Shaobo Han, Simon S. Du

This paper studies zero-shot domain adaptation where each domain is indexed on a multi-dimensional array, and we only have data from a small subset of domains. Our goal is to produce predictors that perform well on \emph{unseen} domains. We propose a model which consists of a domain-invariant latent representation layer and a domain-specific linear prediction layer with a low-rank tensor structure. Theoretically, we present explicit sample complexity bounds to characterize the prediction error on unseen domains in terms of the number of domains with training data and the number of data per domain. To our knowledge, this is the first finite-sample guarantee for zero-shot domain adaptation. In addition, we provide experiments on two-way MNIST and four-way fiber sensing datasets to demonstrate the effectiveness of our proposed model.

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