While many have shown how Large Language Models (LLMs) can be applied to a diverse set of tasks, the critical issues of data contamination and memorization are often glossed over. In this work, we address this concern for tabular data. Starting with simple qualitative tests for whether an LLM knows the names and values of features, we introduce a variety of different techniques to assess the degrees of contamination, including statistical tests for conditional distribution modeling and four tests that identify memorization. Our investigation reveals that LLMs are pre-trained on many popular tabular datasets. This exposure can lead to invalid performance evaluation on downstream tasks because the LLMs have, in effect, been fit to the test set. Interestingly, we also identify a regime where the language model reproduces important statistics of the data, but fails to reproduce the dataset verbatim. On these datasets, although seen during training, good performance on downstream tasks might not be due to overfitting. Our findings underscore the need for ensuring data integrity in machine learning tasks with LLMs. To facilitate future research, we release an open-source tool that can perform various tests for memorization https://github.com/interpretml/

In this paper, we address the issue of using logic rules to explain the results from legal case retrieval. The task is critical to legal case retrieval because the users (e.g., lawyers or judges) are highly specialized and require the system to provide logical, faithful, and interpretable explanations before making legal decisions. Recently, research efforts have been made to learn explainable legal case retrieval models. However, these methods usually select rationales (key sentences) from the legal cases as explanations, failing to provide faithful and logically correct explanations. In this paper, we propose Neural-Symbolic enhanced Legal Case Retrieval (NS-LCR), a framework that explicitly conducts reasoning on the matching of legal cases through learning case-level and law-level logic rules. The learned rules are then integrated into the retrieval process in a neuro-symbolic manner. Benefiting from the logic and interpretable nature of the logic rules, NS-LCR is equipped with built-in faithful explainability. We also show that NS-LCR is a model-agnostic framework that can be plugged in for multiple legal retrieval models. To showcase NS-LCR's superiority, we enhance existing benchmarks by adding manually annotated logic rules and introducing a novel explainability metric using Large Language Models (LLMs). Our comprehensive experiments reveal NS-LCR's effectiveness for ranking, alongside its proficiency in delivering reliable explanations for legal case retrieval.

Deep Neural Nets (DNNs) have become a pervasive tool for solving many emerging problems. However, they tend to overfit to and memorize the training set. Memorization is of keen interest since it is closely related to several concepts such as generalization, noisy learning, and privacy. To study memorization, Feldman (2019) proposed a formal score, however its computational requirements limit its practical use. Recent research has shown empirical evidence linking input loss curvature (measured by the trace of the loss Hessian w.r.t inputs) and memorization. It was shown to be ~3 orders of magnitude more efficient than calculating the memorization score. However, there is a lack of theoretical understanding linking memorization with input loss curvature. In this paper, we not only investigate this connection but also extend our analysis to establish theoretical links between differential privacy, memorization, and input loss curvature. First, we derive an upper bound on memorization characterized by both differential privacy and input loss curvature. Second, we present a novel insight showing that input loss curvature is upper-bounded by the differential privacy parameter. Our theoretical findings are further empirically validated using deep models on CIFAR and ImageNet datasets, showing a strong correlation between our theoretical predictions and results observed in practice.

In this work, we investigate the interplay between memorization and learning in the context of \emph{stochastic convex optimization} (SCO). We define memorization via the information a learning algorithm reveals about its training data points. We then quantify this information using the framework of conditional mutual information (CMI) proposed by Steinke and Zakynthinou (2020). Our main result is a precise characterization of the tradeoff between the accuracy of a learning algorithm and its CMI, answering an open question posed by Livni (2023). We show that, in the $L^2$ Lipschitz--bounded setting and under strong convexity, every learner with an excess error $\varepsilon$ has CMI bounded below by $\Omega(1/\varepsilon^2)$ and $\Omega(1/\varepsilon)$, respectively. We further demonstrate the essential role of memorization in learning problems in SCO by designing an adversary capable of accurately identifying a significant fraction of the training samples in specific SCO problems. Finally, we enumerate several implications of our results, such as a limitation of generalization bounds based on CMI and the incompressibility of samples in SCO problems.

We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstrate that, via mean-field games (MFGs), the WPO formulation reveals mathematical structure that describes the inductive bias of diffusion and score-based models. In particular, MFGs yield optimality conditions in the form of a pair of coupled partial differential equations: a forward-controlled Fokker-Planck (FP) equation, and a backward Hamilton-Jacobi-Bellman (HJB) equation. Via a Cole-Hopf transformation and taking advantage of the fact that the cross-entropy can be related to a linear functional of the density, we show that the HJB equation is an uncontrolled FP equation. Second, with the mathematical structure at hand, we present an interpretable kernel-based model for the score function which dramatically improves the performance of SGMs in terms of training samples and training time. In addition, the WPO-informed kernel model is explicitly constructed to avoid the recently studied memorization effects of score-based generative models. The mathematical form of the new kernel-based models in combination with the use of the terminal condition of the MFG reveals new explanations for the manifold learning and generalization properties of SGMs, and provides a resolution to their memorization effects. Finally, our mathematically informed, interpretable kernel-based model suggests new scalable bespoke neural network architectures for high-dimensional applications.

Compared with gradient based artificial neural networks, biological neural networks usually show a more powerful generalization ability to quickly adapt to unknown environments without using any gradient back-propagation procedure. Inspired by the distributed memory mechanism of human brains, we propose a novel gradient-free Distributed Memorization Learning mechanism, namely DML, to support quick domain adaptation of transferred models. In particular, DML adopts randomly connected neurons to memorize the association of input signals, which are propagated as impulses, and makes the final decision by associating the distributed memories based on their confidence. More importantly, DML is able to perform reinforced memorization based on unlabeled data to quickly adapt to a new domain without heavy fine-tuning of deep features, which makes it very suitable for deploying on edge devices. Experiments based on four cross-domain real-world datasets show that DML can achieve superior performance of real-time domain adaptation compared with traditional gradient based MLP with more than 10% improvement of accuracy while reducing 87% of the timing cost of optimization.

Vision-Language Models (VLMs) have emerged as the state-of-the-art representation learning solution, with myriads of downstream applications such as image classification, retrieval and generation. A natural question is whether these models memorize their training data, which also has implications for generalization. We propose a new method for measuring memorization in VLMs, which we call d\'ej\`a vu memorization. For VLMs trained on image-caption pairs, we show that the model indeed retains information about individual objects in the training images beyond what can be inferred from correlations or the image caption. We evaluate d\'ej\`a vu memorization at both sample and population level, and show that it is significant for OpenCLIP trained on as many as 50M image-caption pairs. Finally, we show that text randomization considerably mitigates memorization while only moderately impacting the model's downstream task performance.

Neural networks are known to exploit spurious artifacts (or shortcuts) that co-occur with a target label, exhibiting heuristic memorization. On the other hand, networks have been shown to memorize training examples, resulting in example-level memorization. These kinds of memorization impede generalization of networks beyond their training distributions. Detecting such memorization could be challenging, often requiring researchers to curate tailored test sets. In this work, we hypothesize -- and subsequently show -- that the diversity in the activation patterns of different neurons is reflective of model generalization and memorization. We quantify the diversity in the neural activations through information-theoretic measures and find support for our hypothesis on experiments spanning several natural language and vision tasks. Importantly, we discover that information organization points to the two forms of memorization, even for neural activations computed on unlabelled in-distribution examples. Lastly, we demonstrate the utility of our findings for the problem of model selection. The associated code and other resources for this work are available at https://rachitbansal.github.io/information-measures.

Learning multi-lingual sentence embeddings is a fundamental task in natural language processing. Recent trends in learning both mono-lingual and multi-lingual sentence embeddings are mainly based on contrastive learning (CL) among an anchor, one positive, and multiple negative instances. In this work, we argue that leveraging multiple positives should be considered for multi-lingual sentence embeddings because (1) positives in a diverse set of languages can benefit cross-lingual learning, and (2) transitive similarity across multiple positives can provide reliable structural information for learning. In order to investigate the impact of multiple positives in CL, we propose a novel approach, named MPCL, to effectively utilize multiple positive instances to improve the learning of multi-lingual sentence embeddings. Experimental results on various backbone models and downstream tasks demonstrate that MPCL leads to better retrieval, semantic similarity, and classification performances compared to conventional CL. We also observe that in unseen languages, sentence embedding models trained on multiple positives show better cross-lingual transfer performance than models trained on a single positive instance.

Self-supervised learning (SSL) has recently received significant attention due to its ability to train high-performance encoders purely on unlabeled data--often scraped from the internet. This data can still be sensitive and empirical evidence suggests that SSL encoders memorize private information of their training data and can disclose them at inference time. Since existing theoretical definitions of memorization from supervised learning rely on labels, they do not transfer to SSL. To address this gap, we propose SSLMem, a framework for defining memorization within SSL. Our definition compares the difference in alignment of representations for data points and their augmented views returned by both encoders that were trained on these data points and encoders that were not. Through comprehensive empirical analysis on diverse encoder architectures and datasets we highlight that even though SSL relies on large datasets and strong augmentations--both known in supervised learning as regularization techniques that reduce overfitting--still significant fractions of training data points experience high memorization. Through our empirical results, we show that this memorization is essential for encoders to achieve higher generalization performance on different downstream tasks. In recent years, self-supervised learning (SSL) has emerged as a new potent learning paradigm. SSL encoders can be trained without reliance on labeled data, which is often hard and expensive to obtain. Instead, SSL leverages the existence of large amounts of unlabeled data--often scraped from the internet--to obtain state-of-the-art performance in various domains, ranging from computer vision (He et al., 2022; Chen et al., 2020; Chen & He, 2021; Caron et al., 2021) to natural language processing (Devlin et al., 2018; Radford et al.). Empirical studies suggest that SSL encoders can disclose information about their training data at inference time (Meehan et al., 2023). An unintended revelation of private information is often associated to machine learning models' ability to memorize their training data (Zhang et al., 2016; Arpit et al., 2017; Chatterjee, 2018; Carlini et al., 2019; 2021; 2022). Additionally, it was found that in supervised learning memorization happens in the feature extractor (encoder) layers (Feldman & Zhang, 2020; Maini et al., 2023). Those are exactly the type of layers that SSL trains. Yet, given that SSL differs significantly from supervised learning in terms of learning objective, data processing, and augmentation strength, it remains unclear whether the trends from supervised learning transfer to the self-supervised learning. Part of the work was done while the authors were at the University of Toronto and the Vector Institute. Higher memorization scores indicate stronger memorization. We observe that outliers and atypical examples experience higher memorization than more standard samples.