A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language model, trained to predict the next token, can perform arithmetic computations generalizing beyond training data. Binary addition and multiplication constitute a good testbed for this purpose, since they require a very small vocabulary and exhibit relevant input/output discontinuities making smooth input interpolation ineffective for novel data. We successfully trained a light language model to learn these tasks and ran a number of experiments to investigate the extrapolation capabilities and internal information processing. Our findings support the hypotheses that the language model works as an Encoding-Regression-Decoding machine where the computation takes place in the value space once the input token representation is mapped to an appropriate internal representation.

Recent efforts at explaining the interplay of memorization and generalization in deep overparametrized networks have posited that neural networks $\textit{memorize}$ "hard" examples in the final few layers of the model. Memorization refers to the ability to correctly predict on $\textit{atypical}$ examples of the training set. In this work, we show that rather than being confined to individual layers, memorization is a phenomenon confined to a small set of neurons in various layers of the model. First, via three experimental sources of converging evidence, we find that most layers are redundant for the memorization of examples and the layers that contribute to example memorization are, in general, not the final layers. The three sources are $\textit{gradient accounting}$ (measuring the contribution to the gradient norms from memorized and clean examples), $\textit{layer rewinding}$ (replacing specific model weights of a converged model with previous training checkpoints), and $\textit{retraining}$ (training rewound layers only on clean examples). Second, we ask a more generic question: can memorization be localized $\textit{anywhere}$ in a model? We discover that memorization is often confined to a small number of neurons or channels (around 5) of the model. Based on these insights we propose a new form of dropout -- $\textit{example-tied dropout}$ that enables us to direct the memorization of examples to an apriori determined set of neurons. By dropping out these neurons, we are able to reduce the accuracy on memorized examples from $100\%\to3\%$, while also reducing the generalization gap.

The rapid advancement of deep neural networks has significantly improved various tasks, such as image and speech recognition. However, as the complexity of these models increases, so does the computational cost and the number of parameters, making it difficult to deploy them on resource-constrained devices. This paper proposes a novel memorization-based inference (MBI) that is compute free and only requires lookups. Specifically, our work capitalizes on the inference mechanism of the recurrent attention model (RAM), where only a small window of input domain (glimpse) is processed in a one time step, and the outputs from multiple glimpses are combined through a hidden vector to determine the overall classification output of the problem. By leveraging the low-dimensionality of glimpse, our inference procedure stores key value pairs comprising of glimpse location, patch vector, etc. in a table. The computations are obviated during inference by utilizing the table to read out key-value pairs and performing compute-free inference by memorization. By exploiting Bayesian optimization and clustering, the necessary lookups are reduced, and accuracy is improved. We also present in-memory computing circuits to quickly look up the matching key vector to an input query. Compared to competitive compute-in-memory (CIM) approaches, MBI improves energy efficiency by almost 2.7 times than multilayer perceptions (MLP)-CIM and by almost 83 times than ResNet20-CIM for MNIST character recognition.

Memorization, or the tendency of large language models (LLMs) to output entire sequences from their training data verbatim, is a key concern for safely deploying language models. In particular, it is vital to minimize a model's memorization of sensitive datapoints such as those containing personal identifiable information (PII). The prevalence of such undesirable memorization can pose issues for model trainers, and may even require discarding an otherwise functional model. We therefore seek to predict which sequences will be memorized before a large model's full train-time by extrapolating the memorization behavior of lower-compute trial runs. We measure memorization of the Pythia model suite and plot scaling laws for forecasting memorization, allowing us to provide equi-compute recommendations to maximize the reliability (recall) of such predictions. We additionally provide further novel discoveries on the distribution of memorization scores across models and data.

Machine learning systems such as large scale recommendation systems or natural language processing systems are usually trained on billions of training points and are associated with hundreds of billions or trillions of parameters. Improving the learning process in such a way that both the training load is reduced and the model accuracy improved is highly desired. In this paper we take a first step toward solving this problem, studying influence functions from the perspective of simplifying the computations they involve. We discuss assumptions, under which influence computations can be performed on significantly fewer parameters. We also demonstrate that the sign of the influence value can indicate whether a training point is to memorize, as opposed to generalize upon. For this purpose we formally define what memorization means for a training point, as opposed to generalization. We conclude that influence functions can be made practical, even for large scale machine learning systems, and that influence values can be taken into account by algorithms that selectively remove training points, as part of the learning process.

The Neural Tangent Kernel (NTK) has emerged as a powerful tool to provide memorization, optimization and generalization guarantees in deep neural networks. A line of work has studied the NTK spectrum for two-layer and deep networks with at least a layer with $\Omega(N)$ neurons, $N$ being the number of training samples. Furthermore, there is increasing evidence suggesting that deep networks with sub-linear layer widths are powerful memorizers and optimizers, as long as the number of parameters exceeds the number of samples. Thus, a natural open question is whether the NTK is well conditioned in such a challenging sub-linear setup. In this paper, we answer this question in the affirmative. Our key technical contribution is a lower bound on the smallest NTK eigenvalue for deep networks with the minimum possible over-parameterization: the number of parameters is roughly $\Omega(N)$ and, hence, the number of neurons is as little as $\Omega(\sqrt{N})$. To showcase the applicability of our NTK bounds, we provide two results concerning memorization capacity and optimization guarantees for gradient descent training.

Pre-trained Language Models such as BERT are impressive machines with the ability to memorize, possibly generalized learning examples. We present here a small, focused contribution to the analysis of the interplay between memorization and performance of BERT in downstream tasks. We propose PreCog, a measure for evaluating memorization from pre-training, and we analyze its correlation with the BERT's performance. Our experiments show that highly memorized examples are better classified, suggesting memorization is an essential key to success for BERT.

We consider a K-armed bandit problem in general graphs where agents are arbitrarily connected and each of them has limited memorizing capabilities and communication bandwidth. The goal is to let each of the agents eventually learn the best arm. It is assumed in these studies that the communication graph should be complete or well-structured, whereas such an assumption is not always valid in practice. Furthermore, limited memorization and communication bandwidth also restrict the collaborations of the agents, since the agents memorize and communicate very few experiences. Additionally, an agent may be corrupted to share falsified experiences to its peers, while the resource limit in terms of memorization and communication may considerably restrict the reliability of the learning process. To address the above issues, we propose a three-staged collaborative learning algorithm. In each step, the agents share their latest experiences with each other through light-weight random walks in a general communication graph, and then make decisions on which arms to pull according to the recommendations received from their peers. The agents finally update their adoptions (i.e., preferences to the arms) based on the reward obtained by pulling the arms. Our theoretical analysis shows that, when there are a sufficient number of agents participating in the collaborative learning process, all the agents eventually learn the best arm with high probability, even with limited memorizing capabilities and light-weight communications. We also reveal in our theoretical analysis the upper bound on the number of corrupted agents our algorithm can tolerate. The efficacy of our proposed three-staged collaborative learning algorithm is finally verified by extensive experiments on both synthetic and real datasets.

Large Language models (LLMs) are trained on large amounts of data, which can include sensitive information that may compromise personal privacy. LLMs showed to memorize parts of the training data and emit those data verbatim when an adversary prompts appropriately. Previous research has primarily focused on data preprocessing and differential privacy techniques to address memorization or prevent verbatim memorization exclusively, which can give a false sense of privacy. However, these methods rely on explicit and implicit assumptions about the structure of the data to be protected, which often results in an incomplete solution to the problem. To address this, we propose a novel framework that utilizes a reinforcement learning approach (PPO) to fine-tune LLMs to mitigate approximate memorization. Our approach utilizes a negative similarity score, such as BERTScore or SacreBLEU, as a reward signal to learn a dissimilarity policy. Our results demonstrate that this framework effectively mitigates approximate memorization while maintaining high levels of coherence and fluency in the generated samples. Furthermore, our framework is robust in mitigating approximate memorization across various circumstances, including longer context, which is known to increase memorization in LLMs.

We approach the problem of improving robustness of deep learning algorithms in the presence of label noise. Building upon existing label correction and co-teaching methods, we propose a novel training procedure to mitigate the memorization of noisy labels, called CrossSplit, which uses a pair of neural networks trained on two disjoint parts of the labelled dataset. CrossSplit combines two main ingredients: (i) Cross-split label correction. The idea is that, since the model trained on one part of the data cannot memorize example-label pairs from the other part, the training labels presented to each network can be smoothly adjusted by using the predictions of its peer network; (ii) Cross-split semi-supervised training. A network trained on one part of the data also uses the unlabeled inputs of the other part. Extensive experiments on CIFAR-10, CIFAR-100, Tiny-ImageNet and mini-WebVision datasets demonstrate that our method can outperform the current state-of-the-art in a wide range of noise ratios.