Firstly, we test the memorization ability and its influence of our HGMM on several small size datasets. The memory influence functions (i.e., formations (12), (13), (14) and (15)) were preloaded in our HGMM and evaluated by the m-fold cross validation (i.e., level-one-out validation, LOO for short). We set the baseline by setting the memory influence function be an identity matrix which is actually L2 loss SVM with decision (7) according to Theorem 4.3 (ii). Table II reports their highest LOO training and testing accuracies. From Table II, it is observed that our HGMM with either memory influence function has 100% training accuracies on all of these datasets.

Classifying the training data correctly without over-fitting is one of the goals in machine learning. In this paper, we propose a generalization-memorization mechanism, including a generalization-memorization decision and a memory modeling principle. Under this mechanism, error-based learning machines improve their memorization abilities of training data without over-fitting. Specifically, the generalization-memorization machines (GMM) are proposed by applying this mechanism. The optimization problems in GMM are quadratic programming problems and could be solved efficiently. It should be noted that the recently proposed generalization-memorization kernel and the corresponding support vector machines are the special cases of our GMM. Experimental results show the effectiveness of the proposed GMM both on memorization and generalization.

Previous knowledge graph embedding approaches usually map entities to representations and utilize score functions to predict the target entities, yet they struggle to reason rare or emerging unseen entities. In this paper, we propose kNN-KGE, a new knowledge graph embedding approach, by linearly interpolating its entity distribution with k-nearest neighbors. We compute the nearest neighbors based on the distance in the entity embedding space from the knowledge store. Our approach can allow rare or emerging entities to be memorized explicitly rather than implicitly in model parameters. Experimental results demonstrate that our approach can improve inductive and transductive link prediction results and yield better performance for low-resource settings with only a few triples, which might be easier to reason via explicit memory.

Modern neural language models widely used in tasks across NLP risk memorizing sensitive information from their training data. As models continue to scale up in parameters, training data, and compute, understanding memorization in language models is both important from a learning-theoretical point of view, and is practically crucial in real world applications. An open question in previous studies of memorization in language models is how to filter out "common" memorization. In fact, most memorization criteria strongly correlate with the number of occurrences in the training set, capturing "common" memorization such as familiar phrases, public knowledge or templated texts. In this paper, we provide a principled perspective inspired by a taxonomy of human memory in Psychology. From this perspective, we formulate a notion of counterfactual memorization, which characterizes how a model's predictions change if a particular document is omitted during training. We identify and study counterfactually-memorized training examples in standard text datasets. We further estimate the influence of each training example on the validation set and on generated texts, and show that this can provide direct evidence of the source of memorization at test time.

Federated learning allows clients to collaboratively learn statistical models while keeping their data local. Federated learning was originally used to train a unique global model to be served to all clients, but this approach might be sub-optimal when clients' local data distributions are heterogeneous. In order to tackle this limitation, recent personalized federated learning methods train a separate model for each client while still leveraging the knowledge available at other clients. In this work, we exploit the ability of deep neural networks to extract high quality vectorial representations (embeddings) from non-tabular data, e.g., images and text, to propose a personalization mechanism based on local memorization. Personalization is obtained interpolating a pre-trained global model with a $k$-nearest neighbors (kNN) model based on the shared representation provided by the global model. We provide generalization bounds for the proposed approach and we show on a suite of federated datasets that this approach achieves significantly higher accuracy and fairness than state-of-the-art methods.

We study the memorization power of feedforward ReLU neural networks. We show that such networks can memorize any $N$ points that satisfy a mild separability assumption using $\tilde{O}\left(\sqrt{N}\right)$ parameters. Known VC-dimension upper bounds imply that memorizing $N$ samples requires $\Omega(\sqrt{N})$ parameters, and hence our construction is optimal up to logarithmic factors. We also give a generalized construction for networks with depth bounded by $1 \leq L \leq \sqrt{N}$, for memorizing $N$ samples using $\tilde{O}(N/L)$ parameters. This bound is also optimal up to logarithmic factors. Our construction uses weights with large bit complexity. We prove that having such a large bit complexity is both necessary and sufficient for memorization with a sub-linear number of parameters.

Deep Neural Networks, often owing to the overparameterization, are shown to be capable of exactly memorizing even randomly labelled data. Empirical studies have also shown that none of the standard regularization techniques mitigate such overfitting. We investigate whether the choice of the loss function can affect this memorization. We empirically show, with benchmark data sets MNIST and CIFAR-10, that a symmetric loss function, as opposed to either cross-entropy or squared error loss, results in significant improvement in the ability of the network to resist such overfitting. We then provide a formal definition for robustness to memorization and provide a theoretical explanation as to why the symmetric losses provide this robustness. Our results clearly bring out the role loss functions alone can play in this phenomenon of memorization.

Memorization studies of deep neural networks (DNNs) help to understand what patterns and how do DNNs learn, and motivate improvements to DNN training approaches. In this work, we investigate the memorization properties of SimCLR, a widely used contrastive self-supervised learning approach, and compare them to the memorization of supervised learning and random labels training. We find that both training objects and augmentations may have different complexity in the sense of how SimCLR learns them. Moreover, we show that SimCLR is similar to random labels training in terms of the distribution of training objects complexity.

In this Course you will learn and gain 6 new habits. Each habit will make big change in your Memorization Ability. Many people who have taken this course before were able to memorize the whole holy Quran short Time. Even some of them were able to memorize the whole Quran in short Time. This course helped myself and when I noticed the amazing results, I have decided to do this course publicly to help million of Muslims around the world.

It is well known that modern deep neural networks are powerful enough to memorize datasets even when the labels have been randomized. Recently, Vershynin (2020) settled a long standing question by Baum (1988), proving that \emph{deep threshold} networks can memorize $n$ points in $d$ dimensions using $\widetilde{\mathcal{O}}(e^{1/\delta^2}+\sqrt{n})$ neurons and $\widetilde{\mathcal{O}}(e^{1/\delta^2}(d+\sqrt{n})+n)$ weights, where $\delta$ is the minimum distance between the points. In this work, we improve the dependence on $\delta$ from exponential to almost linear, proving that $\widetilde{\mathcal{O}}(\frac{1}{\delta}+\sqrt{n})$ neurons and $\widetilde{\mathcal{O}}(\frac{d}{\delta}+n)$ weights are sufficient. Our construction uses Gaussian random weights only in the first layer, while all the subsequent layers use binary or integer weights. We also prove new lower bounds by connecting memorization in neural networks to the purely geometric problem of separating $n$ points on a sphere using hyperplanes.