The impressive generalization performance of modern neural networks is attributed in part to their ability to implicitly memorize complex training patterns. Inspired by this, we explore a novel mechanism to improve model generalization via explicit memorization. Specifically, we propose the residual-memorization (ResMem) algorithm, a new method that augments an existing prediction model (e.g., a neural network) by fitting the model's residuals with a k-nearest neighbor based regressor. The final prediction is then the sum of the original model and the fitted residual regressor. By construction, ResMem can explicitly memorize the training labels, even when the base model has low capacity. We start by formulating a stylized linear regression problem and rigorously show that ResMem results in a more favorable test risk over a base linear neural network. Then, we empirically show that ResMem consistently improves the test set generalization of the original prediction model across standard vision and natural language processing benchmarks.

Stochastic gradients closely relate to both optimization and generalization of deep neural networks (DNNs). Some works attempted to explain the success of stochastic optimization for deep learning by the arguably heavy-tail properties of gradient noise, while other works presented theoretical and empirical evidence against the heavy-tail hypothesis on gradient noise. Unfortunately, formal statistical tests for analyzing the structure and heavy tails of stochastic gradients in deep learning are still under-explored. In this paper, we mainly make two contributions. First, we conduct formal statistical tests on the distribution of stochastic gradients and gradient noise across both parameters and iterations. Our statistical tests reveal that dimension-wise gradients usually exhibit power-law heavy tails, while iteration-wise gradients and stochastic gradient noise caused by minibatch training usually do not exhibit power-law heavy tails. Second, we further discover that the covariance spectra of stochastic gradients have the power-law structures overlooked by previous studies and present its theoretical implications for training of DNNs. While previous studies believed that the anisotropic structure of stochastic gradients matters to deep learning, they did not expect the gradient covariance can have such an elegant mathematical structure. Our work challenges the existing belief and provides novel insights on the structure of stochastic gradients in deep learning.

In the current landscape of explanation methodologies, most predominant approaches, such as SHAP and LIME, employ removal-based techniques to evaluate the impact of individual features by simulating various scenarios with specific features omitted. Nonetheless, these methods primarily emphasize efficiency in the original context, often resulting in general inconsistencies. In this paper, we demonstrate that such inconsistency is an inherent aspect of these approaches by establishing the Impossible Trinity Theorem, which posits that interpretability, efficiency, and consistency cannot hold simultaneously. Recognizing that the attainment of an ideal explanation remains elusive, we propose the utilization of interpretation error as a metric to gauge inefficiencies and inconsistencies. To this end, we present two novel algorithms founded on the standard polynomial basis, aimed at minimizing interpretation error. Our empirical findings indicate that the proposed methods achieve a substantial reduction in interpretation error, up to 31.8 times lower when compared to alternative techniques. Code is available at https://github.com/trusty-ai/efficient-consistent-explanations.

Implementations of Markov chain Monte Carlo (MCMC) methods need to confront two fundamental challenges: accurate representation of prior information and efficient evaluation of likelihoods. Principal component analysis (PCA) and related techniques can in some cases facilitate the definition and sampling of the prior distribution, as well as the training of accurate surrogate models, using for instance, polynomial chaos expansion (PCE). However, complex geological priors with sharp contrasts necessitate more complex dimensionality-reduction techniques, such as, deep generative models (DGMs). By sampling a low-dimensional prior probability distribution defined in the low-dimensional latent space of such a model, it becomes possible to efficiently sample the physical domain at the price of a generator that is typically highly non-linear. Training a surrogate that is capable of capturing intricate non-linear relationships between latent parameters and outputs of forward modeling presents a notable challenge. Indeed, while PCE models provide high accuracy when the input-output relationship can be effectively approximated by relatively low-degree multivariate polynomials, this condition is typically not met when employing latent variables derived from DGMs. In this contribution, we present a strategy combining the excellent reconstruction performances of a variational autoencoder (VAE) with the accuracy of PCA-PCE surrogate modeling in the context of Bayesian ground penetrating radar (GPR) traveltime tomography. Within the MCMC process, the parametrization of the VAE is leveraged for prior exploration and sample proposals. Concurrently, surrogate modeling is conducted using PCE, which operates on either globally or locally defined principal components of the VAE samples under examination.

We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.

Differential Privacy (DP) image data synthesis, which leverages the DP technique to generate synthetic data to replace the sensitive data, allowing organizations to share and utilize synthetic images without privacy concerns. Previous methods incorporate the advanced techniques of generative models and pre-training on a public dataset to produce exceptional DP image data, but suffer from problems of unstable training and massive computational resource demands. This paper proposes a novel DP image synthesis method, termed PRIVIMAGE, which meticulously selects pre-training data, promoting the efficient creation of DP datasets with high fidelity and utility. PRIVIMAGE first establishes a semantic query function using a public dataset. Then, this function assists in querying the semantic distribution of the sensitive dataset, facilitating the selection of data from the public dataset with analogous semantics for pre-training. Finally, we pre-train an image generative model using the selected data and then fine-tune this model on the sensitive dataset using Differentially Private Stochastic Gradient Descent (DP-SGD). PRIVIMAGE allows us to train a lightly parameterized generative model, reducing the noise in the gradient during DP-SGD training and enhancing training stability. Extensive experiments demonstrate that PRIVIMAGE uses only 1% of the public dataset for pre-training and 7.6% of the parameters in the generative model compared to the state-of-the-art method, whereas achieves superior synthetic performance and conserves more computational resources. On average, PRIVIMAGE achieves 30.1% lower FID and 12.6% higher Classification Accuracy than the state-of-the-art method. The replication package and datasets can be accessed online.

Pre-trained large language models based on Transformers have demonstrated amazing in-context learning (ICL) abilities. Given several demonstration examples, the models can implement new tasks without any parameter updates. However, it is still an open question to understand the mechanism of ICL. In this paper, we interpret the inference process of ICL as a gradient descent process in a contrastive learning pattern. Firstly, leveraging kernel methods, we establish the relationship between gradient descent and self-attention mechanism under generally used softmax attention setting instead of linear attention setting. Then, we analyze the corresponding gradient descent process of ICL from the perspective of contrastive learning without negative samples and discuss possible improvements of this contrastive learning pattern, based on which the self-attention layer can be further modified. Finally, we design experiments to support our opinions. To the best of our knowledge, our work is the first to provide the understanding of ICL from the perspective of contrastive learning and has the potential to facilitate future model design by referring to related works on contrastive learning.

Brain tumors are increasingly prevalent, characterized by the uncontrolled spread of aberrant tissues in the brain, with almost 700,000 new cases diagnosed globally each year. Magnetic Resonance Imaging (MRI) is commonly used for the diagnosis of brain tumors and accurate classification is a critical clinical procedure. In this study, we propose an efficient solution for classifying brain tumors from MRI images using custom transfer learning networks. While several researchers have employed various pre-trained architectures such as RESNET-50, ALEXNET, VGG-16, and VGG-19, these methods often suffer from high computational complexity. To address this issue, we present a custom and lightweight model using a Convolutional Neural Network-based pre-trained architecture with reduced complexity. Specifically, we employ the VGG-19 architecture with additional hidden layers, which reduces the complexity of the base architecture but improves computational efficiency. The objective is to achieve high classification accuracy using a novel approach. Finally, the result demonstrates a classification accuracy of 96.42%.

Few-shot learning or meta-learning leverages the data scarcity problem in machine learning. Traditionally, training data requires a multitude of samples and labeling for supervised learning. To address this issue, we propose a one-shot unsupervised meta-learning to learn the latent representation of the training samples. We use augmented samples as the query set during the training phase of the unsupervised meta-learning. A temperature-scaled cross-entropy loss is used in the inner loop of meta-learning to prevent overfitting during unsupervised learning. The learned parameters from this step are applied to the targeted supervised meta-learning in a transfer-learning fashion for initialization and fast adaptation with improved accuracy. The proposed method is model agnostic and can aid any meta-learning model to improve accuracy. We use model agnostic meta-learning (MAML) and relation network (RN) on Omniglot and mini-Imagenet datasets to demonstrate the performance of the proposed method. Furthermore, a meta-learning model with the proposed initialization can achieve satisfactory accuracy with significantly fewer training samples.

Bilingual Lexical Induction (BLI) is a core challenge in NLP, it relies on the relative isomorphism of individual embedding spaces. Existing attempts aimed at controlling the relative isomorphism of different embedding spaces fail to incorporate the impact of semantically related words in the model training objective. To address this, we propose GARI that combines the distributional training objectives with multiple isomorphism losses guided by the graph attention network. GARI considers the impact of semantical variations of words in order to define the relative isomorphism of the embedding spaces. Experimental evaluation using the Arabic language data set shows that GARI outperforms the existing research by improving the average P@1 by a relative score of up to 40.95% and 76.80% for in-domain and domain mismatch settings respectively. We release the codes for GARI at https://github.com/asif6827/GARI.