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Modern Deep Neural Networks (DNNs) have achieved very high performance at the expense of computational resources. To decrease the computational burden, several techniques have proposed to extract, from a given DNN, efficient subnetworks which are able to preserve performance while reducing the number of network parameters. The literature provides a broad set of techniques to discover such subnetworks, but few works have studied the peculiar topologies of such pruned architectures. In this paper, we propose a novel \emph{unrolled input-aware} bipartite Graph Encoding (GE) that is able to generate, for each layer in an either sparse or dense neural network, its corresponding graph representation based on its relation with the input data. We also extend it into a multipartite GE, to capture the relation between layers. Then, we leverage on topological properties to study the difference between the existing pruning algorithms and algorithm categories, as well as the relation between topologies and performance.

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem $y = \beta^{*\top} x +\xi$ with sparse $\beta^*$, neither minimum $\ell_1$ or $\ell_2$ norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of $\ell_1$ and $\ell_2$ interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

This paper reveals that every image can be understood as a first-order norm+linear autoregressive process, referred to as FINOLA, where norm+linear denotes the use of normalization before the linear model. We demonstrate that images of size 256$\times$256 can be reconstructed from a compressed vector using autoregression up to a 16$\times$16 feature map, followed by upsampling and convolution. This discovery sheds light on the underlying partial differential equations (PDEs) governing the latent feature space. Additionally, we investigate the application of FINOLA for self-supervised learning through a simple masked prediction technique. By encoding a single unmasked quadrant block, we can autoregressively predict the surrounding masked region. Remarkably, this pre-trained representation proves effective for image classification and object detection tasks, even in lightweight networks, without requiring fine-tuning. The code will be made publicly available.

Stein Variational Gradient Descent (SVGD) can transport particles along trajectories that reduce the KL divergence between the target and particle distribution but requires the target score function to compute the update. We introduce a new perspective on SVGD that views it as a local estimator of the reversed KL gradient flow. This perspective inspires us to propose new estimators that use local linear models to achieve the same purpose. The proposed estimators can be computed using only samples from the target and particle distribution without needing the target score function. Our proposed variational gradient estimators utilize local linear models, resulting in computational simplicity while maintaining effectiveness comparable to SVGD in terms of estimation biases. Additionally, we demonstrate that under a mild assumption, the estimation of high-dimensional gradient flow can be translated into a lower-dimensional estimation problem, leading to improved estimation accuracy. We validate our claims with experiments on both simulated and real-world datasets.

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part of statistical learning, or as dimensionality reduction with a geometric flavor. Both approaches are tightly linked: it is easier to learn patterns from data in low dimensional spaces than in high-dimensional spaces. It is shown how a diversity of methods and tools boil down to a single core methods, PCA with SVD, such that the efforts to optimize codes for analyzing massive data sets like distributed memory and task-based programming or to improve the efficiency of the algorithms like Randomised SVD can focus on this shared core method, and benefit to all methods.

Contrastive loss has been increasingly used in learning representations from multiple modalities. In the limit, the nature of the contrastive loss encourages modalities to exactly match each other in the latent space. Yet it remains an open question how the modality alignment affects the downstream task performance. In this paper, based on an information-theoretic argument, we first prove that exact modality alignment is sub-optimal in general for downstream prediction tasks. Hence we advocate that the key of better performance lies in meaningful latent modality structures instead of perfect modality alignment. To this end, we propose three general approaches to construct latent modality structures. Specifically, we design 1) a deep feature separation loss for intra-modality regularization; 2) a Brownian-bridge loss for inter-modality regularization; and 3) a geometric consistency loss for both intra- and inter-modality regularization. Extensive experiments are conducted on two popular multi-modal representation learning frameworks: the CLIP-based two-tower model and the ALBEF-based fusion model. We test our model on a variety of tasks including zero/few-shot image classification, image-text retrieval, visual question answering, visual reasoning, and visual entailment. Our method achieves consistent improvements over existing methods, demonstrating the effectiveness and generalizability of our proposed approach on latent modality structure regularization.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Recent advances in representation learning have demonstrated an ability to represent information from different modalities such as video, text, and audio in a single high-level embedding vector. In this work we present a self-supervised learning framework that is able to learn a representation that captures finer levels of granularity across different modalities such as concepts or events represented by visual objects or spoken words. Our framework relies on a discretized embedding space created via vector quantization that is shared across different modalities. Beyond the shared embedding space, we propose a Cross-Modal Code Matching objective that forces the representations from different views (modalities) to have a similar distribution over the discrete embedding space such that cross-modal objects/actions localization can be performed without direct supervision. In our experiments we show that the proposed discretized multi-modal fine-grained representation (e.g., pixel/word/frame) can complement high-level summary representations (e.g., video/sentence/waveform) for improved performance on cross-modal retrieval tasks. We also observe that the discretized representation uses individual clusters to represent the same semantic concept across modalities.

To date, most existing self-supervised learning methods are designed and optimized for image classification. These pre-trained models can be sub-optimal for dense prediction tasks due to the discrepancy between image-level prediction and pixel-level prediction. To fill this gap, we aim to design an effective, dense self-supervised learning method that directly works at the level of pixels (or local features) by taking into account the correspondence between local features. We present dense contrastive learning, which implements self-supervised learning by optimizing a pairwise contrastive (dis)similarity loss at the pixel level between two views of input images. Compared to the baseline method MoCo-v2, our method introduces negligible computation overhead (only <1% slower), but demonstrates consistently superior performance when transferring to downstream dense prediction tasks including object detection, semantic segmentation and instance segmentation; and outperforms the state-of-the-art methods by a large margin. Specifically, over the strong MoCo-v2 baseline, our method achieves significant improvements of 2.0% AP on PASCAL VOC object detection, 1.1% AP on COCO object detection, 0.9% AP on COCO instance segmentation, 3.0% mIoU on PASCAL VOC semantic segmentation and 1.8% mIoU on Cityscapes semantic segmentation. Code is available at: //git.io/AdelaiDet

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific models are learned in the inner-loop, by using only a small amount of data from the current task. A key challenge in scaling these approaches is the need to differentiate through the inner loop learning process, which can impose considerable computational and memory burdens. By drawing upon implicit differentiation, we develop the implicit MAML algorithm, which depends only on the solution to the inner level optimization and not the path taken by the inner loop optimizer. This effectively decouples the meta-gradient computation from the choice of inner loop optimizer. As a result, our approach is agnostic to the choice of inner loop optimizer and can gracefully handle many gradient steps without vanishing gradients or memory constraints. Theoretically, we prove that implicit MAML can compute accurate meta-gradients with a memory footprint that is, up to small constant factors, no more than that which is required to compute a single inner loop gradient and at no overall increase in the total computational cost. Experimentally, we show that these benefits of implicit MAML translate into empirical gains on few-shot image recognition benchmarks.