It has been recognized that heavily overparameterized deep neural networks (DNNs) exhibit surprisingly good generalization performance in various machine-learning tasks. Although benefits of depth have been investigated from different perspectives such as the approximation theory and the statistical learning theory, existing theories do not adequately explain the empirical success of overparameterized DNNs. In this work, we report a remarkable interplay between depth and locality of a target function. We introduce $k$-local and $k$-global functions, and find that depth is beneficial for learning local functions but detrimental to learning global functions. This interplay is not properly captured by the neural tangent kernel, which describes an infinitely wide neural network within the lazy learning regime.
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所涌现物质科学中心（CEMS））；The University of Tokyo（东京大学）
It has been recognized that a heavily overparameterized artificial neural network exhibits surprisingly good generalization performance in various machine-learning tasks. Recent theoretical studies have made attempts to unveil the mystery of the overparameterization. In most of those previous works, the overparameterization is achieved by increasing the width of the network, while the effect of increasing the depth has remained less well understood. In this work, we investigate the effect of increasing the depth within an overparameterized regime. To gain an insight into the advantage of depth…
Locality-Aware Redundancy Pruning for LLM Depth Compression
University of Southern California（美国南加州大学）；Neural Superintelligence Lab, MODULABS（MODULABS神经超级智能实验室）；Seoul National University（首尔国立大学）；Inha University（釜山大学）
Self-attention architectures, which are rapidly pushing the frontier in natural language processing, demonstrate a surprising depth-inefficient behavior: previous works indicate that increasing the internal representation (network width) is just as useful as increasing the number of self-attention layers (network depth). We theoretically predict a width-dependent transition between depth-efficiency and depth-inefficiency in self-attention. We conduct systematic empirical ablations on networks of depths 6 to 48 that clearly reveal the theoretically predicted behaviors, and provide explicit quan…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）
Neural networks have achieved state of the art results in many areas, supposedly due to parameter sharing, locality, and depth. Tensor networks (TNs) are linear algebraic representations of quantum many-body states based on their entanglement structure. TNs have found use in machine learning. We devise a novel TN based model called Deep convolutional tensor network (DCTN) for image classification, which has parameter sharing, locality, and depth. It is based on the Entangled plaquette states (EPS) TN. We show how EPS can be implemented as a backpropagatable layer. We test DCTN on MNIST, Fashio…
University of Florence（佛罗伦萨大学）；University of Siena（锡耶纳大学）
This paper proposes an in-depth re-thinking of neural computation that parallels apparently unrelated laws of physics, that are formulated in the variational framework of the least action principle. The theory holds for neural networks that are also based on any digraph, and the resulting computational scheme exhibits the intriguing property of being truly biologically plausible. The scheme, which is referred to as SpatioTemporal Local Propagation (STLP), is local in both space and time. Space locality comes from the expression of the network connections by an appropriate Lagrangian term, so a…
The University of Texas at Dallas（德克萨斯大学达拉斯分校）；Microsoft Corporation（微软公司）
Recently, Transformer-based architectures have been explored for speaker embedding extraction. Although the Transformer employs the self-attention mechanism to efficiently model the global interaction between token embeddings, it is inadequate for capturing short-range local context, which is essential for the accurate extraction of speaker information. In this study, we enhance the Transformer with the enhanced locality modeling in two directions. First, we propose the Locality-Enhanced Conformer (LE-Confomer) by introducing depth-wise convolution and channel-wise attention into the Conformer…
In current deep network architectures, deeper layers in networks tend to contain hundreds of independent neurons which makes it hard for humans to understand how they interact with each other. By organizing the neurons by correlation, humans can observe how clusters of neighbouring neurons interact with each other. In this paper, we propose a novel algorithm for back propagation, called Locality Guided Neural Network(LGNN) for training networks that preserves locality between neighbouring neurons within each layer of a deep network. Heavily motivated by Self-Organizing Map (SOM), the goal is t…
Interplay between depth and width for interpolation in neural ODEs
Universidad Autónoma de Madrid（马德里自治大学）；ENS Paris Saclay（巴黎萨克雷高等师范学校）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Fundación Deusto（德乌斯托基金会）
Cogent Labs（Cogent实验室）；University of Torino（都灵大学）；Collegio Carlo Alberto（阿尔贝托国王学院）
Modern neural networks (NN) featuring a large number of layers (depth) and units per layer (width) have achieved a remarkable performance across many domains. While there exists a vast literature on the interplay between infinitely wide NNs and Gaussian processes, a little is known about analogous interplays with respect to infinitely deep NNs. NNs with independent and identically distributed (i.i.d.) initializations exhibit undesirable forward and backward propagation properties as the number of layers increases. To overcome these drawbacks, Peluchetti and Favaro (2020) considered fully-conne…
Marquette University（马凯特大学）；University of Chicago（芝加哥大学）
This paper explores the implicit bias of overparameterized neural networks of depth greater than two layers. Our framework considers a family of networks of varying depth that all have the same capacity but different implicitly defined representation costs. The representation cost of a function induced by a neural network architecture is the minimum sum of squared weights needed for the network to represent the function; it reflects the function space bias associated with the architecture. Our results show that adding linear layers to a ReLU network yields a representation cost that reflects a…
Aalto University（阿尔托大学）；Federal Institute of Ceará（塞阿拉联邦研究所）；University of Manchester（曼彻斯特大学）
Graph pooling is a central component of a myriad of graph neural network (GNN) architectures. As an inheritance from traditional CNNs, most approaches formulate graph pooling as a cluster assignment problem, extending the idea of local patches in regular grids to graphs. Despite the wide adherence to this design choice, no work has rigorously evaluated its influence on the success of GNNs. In this paper, we build upon representative GNNs and introduce variants that challenge the need for locality-preserving representations, either using randomization or clustering on the complement graph. Stri…
Meta AI, FAIR（Meta人工智能，基础人工智能研究院）；Univ. Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；IRISA（雷恩信息与随机系统研究所）
Image copy detection and retrieval from large databases leverage two components. First, a neural network maps an image to a vector representation, that is relatively robust to various transformations of the image. Second, an efficient but approximate similarity search algorithm trades scalability (size and speed) against quality of the search, thereby introducing a source of error. This paper improves the robustness of image copy detection with active indexing, that optimizes the interplay of these two components. We reduce the quantization loss of a given image representation by making imperc…
