Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUnderstanding Generalization through Visualizations
350
0
0.0
(
0
)
Added by
Wenqian Ronny Huang
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The power of neural networks lies in their ability to generalize to unseen data, yet the underlying reasons for this phenomenon remain elusive. Numerous rigorous attempts have been made to explain generalization, but available bounds are still quite loose, and analysis does not always lead to true understanding. The goal of this work is to make generalization more intuitive. Using visualization methods, we discuss the mystery of generalization, the geometry of loss landscapes, and how the curse (or, rather, the blessing) of dimensionality causes optimizers to settle into minima that generalize well.
rate research
Read More
We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation $r$ of the training data, and then fitting a simple (e.g., linear) classifier $g$ to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if $mathsf{C}(g) ll n$, where $mathsf{C}(g)$ is an appropriately-defined measure of the simple classifier $g$s complexity, and $n$ is the number of training samples. We stress that our bound is independent of the complexity of the representation $r$. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.
Graph neural networks (GNNs) can process graphs of different sizes, but their ability to generalize across sizes, specifically from small to large graphs, is still not well understood. In this paper, we identify an important type of data where generalization from small to large graphs is challenging: graph distributions for which the local structure depends on the graph size. This effect occurs in multiple important graph learning domains, including social and biological networks. We first prove that when there is a difference between the local structures, GNNs are not guaranteed to generalize across sizes: there are bad global minima that do well on small graphs but fail on large graphs. We then study the size-generalization problem empirically and demonstrate that when there is a discrepancy in local structure, GNNs tend to converge to non-generalizing solutions. Finally, we suggest two approaches for improving size generalization, motivated by our findings. Notably, we propose a novel Self-Supervised Learning (SSL) task aimed at learning meaningful representations of local structures that appear in large graphs. Our SSL task improves classification accuracy on several popular datasets.
Catastrophic forgetting affects the training of neural networks, limiting their ability to learn multiple tasks sequentially. From the perspective of the well established plasticity-stability dilemma, neural networks tend to be overly plastic, lacking the stability necessary to prevent the forgetting of previous knowledge, which means that as learning progresses, networks tend to forget previously seen tasks. This phenomenon coined in the continual learning literature, has attracted much attention lately, and several families of approaches have been proposed with different degrees of success. However, there has been limited prior work extensively analyzing the impact that different training regimes -- learning rate, batch size, regularization method-- can have on forgetting. In this work, we depart from the typical approach of altering the learning algorithm to improve stability. Instead, we hypothesize that the geometrical properties of the local minima found for each task play an important role in the overall degree of forgetting. In particular, we study the effect of dropout, learning rate decay, and batch size, on forming training regimes that widen the tasks local minima and consequently, on helping it not to forget catastrophically. Our study provides practical insights to improve stability via simple yet effective techniques that outperform alternative baselines.
Hessian captures important properties of the deep neural network loss landscape. Previous works have observed low rank structure in the Hessians of neural networks. We make several new observations about the top eigenspace of layer-wise Hessian: top eigenspaces for different models have surprisingly high overlap, and top eigenvectors form low rank matrices when they are reshaped into the same shape as the corresponding weight matrix. Towards formally explaining such structures of the Hessian, we show that the new eigenspace structure can be explained by approximating the Hessian using Kronecker factorization; we also prove the low rank structure for random data at random initialization for over-parametrized two-layer neural nets. Our new understanding can explain why some of these structures become weaker when the network is trained with batch normalization. The Kronecker factorization also leads to better explicit generalization bounds.
Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically effective approach is to reduce the overall storage and computation costs of RNNs by network pruning techniques. Despite their successful applications, those pruning methods based on Lasso either produce irregular sparse patterns in weight matrices, which is not helpful in practical speedup. To address these issues, we propose structured pruning method through neuron selection which can reduce the sizes of basic structures of RNNs. More specifically, we introduce two sets of binary random variables, which can be interpreted as gates or switches to the input neurons and the hidden neurons, respectively. We demonstrate that the corresponding optimization problem can be addressed by minimizing the L0 norm of the weight matrix. Finally, experimental results on language modeling and machine reading comprehension tasks have indicated the advantages of the proposed method in comparison with state-of-the-art pruning competitors. In particular, nearly 20 x practical speedup during inference was achieved without losing performance for language model on the Penn TreeBank dataset, indicating the promising performance of the proposed method
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
