skip to main content

Explore Research Products in the NSF-PAR

Title: From Boltzmann Machines to Neural Networks and Back Again
Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann Machines, probably the most well-studied class of latent variable models. Our results are based on new connections to learning two-layer neural networks under ℓ∞ bounded input; for both problems, we give nearly optimal results under the conjectured hardness of sparse parity with noise. Using the connection between RBMs and feedforward networks, we also initiate the theoretical study of supervised RBMs [Hinton, 2012], a version of neural-network learning that couples distributional assumptions induced from the underlying graphical model with the architecture of the unknown function class. We then give an algorithm for learning a natural class of supervised RBMs with better runtime than what is possible for its related class of networks without distributional assumptions.  more » « less
Award ID(s):
1909204
NSF-PAR ID:
10297549
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Advances in neural information processing systems
ISSN:
1049-5258
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ( , ArXivorg)
    null (Ed.)
    Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradient direction. Existing convergence results for gradient descent-based methods heavily rely on the fact that the gradient direction is used for updating. This paper presents a new class of convergence analysis for FL, Federated Learning Neural Tangent Kernel (FL-NTK), which corresponds to over-paramterized ReLU neural networks trained by gradient descent in FL and is inspired by the analysis in Neural Tangent Kernel (NTK). Theoretically, FL-NTK converges to a global-optimal solution at a linear rate with properly tuned learning parameters. Furthermore, with proper distributional assumptions, FL-NTK can also achieve good generalization. 
    more » « less
  2. ; ; ; ( , Proceedings of Machine Learning Research)
    Meila, Marina ; Zhang, Tong (Ed.)
    Federated Learning (FL) is an emerging learning scheme that allows different distributed clients to train deep neural networks together without data sharing. Neural networks have become popular due to their unprecedented success. To the best of our knowledge, the theoretical guarantees of FL concerning neural networks with explicit forms and multi-step updates are unexplored. Nevertheless, training analysis of neural networks in FL is non-trivial for two reasons: first, the objective loss function we are optimizing is non-smooth and non-convex, and second, we are even not updating in the gradient direction. Existing convergence results for gradient descent-based methods heavily rely on the fact that the gradient direction is used for updating. The current paper presents a new class of convergence analysis for FL, Federated Neural Tangent Kernel (FL-NTK), which corresponds to overparamterized ReLU neural networks trained by gradient descent in FL and is inspired by the analysis in Neural Tangent Kernel (NTK). Theoretically, FL-NTK converges to a global-optimal solution at a linear rate with properly tuned learning parameters. Furthermore, with proper distributional assumptions, FL-NTK can also achieve good generalization. The proposed theoretical analysis scheme can be generalized to more complex neural networks. 
    more » « less
  3. ; ; ; ; ( , Transactions on machine learning research)
    In supervised continual learning, a deep neural network (DNN) is updated with an ever-growing data stream. Unlike the offline setting where data is shuffled, we cannot make any distributional assumptions about the data stream. Ideally, only one pass through the dataset is needed for computational efficiency. However, existing methods are inadequate and make many assumptions that cannot be made for real-world applications, while simultaneously failing to improve computational efficiency. In this paper, we propose a novel continual learning method, SIESTA based on wake/sleep framework for training, which is well aligned to the needs of on-device learning. The major goal of SIESTA is to advance compute efficient continual learning so that DNNs can be updated efficiently using far less time and energy. The principal innovations of SIESTA are: 1) rapid online updates using a rehearsal-free, backpropagation-free, and data-driven network update rule during its wake phase, and 2) expedited memory consolidation using a compute-restricted rehearsal policy during its sleep phase. For memory efficiency, SIESTA adapts latent rehearsal using memory indexing from REMIND. Compared to REMIND and prior arts, SIESTA is far more computationally efficient, enabling continual learning on ImageNet-1K in under 2 hours on a single GPU; moreover, in the augmentation-free setting it matches the performance of the offline learner, a milestone critical to driving adoption of continual learning in real-world applications. 
    more » « less
  4. ; ; ( , Annual Conference on Neural Information Processing Systems)
    Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there is a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM is still not understood. We address this issue for multiple popular ERM problems including kernel SVMs, kernel ridge regression, and training the final layer of a neural network. In particular, we give conditional hardness results for these problems based on complexity-theoretic assumptions such as the Strong Exponential Time Hypothesis. Under these assumptions, we show that there are no algorithms that solve the aforementioned ERM problems to high accuracy in sub-quadratic time. We also give similar hardness results for computing the gradient of the empirical loss, which is the main computational burden in many non-convex learning tasks. 
    more » « less
  5. ; ( , Neural Information Processing - Letters and Reviews)
    We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural distributional assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of ReLUs). We make no assumptions on the structure of the network or the labels. Given sufficiently-strong polynomial eigenvalue decay, we obtain {\em fully}-polynomial time algorithms in {\em all} the relevant parameters with respect to square-loss. Milder decay assumptions also lead to improved algorithms. This is the first purely distributional assumption that leads to polynomial-time algorithms for networks of ReLUs, even with one hidden layer. Further, unlike prior distributional assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email