Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization

• URL: http://arxiv.org/abs/2203.05006v1
• Date: Wed, 9 Mar 2022 19:04:08 GMT
• Title: Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization
• Authors: Sam Buchanan, Jingkai Yan, Ellie Haber, John Wright
• Abstract summary: We propose a new computational primitive for building invariant networks based instead on optimization. We provide empirical and theoretical corroboration of the efficiency gains and soundness of our proposed method. We demonstrate its utility in constructing an efficient invariant network for a simple hierarchical object detection task.
• Score: 8.37077056358265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of transformations, making them unable to cope with natural variabilities in visual data such as changes in pose and perspective. We identify a common limitation of these approaches--they rely on sampling to traverse the high-dimensional space of transformations--and propose a new computational primitive for building invariant networks based instead on optimization, which in many scenarios provides a provably more efficient method for high-dimensional exploration than sampling. We provide empirical and theoretical corroboration of the efficiency gains and soundness of our proposed method, and demonstrate its utility in constructing an efficient invariant network for a simple hierarchical object detection task when combined with unrolled optimization. Code for our networks and experiments is available at https://github.com/sdbuch/refine.

Related papers

• Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling [9.20186865054847]
  Anomaly detection (AD) is increasingly recognized as a key component for ensuring the resilience of future communication systems. This work considers AD in network flows using incomplete measurements. We propose a novel block-successive convex approximation algorithm based on a regularized model-fitting objective. Inspired by Bayesian approaches, we extend the model architecture to perform online adaptation to per-flow and per-time-step statistics.
  arXiv  Detail & Related papers  (2024-09-17T19:59:57Z)
• Improving Equivariant Model Training via Constraint Relaxation [31.507956579770088]
  Equivariant neural networks have been widely used in a variety of applications due to their ability to generalize well in tasks where the underlying data symmetries are known. We propose a novel framework for improving the optimization of such models by relaxing the hard equivariance constraint during training. We provide experimental results on different state-of-the-art network architectures, demonstrating how this training framework can result in equivariant models with improved generalization performance.
  arXiv  Detail & Related papers  (2024-08-23T17:35:08Z)
• Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling [22.256068524699472]
  In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. We combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.
  arXiv  Detail & Related papers  (2024-08-13T08:09:05Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Deep Neural Networks with Efficient Guaranteed Invariances [77.99182201815763]
  We address the problem of improving the performance and in particular the sample complexity of deep neural networks. Group-equivariant convolutions are a popular approach to obtain equivariant representations. We propose a multi-stream architecture, where each stream is invariant to a different transformation.
  arXiv  Detail & Related papers  (2023-03-02T20:44:45Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• A Simple Strategy to Provable Invariance via Orbit Mapping [14.127786615513978]
  We propose a method to make network architectures provably invariant with respect to group actions. In a nutshell, we intend to 'undo' any possible transformation before feeding the data into the actual network.
  arXiv  Detail & Related papers  (2022-09-24T03:40:42Z)
• The Self-Optimal-Transport Feature Transform [2.804721532913997]
  We show how to upgrade the set of features of a data instance to facilitate downstream matching or grouping related tasks. A particular min-cost-max-flow fractional matching problem, whose entropy regularized version can be approximated by an optimal transport (OT) optimization, results in our transductive transform. Empirically, the transform is highly effective and flexible in its use, consistently improving networks it is inserted into.
  arXiv  Detail & Related papers  (2022-04-06T20:00:39Z)
• Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration [77.99182201815763]
  Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets.
  arXiv  Detail & Related papers  (2022-02-08T16:16:11Z)
• Revisiting Transformation Invariant Geometric Deep Learning: Are Initial Representations All You Need? [80.86819657126041]
  We show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Exploring Complementary Strengths of Invariant and Equivariant Representations for Few-Shot Learning [96.75889543560497]
  In many real-world problems, collecting a large number of labeled samples is infeasible. Few-shot learning is the dominant approach to address this issue, where the objective is to quickly adapt to novel categories in presence of a limited number of samples. We propose a novel training mechanism that simultaneously enforces equivariance and invariance to a general set of geometric transformations.
  arXiv  Detail & Related papers  (2021-03-01T21:14:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.