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Maximum Manifold Capacity Representations in State Representation Learning

Li Meng, Morten Goodwin, Anis Yazidi, Paal Engelstad

TL;DR

This work presents an innovative integration of MMCR into existing SSL methods, incorporating a discerning regularization strategy that enhances the lower bound of mutual information and proposes a novel state representation learning method extending DIM-UA, embedding a nuclear norm loss to enforce manifold consistency robustly.

Abstract

The expanding research on manifold-based self-supervised learning (SSL) builds on the manifold hypothesis, which suggests that the inherent complexity of high-dimensional data can be unraveled through lower-dimensional manifold embeddings. Capitalizing on this, DeepInfomax with an unbalanced atlas (DIM-UA) has emerged as a powerful tool and yielded impressive results for state representations in reinforcement learning. Meanwhile, Maximum Manifold Capacity Representation (MMCR) presents a new frontier for SSL by optimizing class separability via manifold compression. However, MMCR demands extensive input views, resulting in significant computational costs and protracted pre-training durations. Bridging this gap, we present an innovative integration of MMCR into existing SSL methods, incorporating a discerning regularization strategy that enhances the lower bound of mutual information. We also propose a novel state representation learning method extending DIM-UA, embedding a nuclear norm loss to enforce manifold consistency robustly. On experimentation with the Atari Annotated RAM Interface, our method improves DIM-UA significantly with the same number of target encoding dimensions. The mean F1 score averaged over categories is 78% compared to 75% of DIM-UA. There are also compelling gains when implementing SimCLR and Barlow Twins. This supports our SSL innovation as a paradigm shift, enabling more nuanced high-dimensional data representations.

Maximum Manifold Capacity Representations in State Representation Learning

TL;DR

This work presents an innovative integration of MMCR into existing SSL methods, incorporating a discerning regularization strategy that enhances the lower bound of mutual information and proposes a novel state representation learning method extending DIM-UA, embedding a nuclear norm loss to enforce manifold consistency robustly.

Abstract

The expanding research on manifold-based self-supervised learning (SSL) builds on the manifold hypothesis, which suggests that the inherent complexity of high-dimensional data can be unraveled through lower-dimensional manifold embeddings. Capitalizing on this, DeepInfomax with an unbalanced atlas (DIM-UA) has emerged as a powerful tool and yielded impressive results for state representations in reinforcement learning. Meanwhile, Maximum Manifold Capacity Representation (MMCR) presents a new frontier for SSL by optimizing class separability via manifold compression. However, MMCR demands extensive input views, resulting in significant computational costs and protracted pre-training durations. Bridging this gap, we present an innovative integration of MMCR into existing SSL methods, incorporating a discerning regularization strategy that enhances the lower bound of mutual information. We also propose a novel state representation learning method extending DIM-UA, embedding a nuclear norm loss to enforce manifold consistency robustly. On experimentation with the Atari Annotated RAM Interface, our method improves DIM-UA significantly with the same number of target encoding dimensions. The mean F1 score averaged over categories is 78% compared to 75% of DIM-UA. There are also compelling gains when implementing SimCLR and Barlow Twins. This supports our SSL innovation as a paradigm shift, enabling more nuanced high-dimensional data representations.
Paper Structure (22 sections, 10 equations, 3 figures, 6 tables, 3 algorithms)

This paper contains 22 sections, 10 equations, 3 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-view self-supervised learning
  4. Manifold representations
  5. State representation learning
  6. Method
  7. Čech nerve
  8. Encoding space
  9. Unbalanced atlas
  10. Maximum manifold capacity
  11. Capacity as a regularizer
  12. Theorem 1.
  13. DeepInfoMax with capacity
  14. Experimental Details
  15. Results
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Presented on the left is an atlas of the circle, while on the right side is the Čech nerve of the circle. Each vertex of the graph indicates an individual chart of the atlas. Edges are drawn between pairs of vertices to indicate that their respective charts intersect with a non-empty region of overlap.
  • Figure 2: The F1 scores for different values of $\epsilon$ in (a) and different numbers of output units in (b). All other hyper-parameters are kept the same. Each value is an average of the F1 scores from five independent experiments.
  • Figure 3: The accuracy scores on CIFAR10 for choosing different numbers of heads while keeping the total number of output units fixed (i.e., $1\times2048$, $2\times1024$, $4\times512$, $8\times256$).

Theorems & Definitions (1)

  • proof