Twincher: Bijective Representation Learning for Robust Inversion of Continuous Systems

TL;DR

Twincher is a novel architecture that learns bijective representations of continuous systems, enabling robust and efficient inverse inference with improved data efficiency and noise robustness.

Contribution

The paper introduces Twincher, a new architecture based on structured diffeomorphic transformations and adversarial training for bijective representation learning.

Findings

Successfully learns bijective representations of synthetic systems.

Enables robust and efficient iterative inverse inference.

Shows improved data efficiency and robustness over baseline methods.

Abstract

Recent advances in AI have been primarily driven by large-scale neural architectures that excel at function approximation, rather than by tailored inductive biases and inference or learning strategies that could be important for resource-efficient real-world perception and planning through the solution of inverse problems. In this work, we consider the possibility of enabling robust inversion of continuous forward processes $p \mapsto y$ by learning representations of $y$ that are bijectively aligned with $p$ while remaining insensitive to perturbations in $y$ caused by noise or model mismatch. We propose Twincher, a class of architectures based on stacks of structured diffeomorphic transformations and tailored adversarial training strategies that enable learning such bijective representations. We provide a public API for training and inference and empirically demonstrate the ability of the proposed architecture to efficiently learn bijective representations of synthetic systems, thereby enabling robust and efficient iterative inverse inference. Compared to a baseline inverse-modeling approach, the method exhibits improved data efficiency and robustness, providing initial evidence for the potential of bijective representation learning in robotics, vision, and physical AI.