Recurrent Complex-Weighted Autoencoders for Unsupervised Object Discovery

Abstract: Current state-of-the-art synchrony-based models encode object bindings with complex-valued activations and compute with real-valued weights in feedforward architectures. We argue for the computational advantages of a recurrent architecture with complex-valued weights. We propose a fully convolutional autoencoder, SynCx, that performs iterative constraint satisfaction: at each iteration, a hidden layer bottleneck encodes statistically regular configurations of features in particular phase relationships; over iterations, local constraints propagate and the model converges to a globally consistent configuration of phase assignments. Binding is achieved simply by the matrix-vector product operation between complex-valued weights and activations, without the need for additional mechanisms that have been incorporated into current synchrony-based models. SynCx outperforms or is strongly competitive with current models for unsupervised object discovery. SynCx also avoids certain systematic grouping errors of current models, such as the inability to separate similarly colored objects without additional supervision.

• The paper introduces SynCx, a recurrent complex-weighted autoencoder that uses complex-valued weights and iterative phase propagation to achieve unsupervised object binding.
• Empirical evaluations show SynCx achieving superior object grouping performance (ARI 0.89 on Tetrominoes) and competitive results on other datasets without relying on external inductive biases.
• This approach simplifies entity segmentation and offers a more principled method for unsupervised object discovery, aligning with neurobiological theories and proving robust in challenging scenarios.

Recurrent Complex-Weighted Autoencoders for Unsupervised Object Discovery

The paper presents a novel approach for unsupervised object discovery through the employment of a recurrent architecture with complex-valued weights. The model, termed SynCx, is designed as a fully convolutional autoencoder that leverages iterative constraint satisfaction, contrasting with the existing synchrony-based models. Current state-of-the-art models utilize real-valued weights and an array of architectural features such as gating mechanisms to achieve object binding, which are shown to possess limitations in certain grouping scenarios and datasets. This paper argues that these extras are unnecessary, and instead, complex-valued weights can natively handle binding through the inherent properties of complex numbers, such as phase relationships.

Key Contributions and Methodology

The principal contribution of this research is the SynCx model, which employs complex-weighted matrix operations to achieve binding between objects. Significant features of SynCx include:

• Complex-Valued Weights: Previous models treated complex-valued activations but operated with real-valued weights. SynCx instead utilizes complex-valued weights entirely, which can handle constructive and destructive interferences devoid of additional mechanisms like χ-binding or cosine binding.
• Iterative Phase Propagation: A distinctive aspect of SynCx is its recurrent nature, where the model iteratively updates the phases of the activation maps, propagating soft constraints throughout. This aligns phases to achieve binding over iterations, akin to forming global interpretations of objects from local features.
• Avoidance of Inductive Biases: The SynCx model does not rely on contrastive training or pre-trained features, factors required by many contemporary models to avoid grouping errors on datasets with similarly colored objects.

Empirical Findings

SynCx has been evaluated on a set of diverse datasets (Tetrominoes, dSprites, and CLEVR) to quantify its object grouping efficacy. Notably, SynCx achieved superior performance on the Tetrominoes dataset, with an ARI of 0.89, indicating its reliability even when objects are similarly colored, a known challenge for other models like RF. While on dSprites and CLEVR, SynCx performed competitively with state-of-the-art models, it demonstrated the significant merit of its unsupervised binding ability without reliance on additional supervision.

Implications and Future Directions

The implications of adopting complex-valued weights for unsupervised learning are substantial. It removes the need for manual feature engineering and complicated network structures, providing a simpler, more principled approach to entity segmentation. The findings suggest potential applications in contexts where color is not a reliable cue and where unsupervised feature discovery remains paramount. Additionally, this research aligns with the temporal correlation hypothesis, strengthening the linkage between computational models and neurobiological phenomena.

Future research could explore augmentations to SynCx, such as integrating spatial priors and enhancing the clustering mechanism to account for phase value variances and outliers, enhancing the robustness of object discovery mechanisms. Additionally, employing a temporal difference loss to refine iterative phase adjustment further represents an intriguing future direction.

Overall, the work substantiates the theoretical considerations of complex-weighted neural structures and positions SynCx as a robust baseline for further explorations in synchrony and binding implementations within unsupervised neural networks.