Predictive Coding beyond Gaussian Distributions (2211.03481v1)

Abstract: A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a neuroscience-inspired method that performs inference on hierarchical Gaussian generative models. These methods, however, fail to keep up with modern neural networks, as they are unable to replicate the dynamics of complex layers and activation functions. In this work, we solve this problem by generalizing PC to arbitrary probability distributions, enabling the training of architectures, such as transformers, that are hard to approximate with only Gaussian assumptions. We perform three experimental analyses. First, we study the gap between our method and the standard formulation of PC on multiple toy examples. Second, we test the reconstruction quality on variational autoencoders, where our method reaches the same reconstruction quality as BP. Third, we show that our method allows us to train transformer networks and achieve a performance comparable with BP on conditional LLMs. More broadly, this method allows neuroscience-inspired learning to be applied to multiple domains, since the internal distributions can be flexibly adapted to the data, tasks, and architectures used.

• The paper extends predictive coding from Gaussian assumptions to arbitrary distributions, enabling its use in modern neural network architectures.
• It introduces an energy formulation based on KL divergences to reconcile expected and observed distributions across network layers.
• Experiments on VAEs and transformer networks show that the generalized PC framework can match backpropagation performance.

Exploring Predictive Coding beyond Gaussian Distributions

In machine learning, predictive coding (PC) offers a neuroscience-inspired alternative to backpropagation (BP), traditionally reliant on Gaussian generative models. While promising in incorporating cognitive and sensory processing principles, classical approaches to PC are limited in their capacity to emulate contemporary complex neural networks. The paper, "Predictive Coding beyond Gaussian Distributions," seeks to surmount these challenges by generalizing PC to address arbitrary probability distributions—an essential stride towards accommodating models such as transformers that deviate from Gaussian assumptions.

Contribution and Methods

The authors formulate an extended framework for PC, allowing for the application of non-Gaussian distribution families. This generalization permits the modeling of complex distributions at each network layer, thus aligning with the intricate structures inherent in modern architectures. This adaptation extends the predictive coding framework without disrupting its foundational properties, maintaining an energy formulation where prediction-error terms are defined as Kullback-Leibler (KL) divergences between expected and observed probability distributions.

Three pivotal experiments underscore their methodological advancements:

1. Evaluation on Toy Examples: The paper contrasts their approach against standard PC formulations, noting performance gaps when extending beyond Gaussian assumptions.
2. Variational Autoencoders (VAEs): The new method exhibited comparable performance to BP in reconstructing variational autoencoders. This illustrates its facility in managing the trainable variances pivotal within such frameworks.
3. Transformer Networks for Language Processing: The paper demonstrates that generalized PC can effectively train transformer networks, achieving competitive results with BP on conditional LLMs. This marks a significant achievement, given that neuroscience-inspired methods have historically faltered in LLMing tasks.

Implications and Future Directions

The enhancements posited by this research have sweeping implications. By broadening the scope of PC to incorporate arbitrary distributions, the training of more sophisticated network architectures becomes feasible. This progression could revolutionize how neuroscience-inspired models are applied across numerous domains, fostering advances in areas reliant on complex task-specific architectures.

In practical terms, this work opens avenues for integrating PC with emerging neuromorphic and analog hardware—technologies that could benefit from PC's local computation characteristics and energy efficiency. The inherent parallelism of PC’s update mechanism offers substantial promise for enhancing computational efficiency, especially in large-scale, complex networks.

Looking forward, further exploration is warranted in determining optimal distributions for specific architecture types, as well as tuning the interplay between performance improvements and biological plausibility. The robustness of this generalized PC framework on extensive datasets and across diverse AI applications remains an intriguing avenue for investigation.

In conclusion, generalizing PC beyond Gaussian distributions effectively bridges a significant methodological gap, potentially accelerating the integration of biologically-plausible learning paradigms within the sphere of cutting-edge AI research. This paper stands as a foundation for future explorations that blend the realms of deep learning and cognitive neuroscience.