Improving Gradient Estimation in Asymmetric Neural Networks through Jacobian Homeostasis

Conceitos essenciais

Equilibrium propagation (EP) is a promising alternative to backpropagation for training neural networks on biological or analog substrates, but requires weight symmetry and infinitesimal perturbations. We show that weight asymmetry introduces bias in the gradient estimates of generalized EP, and propose a homeostatic objective to improve the functional symmetry of the Jacobian, enabling EP to scale to complex tasks like ImageNet 32x32 without perfect weight symmetry.

Resumo

The content discusses the challenges of using equilibrium propagation (EP) for training neural networks on physical substrates, where weight symmetry and infinitesimal perturbations are difficult to achieve.
The key insights are:

Weight asymmetry introduces two sources of bias in the gradient estimates of generalized EP: finite nudge size and Jacobian asymmetry.
The bias from finite nudge can be avoided by using a Cauchy integral to estimate the exact derivatives, as in holomorphic EP (hEP).
The bias from Jacobian asymmetry can be mitigated by introducing a homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point.
The homeostatic objective improves the performance of generalized hEP on complex tasks like ImageNet 32x32, with only a small gap compared to the symmetric case.
The homeostatic objective is more general than just enforcing weight symmetry, as it can also improve training in architectures without reciprocal connections.

Overall, the work provides a theoretical and empirical framework for studying and mitigating the adverse effects of physical constraints on learning algorithms that rely on the substrate's relaxation dynamics.

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Principais Insights Extraídos De

Improving equilibrium propagation without weight symmetry through Jacobian homeostasis

by Axel Laborie... às arxiv.org 04-09-2024

https://arxiv.org/pdf/2309.02214.pdf

Perguntas Mais Profundas

How could the homeostatic objective be implemented in a biologically plausible manner, e.g., through local synaptic plasticity rules

To implement the homeostatic objective in a biologically plausible manner, we can draw inspiration from local synaptic plasticity rules observed in the brain. One approach could involve incorporating a form of spike-timing-dependent plasticity (STDP) that adjusts synaptic weights based on the timing of pre- and post-synaptic spikes. By modulating the strength of connections between neurons based on the temporal relationship of their activity, the network can self-regulate and maintain a balance in the synaptic weights. This mechanism mimics the concept of homeostasis by dynamically adjusting synaptic strengths to promote functional symmetry in the network.

What other types of physical constraints or imperfections in neuromorphic substrates could be addressed using similar techniques

The insights from this work on addressing Jacobian asymmetry and bias in gradient estimates through homeostatic objectives can be extended to tackle various physical constraints and imperfections in neuromorphic substrates. For example:

Noise and Variability: By incorporating homeostatic objectives that promote stability and balance in neural activity, networks can become more robust to noise and variability in neuromorphic hardware.
Energy Efficiency: Implementing homeostatic mechanisms can optimize energy consumption by ensuring that neural networks operate efficiently and maintain stable dynamics.
Hardware Constraints: Addressing issues such as limited connectivity or non-ideal hardware characteristics through homeostatic objectives can enhance the performance and adaptability of neural networks on neuromorphic substrates.

Could the insights from this work be extended to other gradient-based learning algorithms beyond equilibrium propagation

The insights from this work can be extended to other gradient-based learning algorithms beyond equilibrium propagation. For instance:

Backpropagation: The concept of using homeostatic objectives to mitigate bias and improve gradient estimates can be applied to traditional backpropagation algorithms. By introducing mechanisms that promote symmetry and balance in weight updates, backpropagation can benefit from more stable and accurate learning.
Reinforcement Learning: Extending the idea of homeostatic objectives to reinforcement learning algorithms can help in maintaining stability and consistency in learning processes. By incorporating mechanisms that regulate learning dynamics, reinforcement learning models can achieve more reliable and efficient training.
Sparse Coding: Applying homeostatic principles to sparse coding algorithms can enhance the sparsity and efficiency of representations learned by the network. By promoting balanced activation levels and synaptic strengths, sparse coding models can achieve better encoding of information while minimizing redundancy.