[Paper Review] Minimizing Control for Credit Assignment with Strong Feedback

Alexander Meulemans, Matilde Tristany Farinha+3 more|arXiv (Cornell University)|Apr 14, 2022

Neuroinflammation and Neurodegeneration Mechanisms4 citations

TL;DR

This paper introduces Strong-DFC, a biologically plausible credit assignment method that uses strong feedback signals to drive neural networks toward supervised targets, reframing optimization as minimizing control effort rather than minimizing loss. It enables simultaneous learning of forward and feedback weights using fully local, temporally synchronized plasticity rules, achieving competitive performance on vision benchmarks while remaining robust to noise—offering a novel control-theoretic perspective on deep learning that bypasses biologically implausible assumptions like weak feedback or weight tying.

ABSTRACT

The success of deep learning ignited interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals, which is problematic in biologically realistic noisy environments and at odds with experimental evidence in neuroscience showing that top-down feedback can significantly influence neural activity. Building upon deep feedback control (DFC), a recently proposed credit assignment method, we combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization. Instead of gradually changing the network weights towards configurations with low output loss, weight updates gradually minimize the amount of feedback required from a controller that drives the network to the supervised output label. Moreover, we show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using learning rules fully local in space and time. We complement our theoretical results with experiments on standard computer-vision benchmarks, showing competitive performance to backpropagation as well as robustness to noise. Overall, our work presents a fundamentally novel view of learning as control minimization, while sidestepping biologically unrealistic assumptions.

Motivation & Objective

• To address the biological implausibility of backpropagation in cortical networks, particularly its reliance on weak feedback and non-local weight updates.
• To develop a gradient-based credit assignment method compatible with strong top-down feedback, as observed in neuroscience, without requiring tightly coordinated plasticity phases.
• To enable simultaneous learning of forward and feedback weights using only local, temporally aligned signals, consistent with cortical microcircuitry.
• To demonstrate that minimizing control effort—rather than loss—can serve as a principled optimization objective in deep networks.

Proposed method

• The method uses a feedback controller that drives network activity to match a fixed supervised target, rather than weakly nudging the current output.
• Weight updates are derived from the negative gradient of a surrogate loss that quantifies the feedback control energy required to reach the target.
• The learning rule is fully local in space and time, depending only on pre- and post-synaptic activity and feedback signals at each synapse.
• Feedback weights are updated simultaneously with forward weights, eliminating the two-phase training requirement of prior methods like DFC.
• The framework leverages a dynamic feedback mechanism where strong feedback significantly alters neural activity, enabling robustness to noise.
• Theoretical analysis shows that under flexible feedback connectivity conditions, the updates follow the negative gradient of the control energy loss.

Experimental results

Research questions

• RQ1 Can strong feedback signals be used effectively in credit assignment for deep neural networks without compromising learning efficiency?
• RQ2 Does minimizing the control effort required to reach a target output lead to effective and stable training in deep networks?
• RQ3 Can forward and feedback weights be learned simultaneously using only local, temporally aligned plasticity rules?
• RQ4 How does the proposed method compare to backpropagation and standard DFC in terms of performance and robustness to noise?
• RQ5 Is the learning process invariant to sample reuse, suggesting potential for continual learning?

Key findings

• Strong-DFC achieves competitive performance on standard computer vision benchmarks, approaching the accuracy of backpropagation.
• The method is robust to noise in neural dynamics, outperforming standard DFC under high-noise conditions where DFC fails to train stably.
• Training without re-visiting samples yields nearly identical performance to standard training, indicating that Strong-DFC does not rely on repeated exposure to the same data.
• The alignment between Strong-DFC weight updates and the true gradient of the control loss is high, confirming the method's theoretical grounding.
• The ratio of feedback to forward input magnitude is comparable, demonstrating that feedback plays a significant role in shaping neural activity.
• Condition 1, which ensures the feedback matrix aligns with the network's steady-state dynamics, is well-satisfied, supporting the theoretical assumptions.