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Feedback control guides credit assignment in recurrent neural networks
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Shows that feedback control in pre-trained recurrent networks approximates first- and second-order gradients w.r.t. activations, and that this makes local RFLO-based learning more accurate and efficient during persistent visuomotor perturbation.
Problem
How biological recurrent circuits can perform accurate, efficient credit assignment with local plasticity, and how feedback-driven activity changes interact with local learning during motor adaptation.
Approach
Integrates a learned linear error-feedback projection into recurrent dynamics (feedback control) and shows that this injected signal approximates the true first-order (and partly second-order, Newton) gradient w.r.t. activations, decoupling network dynamics from past activity so that the RFLO eligibility-trace approximation becomes more accurate and efficient.
Key results
- Feedback contribution to network readout increases with perturbation (0 to 60 degrees), and the feedback signal aligns with the true first-order trial gradient w.r.t. activations during predicted movement.
- RFLO with feedback control (RFLO+c) achieves final MSE comparable to online BPTT at minor perturbations, with a growing gap to BPTT at larger perturbations.
- Learning efficiency ratio differs significantly between RFLO with and without control at all tested perturbation magnitudes; the difference disappears with BPTT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RFLO with feedback control during learning (RFLO+c) instead of RFLO without control (ablation) | Recurrent network adaptation · Visuomotor rotation task | MSE | Helped |
| Use RFLO+c instead of RFLO without control (ablation) | Recurrent network adaptation · Visuomotor rotation task with larger perturbations | MSE | Mixed |
| Add feedback control during learning (ablation) | RFLO recurrent-weight updates · Visuomotor rotation task | Global gradient alignment | Helped |
| Add feedback control during learning (ablation) | RFLO recurrent-weight updates · Visuomotor rotation task | Local gradient alignment | No clear effect |
| Add feedback control during learning (ablation) | Online RFLO weight updates · Visuomotor rotation task | Weight-update efficiency | Helped |
| Add feedback control during learning (ablation) | Online BPTT weight updates · Visuomotor rotation task | Weight-update efficiency | No clear effect |
| Inject online feedback control into recurrent activity (ablation) | Pre-trained recurrent network · Visuomotor rotation task | Alignment with first-order activity gradient | Helped |
| Inject online feedback control into recurrent activity (ablation) | Pre-trained recurrent network · Visuomotor rotation task | Sensitivity to past activity | Helped |
| Add the RFLO eligibility-trace derivative term Φ′(aj) (ablation) | Local learning rule from Feulner et al. (2022) · Visuomotor rotation task | Learning stability | Helped |
| Use feedback control during the first perturbed movement (ablation) | Pre-trained recurrent network · 30° target rotation | Movement correction | Helped |
| Use feedback control while training with RFLO (ablation) | Recurrent network · Persistent visuomotor perturbation | Dependence on feedback control at test | Helped |
Surprising findings
- The efficiency advantage of feedback control disappears when using more accurate BPTT gradients.
- Local gradient alignment differs only slightly between RFLO with and without feedback control, yet the difference compounds to a clear global alignment gap.
Limitations
- Evaluated only on a simple single-layer RNN and a simple centre-out reaching task (plus a toy sine/cosine task).
- Feedback is a simple linear projection of signed error; more biologically realistic feedback forms are untested.
- Biological implementation of the feedback signal and the local learning rule is left unresolved.
Experimental setup
Datasets: synthetic instructed-delay centre-out reaching task sine and cosine wave toy task
Benchmarks: synthetic centre-out reaching with visuomotor rotation (30-60 degrees)
Metrics: MSE cosine similarity of gradients Jacobian norm efficiency ratio of global to summed local weight updates
Baselines: BPTT BPTT+c RFLO online BPTT
Builds on: RFLO Feulner et al. 2022 feedback-control RNN Real-Time Recurrent Learning Meulemans et al. 2022 target propagation/optimal control
Closest papers by meaning
- Biological credit assignment through dynamic inversion of feedforward networks (NeurIPS 2020 · similarity 0.92)
- Credit Assignment in Neural Networks through Deep Feedback Control (NeurIPS 2021 · similarity 0.91)
- Learning to Learn with Feedback and Local Plasticity (NeurIPS 2020 · similarity 0.89)
- Learning Nonlinear Dynamics in Efficient, Balanced Spiking Networks Using Local Plasticity Rules (AAAI 2018 · similarity 0.89)
- Learning Dynamics of RNNs in Closed-Loop Environments (NeurIPS 2025 · similarity 0.88)
- Discovering plasticity rules that organize and maintain neural circuits (NeurIPS 2024 · similarity 0.88)
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