Source-linked AI summary
Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control
Rodrigo Laje, Dean V. Buonomano
TL;DR
Chaotic recurrent dynamics are difficult to exploit because noise destabilizes trajectories and recurrent plasticity is often unreliable. The paper trains random recurrent networks to reproduce their innate trajectories, producing locally stable transient channels that improve timing and noisy motor-pattern generation while retaining chaotic dynamics elsewhere.
Problem
Chaos makes recurrent trajectories highly sensitive to noise, while existing learning rules are often ineffective or unstable in high-gain recurrent networks.
Method
The authors use supervised RLS training to make recurrent units reproduce their own noise-free innate trajectory over a defined training window.
Results
Innate training converted selected chaotic trajectories into locally stable transient channels while preserving chaotic trajectories elsewhere, improving timing and complex motor-pattern generation under noise.
Takeaways & Limitations
Recurrent plasticity can locally suppress chaos and support robust computation through complex, time-varying neural trajectories.
Takeaways & Limitations
The learning strategy is highly supervised, computationally sophisticated, fast, and not biologically realistic; biologically plausible alternatives remain to be tested.
Abstract
from arXiv · showhide
It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset.
INTRODUCTION
Recurrent networks offer computational advantages through complex high-dimensional trajectories, but chaos and unstable recurrent plasticity hinder reliable computation. The paper addresses these challenges by using supervised plasticity to create locally stable trajectories within otherwise chaotic random recurrent networks.
- Complex recurrent trajectories can support computation in high-dimensional activity space.
- High-gain recurrent networks often generate chaotic, self-sustained activity patterns.
- Noise can make chaotic trajectories diverge, preventing reliable reproduction of a computational pattern.
- Recurrent plasticity is difficult because conventional and experimentally derived learning rules are often ineffective or unstable in high-gain recurrent networks.
- Supervised recurrent learning transforms previously chaotic trajectories into locally stable transient channels while preserving coexisting chaotic trajectories.
- These stable trajectories improve timing and complex motor-pattern generation under high noise.
“Innate” Training
Innate training tunes random recurrent networks to reproduce their own noise-free trajectories, creating stimulus-specific stable transient channels within otherwise chaotic dynamics. These channels improve robustness, timing, and complex motor control under noise and perturbation.
- Network dynamics: For large firing-rate networks, g>1 produces increasingly complex and chaotic activity patterns.
- Innate training: Recurrent weights are trained to reproduce an innate trajectory, defined as the noise-free activity elicited by a given input before training.
- Innate training: RLS training over a 2 s window preserves the innate trajectory while making it locally attracting within that window.
- Noise robustness: Over noise amplitudes up to 0.1, trained networks reproduced the In1 trajectory with essentially perfect performance, whereas In2 reproducibility was abolished.
- Noise robustness: R=0.96 ± 0.06 for In1 and R=-0.17 ± 0.16 for In2 quantified accurate trained-trajectory reproduction and stimulus specificity.
- Suppression of chaos: After training, In1 had λ=0.05 ± 0.45, while In2 remained divergent with λ=3.05 ± 0.70.
- Timing: Training created stable transient channels that supported delayed timing outputs across tested recurrent architectures.
- Motor control: Trained networks generated complex handwriting patterns despite continuous noise and returned toward the original trajectory after strong perturbations.
Experimentally Observed Decreases in Variability
After training, recurrent networks generated appropriately timed outputs despite high noise, while activity variance decreased after stimulus onset. This produced distinct pre- and post-stimulus variability patterns alongside robust task performance.
- Before stimulation, continuous high noise produced significant firing-rate jitter and high cross-trial variance.
- Trained networks generated appropriately timed outputs despite readily apparent jitter in individual units under very high noise.
- Training produced a dramatic decrease in activity variance after stimulus onset.
Mechanisms: Network Structure After Training
Training altered recurrent-network structure through stronger, non-Gaussian weights and increased clustering. Shuffling weights while preserving their distribution and connectivity disrupted stability, implicating precise wiring and cyclic motifs.
- 0.147 ± 0.001 was the post-training median absolute synaptic weight, up from 0.1358 ± 0.0004 pre-training.Training produced longer-tailed, non-Gaussian weight distributions without changing which units were connected.
- Shuffling trained weights destroyed network stability despite preserving the weight distribution and binary connectivity.
- 0.0139 ± 0.0001 was the post-training median cyclic clustering coefficient, compared with 0.01270 ± 0.00005 pre-training.Training increased the right tail of cyclic clustering distributions, indicating stronger short-range recurrency.
- Shuffling altered cyclic clustering distributions more consistently than non-cyclic distributions, with all cyclic comparisons yielding p<0.002.The authors suggest cyclic clusters may contribute to complex yet stable trajectories, while input–network interaction also shapes the resulting dynamics.
DISCUSSION
Recurrent synaptic tuning transformed initially chaotic trajectories into locally stable ones while preserving chaotic dynamics elsewhere. These learned stable trajectories persisted over behavioral timescales despite fast unit dynamics.
- Training transformed initially chaotic trajectories into locally stable trajectories through appropriate tuning of recurrent synapses.
- The trained networks contained coexisting stable and chaotic trajectories, providing two self-generated modes of neural dynamics.
- Learned trajectories remained locally stable for many seconds despite 10 ms unit time constants.The discussion places these stable trajectories within the timescale of most behavioral tasks.
Plasticity Within Recurrent Networks
The study demonstrates that supervised recurrent plasticity can enhance computation in high-gain random recurrent networks, while acknowledging that the specific learning strategy is not biologically realistic. This approach is relevant to computational neuroscience and reservoir computing because it combines complex dynamics with reduced noise sensitivity.
- Recurrent plasticity in high-gain networks dramatically enhanced their computational power relative to prior approaches described by the authors.
- The learning rule was highly supervised and not biologically realistic, using computationally sophisticated, unrealistically fast RLS and separate target patterns for each unit.
- Future research must determine whether similar dynamical regimes can be achieved with biologically plausible learning rules.
- Modifying recurrent weights may let reservoir-computing networks harness complex dynamics while avoiding their usual noise sensitivity.
Structure and Mechanisms of Underlying Stable Trajectories
After training, the same nonlinear recurrent network can produce different responses to different inputs, while its recurrent weights develop reproducible, non-random structural signatures associated with stable trajectories.
- Input–recurrent interactions: Input connectivity and recurrent weights jointly shape whether a continuous-time nonlinear network follows locally stable or unstable trajectories.The same trained network can respond very differently to different inputs.
- Recurrent weight structure: Training robustly increases the median absolute recurrent weight and produces a non-Gaussian, long-tailed weight distribution.
- Recurrent weight structure: Training also changes cyclic clustering coefficients to a highly non-random distribution, suggesting altered short-range recurrent circuitry may support stable trajectories.
Computational Implications and Experimental Predictions
The trained networks generate robust, reproducible trajectories for timing and complex motor output, and reproduce stimulus-related reductions in neural variability. These results motivate testable predictions about learned, stimulus-specific trajectories in cortical circuits.
- Experimental correspondence: Stimulus-evoked trajectories show lower cross-trial variability than spontaneous activity, and the networks reproduce the observed variance decrease after stimulus onset.
- Experimental predictions: The paper predicts that familiar stimuli elicit preferred stable trajectories lasting many seconds and robust to noise, unlike spontaneously active unstable trajectories.
- Experimental predictions: The predicted variance drop should be larger and longer-lasting for overtrained stimuli than for novel or irrelevant stimuli.
- Computational consequences: Trained recurrent networks time events under substantial noise and generate complex time-varying motor patterns.
- Computational consequences: Dynamic or transient attractors let networks return to trained patterns after large perturbations, providing high robustness in a high-dimensional nonlinear system.
- Neuroscientific implication: The findings address how neural circuits could combine chaotic regimes with reproducible trajectories required for sensory and motor processing.
Comparison to other chaos-related regimes
The trained networks differ from previously described chaos-related regimes because their locally stable trajectories result from explicit system modifications and remain transient within an otherwise chaotic system.
- Distinctive mechanism: Unlike natural stable-transient regimes in intact systems, the reported stable transient channel is created by explicit modifications to the system.
- Regular chaos: Regular chaos can contain locally convergent trajectory segments, but long stable trajectories are unlikely because trajectories generally diverge.
- Stable chaos: Stable chaos involves irregular transients with negative LLE that generally approach periodic solutions, whereas these networks can remain formally chaotic outside training windows or under different inputs.
- Stable chaos: The reported networks exhibit locally stable trajectories under large perturbations, unlike the finite-size perturbation behavior described for stable chaos.
- Strange nonchaotic attractors: Strange nonchaotic attractors are invariant complex solutions, whereas the networks’ stable trajectories are transient and the non-positive LLE can be limited to trained trajectories.
- Transient chaos: Transient chaos has locally positive LLE during transients, opposite to the locally non-positive LLE reported for these stable transients.