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Controlled maximal variability along with reliable performance in recurrent neural networks
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Proposes NeuroMOP, which trains a feedforward value-function network to control input currents into a fixed random chaotic RNN so as to maximize future action-state entropy while avoiding terminal (absorbing) states, yielding high controlled neural variability with reliable task performance.
Problem
How neural variability can be maximized in neural networks without compromising behavioral/task performance, whereas prior work typically suppresses variability after learning to achieve high task performance.
Approach
Extends the maximum occupancy principle (MOP) from behavior to neural activity: an intrinsic, reward-free objective maximizing discounted future action entropy, with terminal states defined as absorbing dead states, so that the controller injects structured stochastic currents into a fixed random RNN and switches between stochastic and deterministic modes; the optimal policy is a Boltzmann over a
Key results
- In the energy-constraint task, NeuroMOP reaches the full episode length (T=1000) while showing larger average neural standard deviation than the epsilon-greedy R network, which suppresses activity to a low-energy silent regime.
- In the constrained neural space task, NeuroMOP confines two readout neurons within a square boundary while filling its interior, whereas the R network fails to occupy the region except at extremely small epsilon.
- Context-dependent NeuroMOP learns six shape constraints with a single network, with mean lifetimes reaching the training end of tend=5000 for some shapes and difficulty varying by shape.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| adapt action entropy to reduce stochasticity near the energy threshold | NeuroMOP · Energy constraint | lifetime | Helped |
| use state-dependent action selection rather than the R network’s fixed ε-greedy stochasticity | NeuroMOP versus R network · Constrained neural space | occupancy of available activity region | Helped |
| add context input to condition the value approximator on the required shape | NeuroMOP · Context-dependent neural space constraints | lifetime | Helped |
| add the approximated state-entropy term, increasing β (ablation) | NeuroMOP · Energy constraint | average standard deviation of activity jumps | Helped |
| add the approximated state-entropy term, increasing β (ablation) | NeuroMOP · Energy constraint | average standard deviation across trajectories | No clear effect |
| add the approximated state-entropy term with β = 1.5 (ablation) | NeuroMOP · Energy constraint | effective action dimensionality | Hurt |
| use noisy rather than deterministic RNN dynamics (ablation) | NeuroMOP · Energy constraint with noisy RNN | lifetime | Hurt |
| replace the saturating tanh transfer function with ReLU (ablation) | NeuroMOP · Energy constraint with ReLU RNN | lifetime | Helped |
| add extrinsic rewards to the MOP framework (ablation) | NeuroMOP · RNN behavior | variability | Hurt |
Surprising findings
- Reward-maximizing R networks can only avoid terminal states after extensive training and only by quenching their stochasticity, whereas MOP agents adapt entropy state-dependently.
- Introducing extrinsic reward into the MOP framework largely reduces network behavioral variability.
Limitations
- The policy is not learned; an oracle computes the exact optimal Boltzmann policy, and the computation of action selection remains costly.
- Only deterministic RNN dynamics with fixed weights are studied; spiking and Poisson-like variability is not addressed.
- Learning the structure of terminal states is not addressed.
Experimental setup
Benchmarks: energy constraint task constrained neural space (square boundaries) context-dependent shape constraints cartpole balancing (appendix)
Metrics: lifetime average standard deviation of activity effective action dimensionality state occupancy density
Baselines: R network (epsilon-greedy reward maximizer) free (uncontrolled) RNN
Builds on: maximum occupancy principle soft Q-learning / maximum entropy RL epsilon-greedy exploration
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