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Complex priors and flexible inference in recurrent circuits with dendritic nonlinearities
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Builds a recurrent neural circuit with dendritic ReLU tree nonlinearities trained with a diffusion-model denoising objective, whose oscillation-gated somatic noise yields prior samples and, with gated sensory/contextual inputs, posterior samples.
Problem
How the brain represents complex, high-dimensional structured priors (e.g., low-dimensional nonlinear manifolds) and flexibly combines them with sensory and contextual evidence for inference, given that existing neural sampling models handle only simple distributions.
Approach
Map diffusion-model reverse denoising steps onto a recurrent circuit whose dendritic trees (trained ANN with ReLU, tree-structured) compute the denoising mean, with a global oscillation beta_t modulating dendritic nonlinearity and somatic noise, so the dynamics sample from the prior once per cycle; likelihood gradients added as gated inputs yield posterior sampling.
Key results
- Neural circuit samples on a swiss-roll manifold show near-zero autocorrelation at short lags and marginal density matching uniform ground truth (KS p-value 0.145 along nonlinear dimension).
- Shallower, wider dendritic trees (depth 2 and 4) learned fastest and reached lower KL divergence than deeper trees in a grid search.
- Approximating the likelihood at x_{t-1} instead of mu_theta introduces KL discrepancies largest early in the reverse process that shrink toward zero over the cycle.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use neural sampling to generate samples from the Swiss-roll prior | Recurrent circuit with dendritic nonlinearities · Swiss-roll manifold, nonlinear dimension | KS-test p-value: 0.145 | No clear effect |
| Use neural sampling to generate samples from the Swiss-roll prior | Recurrent circuit with dendritic nonlinearities · Swiss-roll manifold, linear dimension | KS-test p-value: 0.125 | No clear effect |
| Vary dendritic tree depth and width while keeping parameter counts roughly constant (ablation) | Dendritic network trained on the Swiss-roll manifold · Swiss-roll manifold | Learning speed | Mixed |
| Replace dendritic nonlinearities with a fully connected stochastic neural network (ablation) | Neural sampling circuit · Swiss-roll manifold | Manifold sample quality | No clear effect |
Surprising findings
- Speed of learning does not scale monotonically with dendritic tree depth; the 7-layer network learned faster than the 5-layer network.
Limitations
- Learning of the circuit is not addressed; the authors focus only on dynamics and sampling quality with a dendritic model trained offline.
- Demonstrations are limited to toy 2D/10D manifolds and simple likelihoods (linear constraint, discrete context).
- Approximations (likelihood evaluated at x_{t-1}, sequential sampling) introduce biases, though small in the examples tested.
Experimental setup
Datasets: synthetic swiss-roll manifold (2D embedded in 10D) synthetic trimodal 2D mixture of manifolds
Metrics: KL divergence (histogram estimator) autocorrelation of samples Kolmogorov-Smirnov test
Baselines: DM reverse process
Builds on: denoising diffusion probabilistic models neural sampling score-based posterior sampling (Dhariwal and Nichol) tempered transitions
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