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Inference with correlated priors using sisters cells
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Proposes a sister-cell circuit motif, inspired by the olfactory bulb, that encodes correlated latent priors through covariance of sister-cell connectivity, avoiding direct granule-cell interactions, and analyses its geometry, inference performance, and estimability from responses.
Problem
Performing probabilistic inference of latent causes with correlated priors in neural circuits is architecturally hard because direct pairwise interactions among latent-cause units are biologically implausible or costly when the number of causes is large.
Approach
Sister cells receive the same receptor input but have different connections to latent-cause units; the covariance of their connection weights across sisters encodes the pairwise prior correlation, so correlated priors are implemented indirectly without direct latent-latent connections. Geometric arguments construct weight vectors whose inner products give the desired correlations, with zero-affini
Key results
- With correlated prior (5 correlated latents, 50 channels, 200 latents), the correlated-prior circuit achieves lower inference error than the independent-prior circuit across receptor noise levels, except at the highest noise where both perform equally poorly.
- Connectivity bound: correlations among n latents can be encoded when n <= S - M (sisters minus input channels), and there are nm - n(n+1)/2 degrees of freedom in the solution.
- Estimated priors from recorded sister-cell responses show mostly mild anticorrelation; the estimates for odour pairs co-occurring in essential oils are near zero, not positive as predicted.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a correlated prior instead of assuming feature independence | Sister-cell inference circuit · Noisy inference of five latent features | Euclidean error | Helped |
| Use a correlated prior instead of assuming feature independence | Sister-cell inference circuit · Highest receptor-noise levels | Euclidean error | No clear effect |
| Use sparse connectivity rather than random dense connectivity (ablation) | Sister-cell circuit encoding the same affinity and correlated prior · Sister-cell response similarity | Pearson correlation | Helped |
| Use weighted sparse connectivity rather than uniform sparse connectivity (ablation) | Sister-cell circuit encoding the same affinity and correlated prior · Sister-cell response heterogeneity across input channels | Pearson correlation | Mixed |
| Estimate inferred concentrations using a vapour-pressure function rather than assuming a constant concentration (ablation) | Correlated-prior estimates from recorded sister-cell responses · Olfactory response data | Estimated prior correlation | Helped |
Surprising findings
- Estimated priors from experimental sister-cell responses show anticorrelation for pairs that co-occur in essential oils, contrary to the naive expectation of positive correlation.
- Estimated correlated priors are all near zero for essential-oil co-occurring pairs, suggesting lack of the expected correlation.
Limitations
- Proof-of-concept with linear isotropic Gaussian observation model that may be too simplistic for real olfactory systems.
- Estimation of priors from sister responses relies on a grandmother-cell (one-hot) assumption that is not tested when relaxed.
- Limited evaluation: only a single stimulus corrupted across noise levels was tested in inference experiments.
Experimental setup
Datasets: experimentally recorded olfactory sister cell calcium responses (from cited study) essential oils database of 214 essential oils and monomolecular components
Metrics: Euclidean error between true and inferred feature vectors Pearson correlation of sister cell responses (response heter estimated prior correlations vs essential oil co-occurrence
Baselines: independent-prior inference circuit
Builds on: Gaussian Markov random field
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