computation-aware-kalman-neural-dynamics

name	computation-aware-kalman-neural-dynamics
description	Computation-Aware Kalman Filtering with Model Selection for Neural Dynamics - solving scale-imbalanced neural data analysis
version	1
category	neuroscience
activation_keywords	["neural dynamics","Kalman filtering","Bayesian inference","model selection","uncertainty quantification","computational uncertainty","latent variable model","neural recording","state-space model"]
created	2026-06-06T00:00:00.000Z
paper_id	arXiv:2606.01468
authors	JR Huml, Jonathan Wenger, John P. Cunningham
venue	2nd International Conference on Probabilistic Numerics (2026)

Computation-Aware Kalman Filtering with Model Selection for Neural Dynamics

Paper Summary

Problem: Modern neural datasets (single-cell recordings) are scale-imbalanced - fewer trials than recorded neurons. Bayesian methods model uncertainty well but scale poorly; deep networks scale well but lack uncertainty quantification.

Solution: Computation-Aware State-Space Model (CASSM) - extends computational uncertainty to model selection with novel training loss and optimization scheme.

Key Innovation: Tractable inference in large state-spaces while maintaining uncertainty calibration - competitive with data-hungry deep networks but with principled Bayesian framework.

Core Methodology

1. Scale-Imbalanced Regime

• Definition: Number of trials << number of recorded neurons
• Challenge: Standard Bayesian methods (Kalman) have O(n²) complexity
• Example: 50 trials, 1000 neurons → severe overfitting risk

2. Computation-Aware Framework

# Conceptual framework
class CASSM:
    """
    Computation-Aware State-Space Model for Neural Dynamics
    
    Key Components:
    1. Latent state dynamics: z_t = f(z_{t-1}) + noise
    2. Observation model: y_t = g(z_t) + noise
    3. Computational uncertainty: accounts for approximation error
    4. Model selection: adaptive hyperparameter optimization
    """
    
    def __init__(self, n_neurons, n_trials, state_dim):
        self.scale_imbalanced = n_trials < n_neurons
        self.state_dim = state_dim
        self.computational_budget = estimate_complexity(n_neurons, state_dim)
    
    def inference(self, observations):
        # Computation-aware filtering
        state_posterior, uncertainty = kalman_with_computational_error(
            observations,
            computational_budget=self.computational_budget
        )
        return state_posterior, uncertainty

3. Model Selection via Novel Training Loss