On the Optimal Temporal Resolution for Information Representation in Neural Activity: A Theoretical Analysis

Although neural activity is organized across multiple temporal and spatial scales, the principles determining information representation across scales remain unclear. In particular, while recent empirical results have reported mesoscale optimality in neural decoding, no theoretical accounts exist that can explain when and why such intermediate scales emerge as optimal. Here, we develop an analytical framework to determine optimal temporal scales of neural information representation and their dependence on signal and noise dynamics.

We formulate a multiscale model where neural population activity is represented by temporally encoded trial vectors at micro-, coarse meso-, fine meso- and macroscale resolutions. Neural responses are modeled as stimulus-dependent mean activations corrupted by temporally correlated noise, with signal and noise autocorrelation decay rates varied parametrically. Representational quality is quantified using the sensitivity index (d-prime), measuring the ability of an optimal decoder to distinguish stimulus conditions.

We derive closed-form expressions for the sensitivity index at each temporal scale and identify signal and noise autocorrelations as key determinants of decodability. We then validate our theoretical predictions against empirical decodability estimates from synthetic neural data. Comparing these expressions under various combinations of signal and noise autocorrelations across time reveals two main regimes. First, when signal and noise correlations are absent or persistent over time, the optimal resolution falls at one of the two extremes: macroscale (resp. microscale) if signal autocorrelations are significantly stronger (resp. weaker) than noise autocorrelations. When both signal and noise autocorrelations decay, temporal integration creates a trade-off: moderate integration improves decodability by suppressing noise while preserving coherent signal, whereas excessive integration degrades signal and decodability. Therefore, only in the latter regime, mesoscale representations emerge as the optimal regime across a broad range of biologically plausible parameters.

This work provides a theoretical explanation for how optimal temporal scales depend on the interplay between signal and noise autocorrelations. The framework establishes temporal integration as a principled mechanism linking multiscale neural dynamics to information representation, explains when preprocessing operations such as binning and smoothing enhance or degrade decodability, and provides testable predictions across recording modalities and neural systems.