Multiscale causal emergence in task-optimized recurrent neural networks

Understanding how cognitive computations emerge from neural dynamics requires tools that can identify causally relevant structure across multiple scales - from individual units to population-level representations. Erik Hoel's Causal Emergence 2.0 (CE 2.0) provides a principled mathematical framework for this, but its formulation assumes discrete, autonomous, stationary Markov systems, rendering it inapplicable to task-optimized recurrent neural networks (RNNs) in their native form. Here, we introduce an extended framework, Driven Causal Emergence (DCE), that adapts CE 2.0 to the analysis of continuous, input-driven, non-stationary systems. Three core contributions make this possible. First, we replace arbitrary state-space discretization with geometry-aware coarse-graining derived from the intrinsic attractor structure of trained RNNs, using flow-field fixed-point analysis and persistent homology to define dynamically consistent macrostates that respect the network's learned computational geometry. Second, we extend the causal primitives formalism to driven Markov kernels, conditioning the transition probability matrices on task inputs via a systematic perturbation scheme, allowing causal contributions to be apportioned across scales separately for distinct trial epochs and task conditions. Third, we introduce a phase-resolved emergent complexity measure that tracks how the multiscale distribution of causal contributions evolves across task time, capturing the dynamic reorganization of causal structure between, for example, stimulus encoding, maintenance, and readout phases. We apply DCE to RNNs trained on a battery of canonical cognitive tasks (including perceptual decision-making, working memory, context-dependent integration, and motor timing) and ask whether different cognitive computations exhibit qualitatively distinct multiscale causal signatures. By grounding these analyses in networks trained to replicate well-characterized behavioural and neural phenomena, we argue that DCE offers a principled bridge between the computational level of cognitive function and the implementational level of neural population dynamics, opening a new avenue for understanding the brain's causal hierarchy.