Theoretical Framework & Computational Model
Interactive simulations of the compositional subspace model with adjustable parameters
The brain performs multiple tasks by reusing representational subspaces. Each task is executed by: (1) encoding the stimulus in a shared sensory subspace, (2) using a task-belief signal to selectively gate which sensory subspace is engaged, (3) transforming information from the relevant sensory subspace to the appropriate motor subspace, and (4) scaling (gain modulating) representations to amplify task-relevant and suppress task-irrelevant dimensions.
Interactive Simulation 1: Gain Modulation & Compression
Adjust the task belief strength to see how gain modulation amplifies task-relevant dimensions and suppresses irrelevant ones. The Compression Index (CPI) measures the log-ratio of colour vs. shape separability.
Interactive Simulation 2: Sensory-Motor Transformation Dynamics
Visualize how neural representations evolve over time during a trial. Information flows from the sensory subspace to the motor subspace, with the transformation being task-specific.
Interactive Simulation 3: Task Discovery Dynamics
Simulate how task belief evolves during a block and how it modulates the engagement of shared subspaces. This models the S1→C2→C1 task sequence where monkeys must discover the new task from feedback.
Theory Summary
Sequential Compositionality
Tasks are constructed by sequencing together shared subcomponents. For example, C1 = colour categorization (shared with C2) → axis 1 response (shared with S1). This is a form of "sequential compositionality" where the brain flexibly chains together operations from a library of shared computations.
Task Belief as Control Signal
The neural representation of the current task acts as a top-down control signal that selects which sensory and motor subspaces to engage. This belief is maintained in LPFC during fixation and updated via reward feedback. It enables the animal to navigate a "task manifold" parametrically modulating how different stimulus features influence decision-making.
Gain Modulation for Interference Control
Rather than using orthogonal/independent representations to avoid interference (as some models predict), the brain uses shared representations and dynamically modulates gain to amplify relevant and suppress irrelevant dimensions. This allows for both generalization across tasks and interference control within a single representational space.
Continual Learning Implications
Shared representations may facilitate continual learning. By suppressing irrelevant features, the brain constrains synaptic plasticity to task-relevant neural populations (since learning rules are activity-dependent and reward-gated). This addresses the credit assignment problem and may help explain resistance to catastrophic forgetting.