Theoretical Framework & Computational Model

Interactive simulations of the compositional subspace model with adjustable parameters

Core Theory: Compositional Task Execution via Shared Subspaces

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.

Model Architecture
Stimulus Colour + Shape morph levels Colour Subspace Shared C1 & C2 Shape Subspace Used in S1 Task Belief Gain modulation Transformation Sensory → Motor Task-specific mapping Axis 1 Response Shared S1 & C1 Axis 2 Response Used in C2

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.

Task
Task Belief Strength 0.80
Colour Gain 1.00
Shape Gain 1.00
Noise (σ) 0.30
N Neurons 50
0.00
CPI
0.00
Colour Sep.
0.00
Shape Sep.
Neural Population Geometry C1
Red-Bunny
Red-Tee
Green-Bunny
Green-Tee

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.

Task
Transformation Speed 0.50
Sensory Onset (ms) 80
Motor Delay (ms) 60
Subspace Encoding Over Time
Colour Subspace
Shape Subspace
Motor Subspace
3D State Space Trajectory

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.

Learning Rate 0.15
Initial Belief (C1 vs S1) 0.30
Colour-Shape Gain Coupling 0.70
Number of Trials 110
Task Belief & Subspace Engagement Over Trials
Task Belief (C1)
Colour Subspace
Shape Subspace
Behavioural Performance & CPI
Accuracy
CPI

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.