Flexible multitask computation in recurrent networks utilizes shared dynamical motifs

• https://github.dev/lauradriscoll/flexible_multitask

• set up 4 period (context, stimulus, memory, response)
  

  - input: 1(fixation) + 2(modalities) x 2(Asin(theta)andAcos(theta)) + 15(rule)
  - output: 1(fixation) + 1(modality) x 2(sin(phi) and cos(phi))

• fixed point and stability of that fixed point via analyzing linearization matrix (jacobian)

  • used approximation https://joss.theoj.org/papers/10.21105/joss.01003 tensorflow based

• single task network

  • shared fixed point in context dynamics, memory dynamics
  • during stimulus period, center → ring movement
  • during memory period, ring attractor shrink on memory PC subspace
    • by introducing interpolation alpha

• two task networks (MemoryPro, MemoryAnti)

  • shared ring attractor & two separate stable FP, one unstable FP
    • by introducing ‘rule input’ interpolation alpha

• task variance analysis - finding dynamical motifs
  - cluster 2 - reaction-timed response, cluster 9 - memory-guided responses
  - figure 3a. - cluster C has block → that color is for response
  - in fig 6, their ‘response’ dynamics interrupted with lesioned cluster c units
  

• exploiting these dynamical motif (similar subspace) with “rule interpolation”
  - (PCA on memory state)
  - task period cluster 6, unit clusters t and u / 9,10 with a-d: shared point/ring attractor
  

• shared stimulus period dynamical motifs

  • during stimulus period, if initial condition is similar, also is evolving steps.
  • during rule (context) period, network prepares future pathways (trajectories)

• interpolation with rule inputs by alpha
  - (PCA on stimulus state)
  - “connection bridge” by alpha was orthogonal to decision boundary
  - similar task share stable and unstable fixed point
  

• lesioning clustered RNN units - they found modular lesion effects on…

  • c: delayed response, f: anti-response task, modality 1/2, t/u: category memory, a/b continuous memory

• reusing dynamical motifs

  • train all task except MemoryAnti, all freeze except the input weights