Flexible information processing in complex networks: from brains to neuromorphic computing

Summary:

• Focus: computational neuroscience

  • How do brains generate complex behaviors?

• Interaction of complex areas:

  • Brain structure

  • Brain activity

  • Behavioral dynamics

• Complexity spans 

  • Single neurons:

    • Response to inputs

    • Dendritic integration, 

    • Action potential (‘decision’), 

    • Synaptic transmission

    • May change over time

  • Neuronal network dynamics:

    • Synchronization, oscillation, activity waves

    • Irregular, chaotic dynamics

    • Network function can depend on dynamical state

  • Functions

    • Signal gating

    • Binding by synchrony

    • Generation of behavioural outputs

  • Focus of talk: how can we use dynamical state dependency to affect computations in brain circuits

• Example: face made out of fruit can be seen holistically or as individual fruit

  • Attention can vary selectively

  • Can override default face detection neural circuitry to focus on fruits

• Collective neuronal oscillations

  • Not clear whether it is an epi-phenomenon or has a functional role in the brain

  • Hypothesis: communication through coherence

    • Suppose two different brain regions undergo oscillations in neural activity

      • Groups of neurons fire at some frequency

      • Individual neurons don’t participate in each firing but fire on-phase within the group’s common frequency

    • If two brain regions’ firing is aligned in phase (adjusted for speed of signal propagation between them) it's easier for them to communicate

    • This hypothesis is currently supported by indirect evidence but evidence base is evolving

• Analyzed the causal structure of brain firing

  • Delayed mutual information analysis

    • Take two signals X, Y, one delayed by a constant time relative to the other

    • Mutual information between X and Y: compare 

      • Join probability p(X,Y) to 

      • Independent probability p(X)p(Y)

      • Evaluate the entropy of the dependence

    • Generally not a symmetric relationship

      • Can be affected by auto-correlation within each time series

      • There are variants to adjust predictions of future X to remove information flow from past states of X (Transfer entropy)

  • Neural population: Wilson-Cowan Neural Oscillator

    • Two populations of neurons that excite/inhibit each other in a feedback cycle

    • These time series can be simplified to produce a time series of phase positions of the system in the cycle (more stable, less variable signal)

    • Can look at the dynamics of multiple such oscillators, accounting for the phase difference between their time series evolution

  • Analyze the behavior of two such oscillators

    • Circuit with biological parameters shows bistability of two phase locked states with offset phase difference

    • Information flows into a specific direction between the two oscillators for these offset phases

    • Two phase delays correspond to two different directions of information flow

  • Can use these dynamics to build dynamic signal routing mechanisms

    • Can flexibly couple / decouple circuits

    • Can flexibly change direction of signal flow

    • Can propagate signals in certain information flow pattern as long as the oscillator stays within its oscillation pattern (basin of attraction)

    • Modifying local oscillation frequency can dynamically change information flow of multiple remote oscillatory networks

    • Signals modify amplitude can communicate different information (Amplitude modulation-like)

    • Can build large hierarchical circuits from networks of multiple oscillatory subnetworks (networks of networks)

  • Modeled the use of these circuits for signal recognition

    • Hopfield Network architecture

    • Different sub-circuits detect different image sub-circuits (e.g. edges, stripes, colors)

    • Oscillator interactions dynamically couple these sub-circuits for image detection depending on the subnetworks performance

    • Only 'valuable' information is propagated through the network as context information

    • Currently researching learning mechanisms for these oscillator-based circuits