Omri Barak

October, 2016

Mixed selectivity and reservoir computing

Understanding the brain

Neural correlates of behaviorA model (more or less formal) that links neural activity to behavior

Neural correlates

Traditionally answered by considering single neurons.

Nice neurons for nice models

Clear (pure) selectivity inspires models

Serre, Oliva, Poggio 2007Ben Yishai et al 1995Blumenfeld et al 2006Machens et al 2005

Input/output specification

Low dimensional dynamics

High dimensional neural network

Behavior

Neural data

The conventional way of understanding

Formalize:

Understand:

Implement:

Mixed selectivity

Neurons change their tuning based on context.

Barak et al 2010Rigotti et al 2013

Raposo et al 2014

Input/output specification

Low dimensional dynamics

High dimensional neural network

Implementation

Behavior

Neural data

Algorithmichypothesis

Machine learning

The conventional way of understanding

Recurrent neural networks(Echo state, Liquid state, Reservoir)

Dominey et al 1995Buonomano and Merzenich 1995Jaeger 2001Maass et al 2002

Comparison to experiment

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Simulation Experiment

Barak et al. 2013

Mixed selectivityA3A1 A2

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Engineered:

Trained:

Data

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Barak et al. 2013

The Machine learning way(Recurrent neural networks)

TrainIt works!It has some stuff that looks like neurons!

We have no clue how it works…

But how does it work??

Input/output specification

Low dimensional dynamics

High dimensional neural network

Implementation

Behavior

Neural data

Algorithmichypothesis

Machine learning

Reverseengineering

Opening the black box

We developed an algorithm to find fixed points in trained neural networks.

Sussillo & Barak 2013

RNNs explain data & mechanism

Context dependent computationMante et al. Nature 2013

Dynamics of dACC during complex taskEnel et al. PLoS Comp Bio 2016

Representing temporal expectationsCarnevale et al. Neuron 2015

Sequene generationRajan et al. Neuron 2016

Similar work is being done in deep (feedforward) neural networks (DiCarlo).

What is missing?

Trajectory vs. dynamicsInvariance of solutionsLimits of the approachDesign considerationsA good forward model help reverse engineering

… Theory

Our approach

Thorough understanding of very simple tasks.

Analytical solutionsBuilding block for more complex tasks.

Rivkind & Barak, Arxiv

Conclusions

Focusing on single neurons has its limits.Understanding population dynamics is a hard task.Combining machine learning and dynamical systems can lead to new insights.Doing this properly requires theoryLow-D dynamics can be the relevant quantity to look for in models & data.

Conceptual framework

Input/output specification

Low dimensional dynamics

High dimensional neural network

Behavior

Neural data

Algorithmichypothesis

Machine learning

Reverseengineering

Implementation

Low D dynamics

Dimensionality reduction

Thank you

Lab members:

Oded BarzelayAlexander RivkindXu Tie

Funding:

ERC FP7 CIG 2013-618543Fondation Adelis;

Collaborators:

David SussilloLarry AbbottMisha TsodyksRanulfo RomoStefano FusiMattia RigottiMelissa WardenEarl MillerFederico CarnevaleNestor Parga

Reward No Reward

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