Abstract

1. Cognitive Neuroimaging Seminar on Monday 18th Attractors in Song Abstract This talk summarizes our recent attempts to integrate action and perception within a single optimization framework. We start with a statistical formulation of Helmholtz's ideas about neural energy to furnish a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring the causes of our sensory inputs and learning regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain's organization and responses. We will demonstrate the brain-like dynamics that this scheme entails by using models of bird songs that are based on chaotic attractors with autonomous dynamics. This provides a nice example of how nonlinear dynamics can be exploited by the brain to represent and predict dynamics in the sensorium..

2. Overview • Inference and learning under the free energy principle • Hierarchical Bayesian inference • Bird songs (inference) • Perceptual categorisation • Prediction and omission • Bird songs (learning) • Repetition suppression • The mismatch negativity • A simple experiment

3. Exchange with the environment Sensation External states Internal states environment agent - m Action Separated by a Markov blanket

4. The free-energy principle Action to minimise a bound on surprise Perception to optimise the bound The conditional density and separation of scales Perceptual inference Perceptual learning Perceptual uncertainty

5. Mean-field partition Activity-dependent plasticity Perception and inference Learning and memory Synaptic activity Synaptic efficacy Functional specialization Attentional gain Enables plasticity Synaptic gain Attention and uncertainty

6. Hierarchical (deep) dynamic models

7. Empirical Bayes and DEM Bottom-up Lateral Recurrent message passing among neuronal populations, with top-down predictions changing to suppress bottom-up prediction error D-Step Perceptual inference Top-down E-Step Perceptual learning Associative plasticity, modulated by precision M-Step Perceptual uncertainty Encoding of precision through classical neuromodulation or plasticity of lateral connections Friston K Kilner J Harrison L A free energy principle for the brain.J. Physiol. Paris. 2006

8. Message passing in neuronal hierarchies Forward prediction error SG L4 IG Backward predictions

9. Overview • Inference and learning under the free energy principle • Hierarchical Bayesian inference • Bird songs (inference) • Perceptual categorisation • Prediction and omission • Bird songs (learning) • Repetition suppression • The mismatch negativity • A simple experiment

10. Synthetic song-birds Vocal centre Syrinx Sonogram Frequency 0.5 1 1.5 Time (sec)

11. prediction and error 20 15 10 5 0 -5 10 20 30 40 50 60 time Causal states 20 15 10 5 0 -5 -10 hidden states 10 20 30 40 50 60 time (bins) 20 15 10 5 0 -5 10 20 30 40 50 60 time Hierarchical recognition Backward predictions 5000 stimulus 4500 Forward prediction error 4000 3500 3000 2500 2000 0.2 0.4 0.6 0.8 time (seconds)

12. Perceptual categorization 5000 5000 5000 Song A Song B Song C 4000 4000 4000 Frequency (Hz) 3000 3000 3000 2000 2000 2000 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 time (seconds)

13. Overview • Inference and learning under the free energy principle • Hierarchical Bayesian inference • Bird songs (inference) • Perceptual categorisation • Prediction and omission • Bird songs (learning) • Repetition suppression • The mismatch negativity • A simple experiment

14. Sequences of sequences Neuronal hierarchy Syrinx sonogram Frequency (KHz) 0.5 1 1.5 Time (sec)

15. 5000 stimulus 4500 4000 3500 3000 2500 2000 0.5 1 1.5 time (seconds) Hierarchical perception prediction and error 50 percept 40 30 Prediction error encoded by superficial pyramidal cells that generate ERPs 20 10 0 -10 -20 20 40 60 80 100 120 time 50 50 50 40 hidden states 40 40 30 30 30 20 20 20 causes 10 10 10 0 0 0 -10 -10 -10 hidden states 20 40 60 80 100 120 -20 time 20 40 60 80 100 120 -20 20 40 60 80 100 120 time time

16. prediction and error hidden states 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 -20 -20 20 40 60 80 100 120 20 40 60 80 100 120 time time … omitting the last chirps causes - level 2 hidden states 50 50 40 40 30 30 20 20 10 10 0 0 -10 -10 -20 20 40 60 80 100 120 20 40 60 80 100 120 time time

17. 4500 4000 3500 Frequency (Hz) 3000 stimulus (sonogram) without last syllable 2500 5000 omission and violation of predictions 4500 4000 3500 Frequency (Hz) 3000 percept percept 2500 0.5 1 1.5 0.5 1 1.5 Time (sec) Time (sec) ERP (error) with omission 100 100 50 50 Stimulus but no percept 0 0 LFP (micro-volts) LFP (micro-volts) Percept but no stimulus -50 -50 -100 -100 500 1000 1500 2000 500 1000 1500 2000 peristimulus time (ms) peristimulus time (ms)

18. Overview • Inference and learning under the free energy principle • Hierarchical Bayesian inference • Bird songs (inference) • Perceptual categorisation • Prediction and omission • Bird songs (learning) • Repetition suppression • The mismatch negativity • A simple experiment

19. Repetition suppression and the MMN The MMN is an enhanced negativity seen in response to any change (deviant) compared to the standard response. Main effect of faces Suppression of inferotemporal responses to repeated faces Henson et al 2000

20. causes 0.5 5000 0.4 4500 0.3 4000 0.2 Frequency (Hz) 3500 0.1 3000 0 2500 -0.1 2000 -0.2 10 20 30 40 50 60 0.1 0.2 0.3 0.4 time Time (sec) Hierarchical learning Synaptic adaptation Synaptic efficacy 35 2 hidden states 30 prediction and error 25 1 20 15 0 10 5 -1 0 -5 -2 10 20 30 40 50 60 10 20 30 40 50 60 time time

21. hidden states percept prediction error 5 5000 10 4000 Simulating ERPs to repeated chirps 0 LFP (micro-volts) Frequency (Hz) 0 3000 -10 2000 -5 0 0.2 0.4 0.1 0.2 0.3 100 200 300 5 10 4000 0 LFP (micro-volts) Frequency (Hz) 0 -10 2000 -5 0 0.2 0.4 0.1 0.2 0.3 100 200 300 5 10 4000 Perceptual inference: suppressing error over peristimulus time Perceptual learning: suppression over repetitions 0 LFP (micro-volts) Frequency (Hz) 0 -10 2000 -5 0 0.2 0.4 0.1 0.2 0.3 100 200 300 5 10 4000 0 LFP (micro-volts) Frequency (Hz) 0 -10 2000 -5 0 0.2 0.4 0.1 0.2 0.3 100 200 300 5 10 4000 0 LFP (micro-volts) Frequency (Hz) 0 -10 2000 -5 0 0.2 0.4 0.1 0.2 0.3 100 200 300 5 10 4000 0 LFP (micro-volts) 0 Frequency (Hz) -10 2000 -5 0 0.2 0.4 0.1 0.2 0.3 100 200 300 Time (sec) peristimulus time (ms) Time (sec)

22. Synaptic efficacy Synaptic gain 3 6 Synthetic MMN 2.5 5 2 4 1.5 3 changes in parameters hyperparameters 1 2 0.5 1 0 0 1 2 3 4 5 1 2 3 4 5 presentation presentation 10 10 10 10 10 primary level prediction error 0 0 0 0 0 -10 -10 -10 -10 -10 First presentation (before learning) Last presentation (after learning) 100 200 300 100 200 300 100 200 300 100 200 300 100 200 300 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 secondary level -0.2 -0.2 -0.2 -0.2 -0.2 -0.4 -0.4 -0.4 -0.4 -0.4 100 200 300 100 200 300 100 200 300 100 200 300 100 200 300 primary level (N1/P1) secondary level (MMN) 20 0.4 15 0.2 10 0 5 Difference waveform Difference waveform 0 -0.2 -5 -0.4 -10 -15 -0.6 0 100 200 300 400 0 100 200 300 400 peristimulus time (ms) peristimulus time (ms)

23. repetition effects STG STG A1 A1 subcortical input Extrinsic connections Synaptic efficacy Synaptic gain Intrinsic connections 200 200 3 6 180 180 2.5 5 160 160 140 140 2 4 120 120 1.5 3 changes in parameters hyperparameters 100 100 80 80 1 2 60 60 40 40 0.5 1 20 20 0 0 0 0 5 1 2 3 4 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 presentation presentation presentation presentation Synthetic and real ERPs

24. Overview • Inference and learning under the free energy principle • Hierarchical Bayesian inference • Bird songs (inference) • Perceptual categorisation • Prediction and omission • Bird songs (learning) • Repetition suppression • The mismatch negativity • A simple experiment

25. CRF V1 ~1o Horizontal V1 ~2o Feedback V2 ~5o Feedback V3 ~10o A brain imaging experiment with sparse visual stimuli V1 Random and unpredictable Extra-classical receptive field ? V2 Coherent and predicable Classical receptive field V2 Classical receptive field V1 top-down suppression of prediction error when coherent? Angelucci et al

26. Suppression of prediction error with coherent stimuli Random Stationary Coherent V1 V5 V2 decreases increases pCG pCG V5 V2 V1 V5 regional responses (90% confidence intervals) Harrison et al NeuroImage 2006

27. Predictions about the brain This model of brain function explains a wide range of anatomical and physiological facts; for example, the hierarchical deployment of cortical areas, recurrent architectures using forward and backward connections and their functional asymmetries (Angelucci et al, 2002). In terms of synaptic physiology, it predicts Hebbian or associative plasticity and, for dynamic models, spike–timing-dependent plasticity. In terms of electrophysiology it accounts for classical and extra-classical receptive field effects and long-latency or endogenous components of evoked cortical responses (Rao and Ballard, 1998). It predicts the attenuation of responses encoding prediction error, with perceptual learning, and explains many phenomena like repetition suppression, mismatch negativity and the P300 in electroencephalography. In psychophysical terms, it accounts for the behavioural correlates of these physiological phenomena, e.g., priming, and global precedence.

28. Summary • A free energy principle can account for several aspects of action and perception • The architecture of cortical systems speak to hierarchical generative models • Estimation of hierarchical dynamic models corresponds to a generalised deconvolution of inputs to disclose their causes • This deconvolution can be implemented in a neuronally plausible fashion by constructing a dynamic system that self-organises when exposed to inputs to suppress its free-energy

29. Thank you And thanks to collaborators: Jean Daunizeau Lee Harrison Stefan Kiebel James Kilner Klaas Stephan And colleagues: Peter Dayan Jörn Diedrichsen Paul Verschure Florentin Wörgötter