József Fiser

1. Exploring a sampling-based framework for probabilistic representation and computation in the cortex József Fiser Brandeis University Pietro Berkes Máté Lengyel, Gergő Orbán Brandeis University University of Cambridge

2. Outline • Challenges of the standard model of vision in the cortex • Proposal: the sampling hypothesis • How viable the sampling model is • Empirical evidence explained

3. Challenges • Behavioral: In many cases, animals' and humans' perception, action and learning is best captured by models that assume probabilistic representation and computation in the brain • Physiological: High level of structured spontaneous activity in the cortex that questions the feed forward nature of information processing and the role of ongoing activity • Coding:High trial-to-trial variability of cell responses even in primary sensory cortices that strongly interferes with reliable neural computation. Systematic variations of neural response variance is not explained by current theories.

4. The sampling hypothesis The cortex performs a probabilistic computation for inference and learning and to achieve this it uses a sampling-based neural representation in which spontaneous activity represents the prior information used for inference. • Probabilistic computation: Represents and computes with probability distributions in order to handle uncertainty. • Sampling-based: Distributions are represented by samples. • Spontaneous = prior: Spontaneous activity is not noise.

5. feature intensity2 orientation2 orientation1 firing rate neuron 1 firing rate trials / time neuron 1 variable 2 neuron2 variable 1 feature intensity1 Logic of sampling-based representation variable 2 variable 1

6. Functional role of spontaneous activity • Brightness coding in the primary visual cortex is factorized (Rossi et al. Science 1996) • Spontaneous activity = samples from the prior

7. Formalizing the relationship between SA and EA • Activity p(y | x) in absence of input stimuli (x) represent samples from the prior p(y) - and this isthe spontaneous activity. Natural scenes Spontaneous activity Evoked activity

8. Drifting grating • Complete dark (spont. activity) • Random noise • Natural scene movie Evidence of sampling based probabilistic representation in the awake cortex Visual Data collection • Awake, head-restrained ferrets • 4 age groups (P30, P45, P90, P120) • Multi-electrode recording with 200 µ spacing from layer 2-3 of V1

9. Results I • SA and EA in the Movie condition converge with age • In the adult animal, they do not differ significantly

10. Results II • The match between SA and EA is specific to natural scenes

11. Results III • The match between SA and EA is not specific to the visual modality

12. FAQ FHS

13. Why sampling just cannot be the answer • It is not clear how the neural circuitry can do it • It requires way too much time to collect sufficient number of samples • It must break down if the input is non-stationary • Limited number of samples must lead to bias in learning Well, let’s see…

14. How can sampling be inplemented in neural networks? Quite naturally • Gibbs sampling • Hamiltonian Monte Carlo – Langevin sampling:

15. A simple model of cue combination based on sampling • Task: given auditory and visual information where is the target? • Hamiltonian Monte Carlo – Langevin sampling:

16. How many samples are needed for accurate estimation? Surprisingly few • With 1 sample, the variance of the estimate is just twice the optimal (ML) variance • Sampling might be optimized by the cortex via minimizing the autocorrelation of successive samples:

17. What happens with non-static input? Things are actually getting better not worse • As long as the internal model is correct, the model will have no problem tracking the signal • Why is this happening? No need for burn-in, plus tighter prior

18. Can we learn with such a small number of sampels? Yes..... • Learning tuning curve positions and variances • Results

19. ✔ • It is not clear how the neural circuitry can do it ✔ • It requires way too much time to collect sufficient number of samples ✔ • It must break down if the input is non-stationary ✔ • Limited number of samples must lead to bias in learning Sampling can be the answer

20. Experimental results explained

21. Simulations Receptive fields • u – membrane pot. Gain [u-Thres]1.2 • ri - Poisson rate • ni - spike count • Trained on 80 000 patches of size 8x8 from the van Hateren image database • Maximum likelihood learning using Expectation Maximization

22. Specific questions • Can we reproduce our KL results? • Does the model agree on characteristics of variability measured in neural activity? • Contrast dependence of variability • Stimulus specificity of variability • Onset effects of variability • Stimulus specificity of co-variability

23. Sanity check • Sampling reproduces the KL divergence results

24. Contrast dependent variability of u Posterior Blank u2 High Blank P(z|x) High u1 • Sampling gives a natural link between contrast and variance

25. Stimulus dependent variability of u and the effect of stimulus onset SIMULATIONS Nonpreferred Preferred time (ms) • Sampling can reproduce both the stimulus independence of variability-change and the quenching effect of stimulus onset

26. Stimulus dependent co-variability of u EXPERIMENT SIMULATION (Yu & Ferster 2010 Neuron) • Sampling produces a reduced co-variability of the membrane potential at stimulus presentation just as it was found in vivo

27. Stimulus dependent co-variability of u EXPERIMENT SIMULATION Similar orientation preference Dissimilar orientation preference (Yu & Ferster 2010 Neuron) • Sampling can reproduce these correlational effects, too

28. Conclusions • Sampling based probabilistic schemes are viable alternatives for neural representation in the cortex providing a unified framework to investigate learning and instantaneous perception • Measures based on comparing SA and EA support the idea that the cortex uses sampling based representation and SA has the functional role of providing prior information for probabilistic perceptual inferences • The sampling based representations corroborate the idea that rather than using mostly first moments, cortical coding is strongly related to signal co-variances and higher order moments of the neural signal

29. Thank you !

30. The standard view on vision • The fundamental method of information processing in the visual system can be described as • deterministic computation with added neural noise • feed-forward • based on mean firings of cells • The function of the primary visual cortex in this framework is • restricted to represent only visual information • to create a faithful representation of the sensory stimulus with a neural code that is as sparse and independent as possible

31. Challenges • Behavioral: In many cases, animals' and humans' perception, action and learning is best captured by models that assume probabilistic representation and computation in the brain

32. 2D to 3D Orientationof stimulus s: stimulus Intensityof stimulus Life is uncertain and ambiguous… • Proposal The brain encodes both the value and the uncertainty of the stimulus during perception.

33. Probabilistic approaches in … • Classical conditioning (Courville et al. TICS 2006) • Perceptual processes (Kersten et al. Ann. Rev. Psych. 2006) • Visuo-motor coordination (Kording & Wolper Nature 2004) • Cue combination (Atkins et al. Vis Res 2001; Ernst & Banks Nature 2002) • Decision making (Trommershäuser et al. TICS 2008) • High-level cognitive processes (Griffiths & Tenenbaum TICS 2006) • Visual statistical learning (Orban et al. PNAS 2008) Is the neural computation deterministic?

34. Probabilistic computation in the brain Computation Orbán et al., 2008 Evidence

35. Challenges • Behavioral: In many cases, animals' and humans' perception, action and learning is best captured by models that assume probabilistic representation and computation in the brain • Physiological: High level of structured spontaneous activity in the cortex that questions the feed forward nature of information processing and the role of ongoing activity

36. Spontaneous activity in the awake brain Is it really noise?

37. Example: Stimulus onset quenches trial-to-trial variability Churchland & >25; Nat Neuro 2010 Why?

38. The sampling hypothesis

39. Probabilistic representation in the cortex Sampling-based Parametric • Probabilistic Population Codes (PPCs) • Earlier proposals: • Lee & Mumford 2003 • Hoyer & Hyvarinen 2003 • Predecessors: Kernel Dens. Estimation • Distr. Population Codes • Implicit examples: • Boltzmann machine • Helmholtz machine • Special cases: • Olshausen & Field 1996 • Karklin & Lewicki 2009

40. A simple model of the early visual system Sparseness and independence • e.g. Olshausen & Field 1996 • probabilistic formulation Perception is an inference process which is always based on internally available prior information

41. Looking for supporting evidence

42. Predictions With accumulating visual experience, the distribution of spontaneous activity should become increasingly similar to the distribution of evoked activity averaged over natural stimuli . • Probability of exhibiting a given neural activity pattern should be identical • Probability of transitioning between particular patterns should also match • Similarity should be specific to natural scenes but not to other stimulus ensembles

43. Data analysis

44. Results II • Both SA and EAMovie become increasingly correlated • Spatial correlations are similar between SA and EAMovie

45. Results III • Temporal correlations are similar between SA and EAMovie

46. White noise • (0-20 KHz) • Complete silence (spont. activity) • Natural speech Evidence of sampling based probabilistic representation in the awake cortex Auditory Data collection • Awake, head-restrained ferrets • One age group (adults) • Single-electrode single-unit recording in A1 Shamma-lab University of Maryland

47. Stimulus dependence of spike count correlations • Sampling can reproduce these correlational effects, too

48. Evidence against sparseness and independence • No support for active sparsification or increase of independence in the cortex

49. Relation between MP, mean, variance and Fano • MP variance decreases, both SC meand and variance increase, but the mean increases stronger therefore the Fano factor still decreases

50. (Ohki et al., 2006) (Hubel and Wiesel, 1962) Standard models of visual recognition Neural bases: System: