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. 2018 Jan 30;115(5):1105-1110.
doi: 10.1073/pnas.1710779115. Epub 2018 Jan 18.

Learning to make external sensory stimulus predictions using internal correlations in populations of neurons

Audrey J Sederberg  1   2 , Jason N MacLean  2   3 , Stephanie E Palmer  4   3   5
Affiliations

Learning to make external sensory stimulus predictions using internal correlations in populations of neurons

Audrey J Sederberg et al. Proc Natl Acad Sci U S A. .

Abstract

To compensate for sensory processing delays, the visual system must make predictions to ensure timely and appropriate behaviors. Recent work has found predictive information about the stimulus in neural populations early in vision processing, starting in the retina. However, to utilize this information, cells downstream must be able to read out the predictive information from the spiking activity of retinal ganglion cells. Here we investigate whether a downstream cell could learn efficient encoding of predictive information in its inputs from the correlations in the inputs themselves, in the absence of other instructive signals. We simulate learning driven by spiking activity recorded in salamander retina. We model a downstream cell as a binary neuron receiving a small group of weighted inputs and quantify the predictive information between activity in the binary neuron and future input. Input weights change according to spike timing-dependent learning rules during a training period. We characterize the readouts learned under spike timing-dependent synaptic update rules, finding that although the fixed points of learning dynamics are not associated with absolute optimal readouts they convey nearly all of the information conveyed by the optimal readout. Moreover, we find that learned perceptrons transmit position and velocity information of a moving-bar stimulus nearly as efficiently as optimal perceptrons. We conclude that predictive information is, in principle, readable from the perspective of downstream neurons in the absence of other inputs. This suggests an important role for feedforward prediction in sensory encoding.

Keywords: information theory; learning; plasticity; prediction; retina.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Spikes in sets of RGCs are informative of both past and future position and velocity of a moving-bar stimulus. (A) A population of RGCs was stimulated using a moving-bar stimulus, with dynamics of the stochastic overdamped harmonic oscillator. (Top) Phase plot of the dynamics with overlaid shading showing the distribution of bar position and velocity over the duration of the recording. (Bottom) Distribution of stochastic “kicks” to velocity. (B) Cross-section of the distribution of position and velocity of the bar stimulus relative to spiking in each of four RGCs, taken at two time points, Δt=−100 ms (Left, past) and Δt=+16.7 ms (Right, future). Prior distribution of position and velocity is shown as gray contours in background to illustrate how spiking in an RGC constrains expected values of bar position and velocity. (C) Stimulus information quantified for each of the four RGCs in B as a function of perispike time, from 150 ms before the RGC spike to 100 ms after. RGC 27 and 49 have large amounts of stimulus-predictive information (Δt>0). (D) Two example readouts (Left: solid black lines indicate strong connections and dashed gray lines weak ones). The readout-spike-triggered distribution of position and velocity was computed at perispike time Δt=−100 ms and Δt=+16.7 ms. Both readouts have high (5.1 and 5.4 bits per s) past information (Δt=−100 ms), but only the green readout has high stimulus-predictive information (4.2 bits per s). (E) Word–word internal predictive information is correlated with word–stimulus predictive information across sets of four cells. (F) The fraction of word–stimulus information carried by a readout is correlated with the fraction of internal word–word information carried by that readout. Grayscale shows density of readouts across the sets in E; superimposed dots show all perceptron readouts for this particular set of four cells. Purple and green dots are the example readouts from D. Error bars for information estimates are smaller than the marker size (<0.2 bits per s in E; <0.02 in F). EOM, equation of motion; info, information; pdf, probability density function; pred, predictive.
Fig. 2.
Fig. 2.
Internal predictive information can guide stimulus prediction without explicit reference to stimulus parameters. (A) Raster plot of spikes from a set of four RGCs (same cells as in Fig. 1) to a 19.2-s clip of a natural movie (frame, Top), with 51 (of 102 total) repetitions of the clip shown. A fish icon in later plots denotes calculations based on responses to the natural-movie stimulus. (B) Internal information reflects the spatial and temporal correlations in the stimulus. Average internal information of four-cell sets during the natural movie (green, longest timescale), moving bar (red), and checkerboard (yellow, shortest timescale). Shaded region represents ±1 SE across cell sets. (C) Stimulus-predictive information during the moving-bar movie is correlated with internal predictive information during the natural movie. Error bars smaller than marker size. (D) The fraction of word–stimulus information carried by a readout during the moving-bar stimulus is correlated with the fraction of internal word–word information carried by that readout during the natural movie. Shading represents average density of readouts across all randomly sampled sets of four cells (n = 240), with the readouts of one set of four cells (red; same set in Fig. 1 and A) overlaid. Most readouts have low predictive information. Error bars are <0.02, smaller than the point size. (E) For sets of 4 and of 10 cells, linear correlations between the readout-word internal predictive information and the readout-stimulus predictive information are high. The distribution of correlations in which readout identity was shuffled is shown for sets of four cells. pred. info., predictive information.
Fig. 3.
Fig. 3.
Near-optimal readouts are learned under STDP rules. (A) Learned readouts (dots) are close to the optimal perceptron hull (gray line); the highest internal predictive information of any readout at or a below a given firing rate. (B) Learned readouts for sets of 4 (black), 7 (red), and 10 (blue) cells capture a large percent of maximal predictive information, defined as the learned readout predictive information divided by the optimal perceptron hull value at that firing rate. Cumulative distributions are across cell sets and initial conditions. (C, Top) Two learned readouts, with their corresponding optimal readout. Each input word either evokes a readout spike (white box) or not (black box). (C, Bottom) Cumulative distribution of the similarity to the optimal rule of learned readouts. Similarity is the fraction of time bins with one or more input spikes for which the learned and optimal rule produced the same output (Materials and Methods). For sets of four cells, a large fraction (39%) of initial conditions led to learned readouts that were optimal. pred-I, predictive information.
Fig. 4.
Fig. 4.
Stimulus information of learned readouts is near-optimal. (A) Identification of a learned readout (blue) and its respective optimal readout (red) from a set of input 10 cells, with sampled readouts (gray) and the optimal perceptron hull (red line; see Fig. S1). Readout-word information is normalized by word–word information during the natural movie. (B) The full word (black line) captures the most stimulus information, but the learned (dashed blue line) and optimal (dotted-dashed red line) readouts have comparable stimulus information. Stimulus information is predictive over the Δt>0 portion of the curves. (C) Efficiency of typical readouts of stimulus predictive information relative to the full cell set (black) and relative to the optimal readout under natural-movie stimulation (red). As set size increases, efficiency remains high relative to the optimal readouts and decreases relative to the full word. Error bars represent SEM across sampled sets of cells. (D) For sets of 10 input cells the fraction of internal word–word information carried by a readout during the natural movie tends to be higher than the fraction of word–stimulus information carried by that readout during the moving-bar stimulus. A single cell set example is plotted as dots overlaid on the density, averaged across all sampled sets of 10 cells. info, information; prob, probability.
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