«Sparse Coding on the Spot: Spontaneous Retinal Waves Sufﬁce for Orientation Selectivity Jonathan J. Hunt jjh Queensland Brain ...»
LETTER Communicated by Leonard E. White
Sparse Coding on the Spot: Spontaneous Retinal Waves
Sufﬁce for Orientation Selectivity
Jonathan J. Hunt
Queensland Brain Institute, University of Queensland, St Lucia,
Queensland 4072, Australia
National Vision Research Institute, Australian College of Optometry,
Carlton, Victoria 3053, Australia
Geoffrey J. Goodhill
Queensland Brain Institute and School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland 4072, Australia Ohshiro, Hussain, and Weliky (2011) recently showed that ferrets reared with exposure to ﬂickering spot stimuli, in the absence of oriented vi- sual experience, develop oriented receptive ﬁelds. They interpreted this as refutation of efﬁcient coding models, which require oriented input in order to develop oriented receptive ﬁelds. Here we show that these data are compatible with the efﬁcient coding hypothesis if the inﬂuence of spontaneous retinal waves is considered. We demonstrate that inde- pendent component analysis learns predominantly oriented receptive ﬁelds when trained on a mixture of spot stimuli and spontaneous retinal waves. Further, we show that the efﬁcient coding hypothesis provides a compelling explanation for the contrast between the lack of receptive ﬁeld changes seen in animals reared with spot stimuli and the signiﬁcant cortical reorganisation observed in stripe-reared animals.
1 Introduction The study of receptive ﬁeld development in the mammalian primary visual cortex has been an important source of insight into developmental plasticity.
There is strong evidence for environmental inﬂuence during critical periods (Stryker, Sherk, Leventhal, & Hirsch, 1978; Sengpiel, Stawinski, & Bonho- effer, 1999; Tanaka, Ribot, Imamura, & Tani, 2006; Hirsch & Spinelli, 1970;
Tani & Tanaka, 2008; Hubel & Wiesel, 1965, 1970; Wiesel & Hubel, 1965a, 1965b; Shatz & Stryker, 1978; Stryker, 1978; Shatz, Lindstrom, & Wiesel, 1977;
c 2012 Massachusetts Institute of Technology Neural Computation 24, 2422–2433 (2012) Sparse Coding on the Spot 2423 Kind et al., 2002; Schwarzkopf, Vorobyov, Mitchell, & Sengpiel, 2007;
Vorobyov, Schwarzkopf, Mitchell, & Sengpiel, 2007; Mitchell, Kennie, Schwarzkopf, & Sengpiel, 2009; Li, Fitzpatrick, & White, 2006), but recep- tive ﬁeld structure develops prior to eye opening (Hubel & Wiesel, 1963;
Crair, Gillespie, & Stryker, 1998) and spontaneous retinal waves are essen- tial for normal development (McLaughlin, Torborg, Feller, & O’Leary, 2003;
Cang et al., 2005; Huberman, Speer, & Chapman, 2006; Gjorgjieva & Eglen, 2011). The relative contributions of these various inﬂuences remain an area of active interest.
One theoretical approach to understanding receptive ﬁeld development, expounded by Barlow (1961), hypothesizes that the role of early sensory cortex is to encode input in efﬁcient representations for comprehension by higher brain areas. Sparse coding has been a particularly successful implementation of this hypothesis. Olshausen and Field (1996) demonstrated that a sparse coding model was able to learn realistic receptive ﬁelds from natural images. More recently, independent component analysis (ICA) has been used (Bell & Sejnowski, 1997; Van Hateren & Van der Schaaf, 1998), which also learns sparse codes when trained on natural scenes (Hyv¨ rinen, Hurri, a & Hoyer, 2009). Sparse coding models have been successful at explaining many aspects of receptive ﬁeld development, including temporal changes (Van Hateren & Ruderman, 1998) and color (Hoyer & Hyv¨ rinen, 2000; Caya wood, Willmore, & Tolhurst, 2004). Of importance to the work presented here, Albert, Schnabel, and Field (2008) demonstrated that ICA trained on a simple model of spontaneous retinal waves also learned oriented receptive ﬁelds.
Recently, Ohshiro, Hussain, and Weliky (2011) demonstrated an intriguing experimental result that appears to refute the efﬁcient coding hypothesis. They reared ferrets with visual experience consisting of ﬂashing spot stimuli. Despite receiving no oriented external visual experience, these animals developed near-normal levels of oriented receptive ﬁelds. Ohshiro and colleagues interpreted this result as a failure of the efﬁcient coding hypothesis and proposed an alternative correlation-based model of receptive ﬁeld development. Here we demonstrate that the inﬂuence of spontaneous retinal waves during development provides an alternative explanation for their ﬁndings. We show that an ICA model of receptive ﬁeld development trained with a mixture of spot stimuli and spontaneous retinal waves continues to learn oriented receptive ﬁelds even when retinal waves constitute only a small proportion of the training input.
We also examine why spontaneous retinal waves are able to exert this disproportionate inﬂuence on receptive ﬁeld formation and demonstrate that the sparsity of the spot stimuli is an important consideration in interpreting the Ohshiro et al. result. In particular, we show that another well-known visual manipulation, stripe rearing, results in changes in receptive ﬁelds that are more compatible with encoding retinal waves. This provides a coherent explanation for the lack of inﬂuence that spot stimuli had on receptive 2424 J. Hunt, M. Ibbotson, and G. Goodhill ﬁeld development, while stripe rearing results in signiﬁcant cortical reorganization (Blakemore & Cooper, 1970; Sengpiel et al., 1999; Tanaka et al., 2006).
2 Methods FastICA (Hyv¨ rinen, 1999) was used for unsupervised learning of static a receptive ﬁelds. The model was trained on 16 × 16 pixel image patches. As is standard practice (Hyv¨ rinen et al., 2009), dimensionality was reduced to a 100 dimensions using principal component analysis prior to ICA training.
The resulting projection matrix was taken to be the receptive ﬁelds.
Patches were acquired from 13 images of the natural world (same images as in Hyv¨ rinen & Hoyer, 2001). Retinal waves were simulated using a a simple percolation model (Albert et al., 2008). In this model, a fraction p sites on a square lattice were initially marked as potentially active. A starting point was chosen at random, and all potentially active points within a radius r were marked as active. The wave was propagated by iteratively activating potential sites with at least t active points within a distance r until no further sites could be activated. After wave propagation was completed, the result was low-pass-ﬁltered to ﬁll in small holes in the wave (see Albert et al., 2008, for full details of the model). This model was used with parameters p = 0.48, r = 3, t = 5. As in Albert et al., the percolation images were downsampled to 128 × 128 pixels before patches were extracted. Stripe-rearing input was simulated by ﬁltering the natural scenes with an oriented gaussian ﬁlter similar to Hsu and Dayan (2007).
Spot patches were created by randomly positioning 6 gaussian spots (σ 2 = 1 pixel) within each patch. The sign of the spot was chosen at random, and 100,000 patches were used for training each condition.
Receptive ﬁeld orientation selectivity index and bandwidth were calcu¨¨ lated as in Ohshiro et al. (2011) using methods from Worgotter, Muche, and Eysel (1991) and Ringach, Shapley, and Hawken (2002). Model training and characterization were implemented in Python using the modular tool kit for data processing (Zito, Wilbert, Wiskott, & Berkes, 2008).
Four types of training input were used in this study: natural scene input (see Figure 1A); percolation patterns (see Figure 1B), which are a model of spontaneous retinal waves, spot patches (see Figure 1C); and stripe-ﬁltered natural scenes (see Figure 1D). Spot patches, similar to the training input in Ohshiro et al. (2011), were the only unoriented stimuli.
The ICA model was trained with different combinations of these input types. As expected, receptive ﬁelds in the natural case and the percolation case are primarily edge-like (see Figures 1E, and 1F). In agreement with Ohshiro and colleagues, and intuition, the spot stimuli do not lead to Sparse Coding on the Spot 2425 Figure 1: Example inputs and receptive ﬁelds. Representative examples of the four input types used for training the ICA model: (A) natural scenes, (B) percolation patterns, (C) spots, and (D) stripe-ﬁltered scenes. (E) Natural scene input leads to strongly oriented receptive ﬁelds, as do the (F) percolation patterns, which simulate spontaneous retinal waves. (G) Spot stimuli do not result in oriented receptive ﬁelds; however, mixtures of natural scenes and spot stimuli (H, I) or percolation patterns and spot stimuli (J, K) all lead to signiﬁcant increases in oriented receptive ﬁelds (quantiﬁed in Figure 2). Stripe-reared mixtures (L) also result in strongly oriented receptive ﬁelds.
edge-like receptive ﬁelds (see Figure 1G). However, when the ICA model is trained on a mixture of spot stimuli and edge stimuli, signiﬁcant edgedetecting structure develops (see Figures 1H–1K). This occurs whether the edge stimuli are natural scenes or percolation patches.
2426 J. Hunt, M. Ibbotson, and G. Goodhill This result is quantiﬁed in Figure 2, which shows the orientation selectivity and bandwidth for the different conditions. The spot condition leads to an almost complete lack of orientation selectivity and broad receptive ﬁelds. However, when even small amounts (20%) of edge-like stimuli are included in the training, there is a dramatic recovery in edge-like structure.
This mixture may represent a better approximation to conditions experienced by the animals in Ohshiro et al. (2011), which spent the majority of their life in the dark. The inﬂuence of edge-like receptive ﬁelds in these mixtures is titrated in Figure 3, which demonstrates that even a small fraction of edge-like input inﬂuences receptive ﬁeld development disproportionality, and 40% edge-like input leads to orientation selectivity levels equal to receptive ﬁelds learned from pure edge-like input. This demonstrates that the inﬂuence of spontaneous retinal waves may explain the oriented receptive ﬁelds found in the spot-reared animals.
The mixtures containing spot stimuli also lead to a broadening of the receptive ﬁelds. This broadening does not occur when receptive ﬁelds are learned using infomax ICA (data not shown), although in that case, the receptive ﬁelds are generally broader in the normal case. Regardless of ICA algorithm, oriented receptive ﬁelds develop with only a small amount of edge-like input in the training data.
In contrast to the lack of change observed in spot rearing, several groups have previously demonstrated that animals reared with visual experience limited to a particular orientation develop signiﬁcant overrepresentation of the exposed orientation (Blakemore & Cooper, 1970; Sengpiel et al., 1999;
Tanaka et al., 2006). We examined whether these different outcomes could be understood by the efﬁcient coding hypothesis. We simulated stripe rearing using a mixture that contained 20% unﬁltered natural scenes (see Figure 1L), which resulted in a two times overrepresentation of horizontal edges. We examined whether different types of receptive ﬁelds are more or less compatible with representing retinal waves. We found that edge-like receptive ﬁelds resulting from training with natural scenes or stripes provided a much sparser representation of percolation patches than the unoriented receptive ﬁelds learned from the spot stimuli (see Figure 4). This was true even in the stripe-rearing case when there was signiﬁcant horizontal overrepresentation. If receptive ﬁelds are optimized during development toward sparsity, while receiving a combination of visual input and spontaneous retinal waves, this result may explain why some experimental manipulations, such as stripe rearing, result in dramatic receptive ﬁeld changes while other, less compatible manipulations result in a compromise that retains signiﬁcant edge structure.
Figure 2: Orientation selectivity and bandwidth. The (A) orientation selectivity and (B) orientation bandwidth of the receptive ﬁelds for the different rearing conditions (NS stands for natural scene input, perc for percolation). The spot condition, trained without oriented input, has little orientation selectivity and broad orientation tuning. However, adding even a small proportion of edged input (20% percolation, 80% spots) results in a signiﬁcant increase in orientation selectivity (p 0.0001) and a signiﬁcant reduction in orientation bandwidth (p 0.0001) to near-normal levels (p = 0.07 for the signiﬁcance of bandwidth differences between natural scenes condition and 20% percolation, 80% spots). When natural scenes rather than percolation mixtures are used, the results show an even sharper return to normal levels of orientation selectivity. Error bars show SEM. p-values are calculated with a two-sided unpaired t-test.
2427 2428 J. Hunt, M. Ibbotson, and G. Goodhill Figure 3: Titration of orientation selectivity with input mixtures. The orientation selectivity of the learned receptive ﬁelds increases rapidly with a small fraction of edge-like training input and asymptotes at ∼40% edge-like input.
This occurs for both percolation mixtures and natural scenes, although natural scene input has a stronger effect.
Figure 4: Sparsity of percolation representations. The probability distribution function of coefﬁcients for percolation patches when represented by different sets of receptive ﬁelds. The kurtosis value (k) is given in the legend. Spotlike receptive ﬁelds are extremely poor at representing edge-like stimuli such as percolation patches sparsely (negative kurtosis). Other edge-like receptive ﬁelds are able to represent other types of edged input relatively sparsely (large positive kurtosis values).
Sparse Coding on the Spot 2429 exposure to oriented input, provided spontaneous retinal waves are included. The input mixture used here is not identical to the experience of the animals, and any neural implementation of sparse coding may differ markedly from ICA; however, these details are unlikely to be crucial to the results. Our key ﬁnding is that sparse coding with a mixture of edge types may lead to important and nonintuitive changes in receptive ﬁeld structure.