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# A Biologically Plausible Neural Network for Slow Feature Analysis

NIPS 2020, (2020)

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Abstract

Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting...More

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Introduction

- Unsupervised learning of meaningful latent features from noisy, high-dimensional data is a fundamental problem for both machine learning and brain function.
- The relevant features in an environment vary on relatively slow timescales when compared to noisy sensory data.
- Temporal slowness has been proposed as a computational principle for extracting relevant latent features [8, 19, 31].
- When trained on natural image sequences, SFA extracts features that resemble response properties of complex cells in early visual processing [2].
- Hierarchical networks of SFA trained on simulated rat visual streams learn representations of position and orientation similar to representations encoded in the hippocampus [9]

Highlights

- Unsupervised learning of meaningful latent features from noisy, high-dimensional data is a fundamental problem for both machine learning and brain function
- Hierarchical networks of Slow Feature Analysis (SFA) trained on simulated rat visual streams learn representations of position and orientation similar to representations encoded in the hippocampus [9]
- To derive an SFA network, we identify an objective function whose optimization leads to an online algorithm that can be implemented in a biologically plausible network
- Our network includes direct lateral inhibitory synapses between excitatory neurons, whereas inhibition is typically modulated by interneurons in biological networks
- Iteration (d) Slowness of SFA output require both the pre- and post-synaptic neurons to store slow variables; signal frequencies in dendrites are slower than in axons, suggesting that it is more likely for slow variables to be stored in the post-synaptic neuron, not the pre-synaptic neuron

Methods

- The authors test Bio-SFA (Alg. 1) on synthetic and naturalistic datasets.
- The evaluation code is available at github.com/flatiron/bio-sfa.
- To measure the performance of the algorithm, the authors compare the “slowness” of the projection Y = M−1WX, with the slowest possible projection.
- This can be quantified using the objective (6).

Conclusion

- The authors derived an online algorithm for SFA with a biologically plausible neural network implementation, which is an important step towards understanding how the brain could use temporal slowness as a computational principle.
- Slowness (a) Layered architecture (b) SFA firing maps (c) ICA firing maps (d) Slowness of SFA output require both the pre- and post-synaptic neurons to store slow variables; signal frequencies in dendrites are slower than in axons, suggesting that it is more likely for slow variables to be stored in the post-synaptic neuron, not the pre-synaptic neuron.
- An interesting future direction is to understand the effect of enforcing a nonnegativity constraint on yt in the objective function (9)

Reference

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- 2. The second layer consists of a 2-dimensional array of 8 × 2 Bio-SFA modules. Each module receives inputs from a 14 × 6 grid of modules from the first layer, again overlapping each other by half their length in each dimension. Since the output of each module in the first layer is 32-dimensional, the vectorized input to each module has dimension 2688 = 32 × 14 × 6. The output of each module in the second layer is a sequence of 32-dimensional vectors.
- 3. The third layer consists of a single Bio-SFA module that receives input from all 8 × 2 modules in the second layer. Thus, the input to the third layer module has dimension 512 = 32 × 8 × 2. The output of the third layer is a sequence of 32-dimensional vectors.
- 4. The fourth layer is an offline ICA algorithm, described below. It receives as input the 32-dimensional vector output of the third layer and produces a 32-dimensional output.
- 2. The projected sequence is quadratically expanded to generate the 560-dimensional expanded sequence, which is centered in the online setting using the running mean.
- 3. Bio-SFA is applied to the expanded sequence to generate a 32-dimensional output.

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