Illustration of the fundamental mathematical difference between standing waves and traveling waves, which are not `spacetime separable’. We suggest these inseparable dynamics in neural activity may have a fundamental role in efficient and generalizable computation.

Relative Representations are a method for mapping points (such as the green circle) from a high dimensional space (left) to a lower dimensional space (right), by represeniting it in a new coordinate system relative to a select set of anchor points (red and blue star). In this work we apply such an idea of relative representations to model-brain mappings and show that it improves interpretability and computational efficiency – surprisingly model-brain RSA scores are roughly consistent even with as few as 10 randomly selected anchor points (10 dimensions) compared to the original 1000’s of dimensions.

My PhD Thesis, studying the inductive biases that enable the efficiency and generalization capability of natural intelligence, yet unmatched by artificial intelligence.

Visualization of the phases of a network of locally coupled kuramoto oscillatos, driven by an input image (left), which converge in phase to segment the image into different shapes, with different oscillatory dynamics for each shape.

Illustration of our flow factorized representation learning: at each point in the latent space we have a distinct set of tangent directions \(\nabla u^k\) which define different transformations we would like to model in the image space. For each path, the latent sample evolves to the target on the potential landscape following dynamic optimal transport.

Illustration of three input signals (top) and a corresponding wave-field with induced traveling waves (bottom). From an instantaneous snapshot of the wave-field at each timestep we are able decode both the time of onset and input channel of each input spike. Furthermore, subsequent spikes in the same channel do not overwrite one-another.

Visualization of the DUET framework. The backbone \(f\) yields a 2d representation for each transformed image \(f(\tau_g(\mathbf{x}))\) (e.g. \(\tau_g\) is a rotation by \(g\) degrees). The group marginal is obtained as the softmax (sm) of the sum of the rows, and is compared to the prescribed target (red) with our group loss \(L_G\). The content is obtained by summing the columns, and contrasted (\(L_C\)) with the other view through a projection head \(h\). The final representation for downstream tasks is the 2d one, which has been optimized through its marginals.

Comparison of latent traversals found with our method compared with state of the art baselines (WarpedSpace and SeFa). We see prior work tends to conflate multiple semantic concepts simultaneously due to the enforced linearity of the transformations. In our work, the inherently non-linear nature of the potential flow transformations more accurately disentangles semantically separate transformations.

Measured orientation selectivity of neurons, as color coded by the bars on the left. We see our LocoRNN’s simulated cortical sheet learns selectivity reminiscent of the orientation columns observed in the Macaque primary visual cortex (source: Principles of Neural Science. E. Kandel, J. Schwartz, T. Jessell, S. Siegelbaum, & A. Hudspeth. 2013.).

Observed transformation (left), Latent Variable Waves (middle), and Reconstruction (right). We see the Neural Wave Machine learns to encode the observed transformations as traveling waves. In our paper, we show that such coordinated synchronous dynamics ultimately result in improved forecasting ability and efficiency when similarly modeling smooth continutous transformations as input.