Structured Bayesian Modeling of Dynamic Receptive1 Fields in Salamander Retinal Ganglion Cells

Biological sensory neurons have selective receptive fields organized along meaningful stimulus coordinates, such as frequency, motion direction, or retinotopic position. Such structure may arise from efficient coding and biological constraints on activity, connectivity, and wiring, as computational studies of simple neurons have shown across modalities. This raises a question: do structured receptive fields confer a computational advantage beyond resource efficiency itself, and does this advantage persist when individual neurons are highly expressive? We address this question in recurrent networks of Expressive Leaky Memory neurons, where we can independently vary neuronal complexity and the organization of feed-forward receptive fields. Across auditory and event-based visual classification tasks, receptive fields aligned with a task-relevant sensory coordinate improve test accuracy relative to budget-matched random receptive fields. This advantage disappears when sensory coordinates are scrambled, or when receptive fields follow task-irrelevant coordinates, showing that the benefit comes from alignment with task geometry rather than restricted connectivity alone. Increasing neuronal complexity reduces the performance advantage of structured receptive fields. Finally, generic synaptic sparsity regularization induces input selectivity and partially recovers performance, but remains substantially below explicitly structured receptive fields, suggesting that sparsity alone is insufficient to recover the full computational benefit of task-aligned receptive fields. Together, our results show that appropriate receptive fields can serve as a computational prior beyond sparsity itself, and that their value depends on the computational expressivity of individual neurons.

Decoding visual stimuli from the spiking activity of retinal ganglion cells (RGCs) informs both our understanding of the retinal code and the design of visual prostheses. Natural vision is dynamic, yet state-of-the-art decoders mostly reconstruct single frames with artificial neural networks that process dense, continuous-valued signals rather than the retina's sparse, asynchronous spikes. We asked whether dynamic scenes can be reconstructed and tracked entirely within the spike domain, and at what computational cost. We built an end-to-end spiking neural network (SNN) whose neurons integrate the recorded RGC spikes over time. Populations of up to 1836 RGCs were recorded ex vivo from mouse retina on high-density microelectrode arrays while flashed images, moving bars, drifting gratings and randomly moving handwritten digits were presented. For moving digits, one shared spiking encoder fed two readouts, one reconstructing the image and one decoding the digit's position. Compute energy was estimated from counted synaptic operations. The SNN decoded what and where at once. It reconstructed the stimuli with a structural similarity (SSIM) of up to 0.93, refining the reconstruction as spikes accumulated, and tracked a randomly moving target with a mean error of 1.33 pixels on a $32\times32$ grid. Its fidelity nearly matched that of the best of 17 larger spiking and artificial decoders (5.9 million to 1.7 billion parameters, versus 5.4 million), and at a mean firing rate of 14.2% it needed an estimated $\sim$70-fold less compute energy than a dense artificial network of the same architecture. Dynamic visual scenes can thus be decoded from retinal population activity in the spike domain, with a compact network and at a compute cost compatible with implantable and wearable neural interfaces, supporting spike-native decoders for visual prostheses.

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by $\ell_1$ regularization, enabling identification of which factors drive observed dynamics. We investigate how these two types of approaches can be optimally combined, exemplarily considering two-photon calcium imaging data where sparse autoregressive dynamics are to be extracted. We propose embedding a vector autoregressive (VAR) model as an interpretable regression technique into a convolutional autoencoder, which provides dimension reduction for tractable temporal modeling. A skip connection separately addresses non-sparse static spatial information, selectively channeling sparse structure into the $\ell_1$-regularized VAR. $\ell_1$-estimation of regression parameters is enabled by differentiating through the piecewise linear solution path. This is contrasted with approaches where the autoencoder does not adapt to the VAR model. Having an embedded statistical model also enables a testing approach for comparing temporal sequences from the same observational unit. Additionally, contribution maps visualize which spatial regions drive the learned dynamics.