Jacob L. Yates

Hadi Vafaii, Jacob L. Yates

Computation in biological systems is fundamentally energy-constrained, yet standard theories of computation treat energy as freely available. Here, we argue that variational free energy minimization under a Poisson assumption offers a principled path toward an energy-aware theory of computation. Our key observation is that the Kullback-Leibler (KL) divergence term in the Poisson free energy objective becomes proportional to the prior firing rates of model neurons, yielding an emergent metabolic cost term that penalizes high baseline activity. This structure couples an abstract information-theoretic quantity -- the *coding rate* -- to a concrete biophysical variable -- the *firing rate* -- which enables a trade-off between coding fidelity and energy expenditure. Such a coupling arises naturally in the Poisson variational autoencoder (P-VAE) -- a brain-inspired generative model that encodes inputs as discrete spike counts and recovers a spiking form of *sparse coding* as a special case -- but is absent from standard Gaussian VAEs. To demonstrate that this metabolic cost structure is unique to the Poisson formulation, we compare the P-VAE against Grelu-VAE, a Gaussian VAE with ReLU rectification applied to latent samples, which controls for the non-negativity constraint. Across a systematic sweep of the KL term weighting coefficient $β$ and latent dimensionality, we find that increasing $β$ monotonically increases sparsity and reduces average spiking activity in the P-VAE. In contrast, Grelu-VAE representations remain unchanged, confirming that the effect is specific to Poisson statistics rather than a byproduct of non-negative representations. These results establish Poisson variational inference as a promising foundation for a resource-constrained theory of computation.

Hayden R. Johnson, Anastasia N. Krouglova, Hadi Vafaii et al.

Many properties of perceptual decision making are well-modeled by deep neural networks. However, such architectures typically treat decisions as instantaneous readouts, overlooking the temporal dynamics of the decision process. We present an image-computable model of perceptual decision making in which choices and response times arise from efficient sensory encoding and Bayesian decoding of neural spiking activity. We use a Poisson variational autoencoder to learn unsupervised representations of visual stimuli in a population of rate-coded neurons, modeled as independent homogeneous Poisson processes. A task-optimized decoder then continually infers an approximate posterior over actions conditioned on incoming spiking activity. Combining these components with an entropy-based stopping rule yields a principled and image-computable model of perceptual decisions capable of generating trial-by-trial patterns of choices and response times. Applied to MNIST digit classification, the model reproduces key empirical signatures of perceptual decision making, including stochastic variability, right-skewed response time distributions, logarithmic scaling of response times with the number of alternatives (Hick's law), and speed-accuracy trade-offs.

Hadi Vafaii, Dekel Galor, Jacob L. Yates

Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their success, traditional VAEs rely on continuous latent variables, which deviates sharply from the discrete nature of biological neurons. Here, we developed the Poisson VAE (P-VAE), a novel architecture that combines principles of predictive coding with a VAE that encodes inputs into discrete spike counts. Combining Poisson-distributed latent variables with predictive coding introduces a metabolic cost term in the model loss function, suggesting a relationship with sparse coding which we verify empirically. Additionally, we analyze the geometry of learned representations, contrasting the P-VAE to alternative VAE models. We find that the P-VAE encodes its inputs in relatively higher dimensions, facilitating linear separability of categories in a downstream classification task with a much better (5x) sample efficiency. Our work provides an interpretable computational framework to study brain-like sensory processing and paves the way for a deeper understanding of perception as an inferential process.

Mingxuan Cai, Dekel Galor, Amit Pal Singh Kohli et al.

Small vibrations observed in video can unveil information beyond what is visual, such as sound and material properties. It is possible to passively record these vibrations when they are visually perceptible, or actively amplify their visual contribution with a laser beam when they are not perceptible. In this paper, we improve upon the active sensing approach by leveraging event-based cameras, which are designed to efficiently capture fast motion. We demonstrate our method experimentally by recovering audio from vibrations, even for multiple simultaneous sources, and in the presence of environmental distortions. Our approach matches the state-of-the-art reconstruction quality at much faster speeds, approaching real-time processing.

Hadi Vafaii, Dekel Galor, Jacob L. Yates

Inference in both brains and machines can be formalized by optimizing a shared objective: maximizing the evidence lower bound (ELBO) in machine learning, or minimizing variational free energy (F) in neuroscience (ELBO = -F). While this equivalence suggests a unifying framework, it leaves open how inference is implemented in neural systems. Here, we introduce FOND (Free energy Online Natural-gradient Dynamics), a framework that derives neural inference dynamics from three principles: (1) natural gradients on F, (2) online belief updating, and (3) iterative refinement. We apply FOND to derive iP-VAE (iterative Poisson variational autoencoder), a recurrent spiking neural network that performs variational inference through membrane potential dynamics, replacing amortized encoders with iterative inference updates. Theoretically, iP-VAE yields several desirable features such as emergent normalization via lateral competition, and hardware-efficient integer spike count representations. Empirically, iP-VAE outperforms both standard VAEs and Gaussian-based predictive coding models in sparsity, reconstruction, and biological plausibility, and scales to complex color image datasets such as CelebA. iP-VAE also exhibits strong generalization to out-of-distribution inputs, exceeding hybrid iterative-amortized VAEs. These results demonstrate how deriving inference algorithms from first principles can yield concrete architectures that are simultaneously biologically plausible and empirically effective.

Michael Ibrahim, Hanqi Zhao, Eli Sennesh et al.

Poisson-distributed latent variable models are widely used in computational neuroscience, but differentiating through discrete stochastic samples remains challenging. Two approaches address this: Exponential Arrival Time (EAT) simulation and Gumbel-SoftMax (GSM) relaxation. We provide the first systematic comparison of these methods, along with practical guidance for practitioners. Our main technical contribution is a modification to the EAT method that theoretically guarantees an unbiased first moment (exactly matching the firing rate), and reduces second-moment bias. We evaluate these methods on their distributional fidelity, gradient quality, and performance on two tasks: (1) variational autoencoders with Poisson latents, and (2) partially observable generalized linear models, where latent neural connectivity must be inferred from observed spike trains. Across all metrics, our modified EAT method exhibits better overall performance (often comparable to exact gradients), and substantially higher robustness to hyperparameter choices. Together, our results clarify the trade-offs between these methods and offer concrete recommendations for practitioners working with Poisson latent variable models.

Stephen L. Keeley, David M. Zoltowski, Yiyi Yu et al.

Gaussian Process Factor Analysis (GPFA) has been broadly applied to the problem of identifying smooth, low-dimensional temporal structure underlying large-scale neural recordings. However, spike trains are non-Gaussian, which motivates combining GPFA with discrete observation models for binned spike count data. The drawback to this approach is that GPFA priors are not conjugate to count model likelihoods, which makes inference challenging. Here we address this obstacle by introducing a fast, approximate inference method for non-conjugate GPFA models. Our approach uses orthogonal second-order polynomials to approximate the nonlinear terms in the non-conjugate log-likelihood, resulting in a method we refer to as \textit{polynomial approximate log-likelihood} (PAL) estimators. This approximation allows for accurate closed-form evaluation of marginal likelihoods and fast numerical optimization for parameters and hyperparameters. We derive PAL estimators for GPFA models with binomial, Poisson, and negative binomial observations and find the PAL estimation is highly accurate, and achieves faster convergence times compared to existing state-of-the-art inference methods. We also find that PAL hyperparameters can provide sensible initialization for black box variational inference (BBVI), which improves BBVI accuracy. We demonstrate that PAL estimators achieve fast and accurate extraction of latent structure from multi-neuron spike train data.