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Active inference is a first principle account of how autonomous agents operate in dynamic, nonstationary environments. This problem is also considered in reinforcement learning, but limited work exists on comparing the two approaches on the same discrete-state environments. In this letter, we provide (1) an accessible overview of the discrete-state formulation of active inference, highlighting natural behaviors in active inference that are generally engineered in reinforcement learning, and (2) an explicit discrete-state comparison between active inference and reinforcement learning on an OpenAI gym baseline. We begin by providing a condensed overview of the active inference literature, in particular viewing the various natural behaviors of active inference agents through the lens of reinforcement learning. We show that by operating in a pure belief-based setting, active inference agents can carry out epistemic exploration-and account for uncertainty about their environment-in a Bayes-optimal fashion. Furtheronment, alongside reinforcement learning agents.Recent work suggests that changing convolutional neural network (CNN) architecture by introducing a bottleneck in the second layer can yield changes in learned function. To understand this relationship fully requires a way of quantitatively comparing trained networks. The fields of electrophysiology and psychophysics have developed a wealth of methods for characterizing visual systems that permit such comparisons. Inspired by these methods, we propose an approach to obtaining spatial and color tuning curves for convolutional neurons that can be used to classify cells in terms of their spatial and color opponency. We perform these classifications for a range of CNNs with different depths and bottleneck widths. Our key finding is that networks with a bottleneck show a strong functional organization almost all cells in the bottleneck layer become both spatially and color opponent, and cells in the layer following the bottleneck become nonopponent. The color tuning data can further be used to form a rich understanding of how color a network encodes color. As a concrete demonstration, we show that shallower networks without a bottleneck learn a complex nonlinear color system, whereas deeper networks with tight bottlenecks learn a simple channel opponent code in the bottleneck layer. We develop a method of obtaining a hue sensitivity curve for a trained CNN that enables high-level insights that complement the low-level findings from the color tuning data. We go on to train a series of networks under different conditions to ascertain the robustness of the discussed results. Ultimately our methods and findings coalesce with prior art, strengthening our ability to interpret trained CNNs and furthering our understanding of the connection between architecture and learned representation. Trained models and code for all experiments are available at https//github.com/ecs-vlc/opponency.A central theme in computational neuroscience is determining the neural correlates of efficient and accurate coding of sensory signals. Deutenzalutamide Diversity, or heterogeneity, of intrinsic neural attributes is known to exist in many brain areas and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. Here we consider this question with data from in vivo recordings of neurons in the electrosensory system of weakly electric fish subject to the same realization of noisy stimuli; we use a generalized linear model (GLM) to assess the accuracy of (Bayesian) decoding of stimulus given a population spiking response. The long recordings enable us to consider many uncoupled networks and a relatively wide range of heterogeneity, as well as many instances of the stimuli, thus enabling us to address this question with statistical power. The GLM decoding is performed on a single long time series of data to mimic realistic conditions rather than using trial-averaged data for better model fits. For a variety of fixed network sizes, we generally find that the optimal levels of heterogeneity are at intermediate values, and this holds in all core components of GLM. These results are robust to several measures of decoding performance, including the absolute value of the error, error weighted by the uncertainty of the estimated stimulus, and the correlation between the actual and estimated stimulus. Although a quadratic fit to decoding performance as a function of heterogeneity is statistically significant, the result is highly variable with low R 2 values. Taken together, intermediate levels of neural heterogeneity are indeed a prominent attribute for efficient coding even within a single time series, but the performance is highly variable.The expected free energy (EFE) is a central quantity in the theory of active inference. It is the quantity that all active inference agents are mandated to minimize through action, and its decomposition into extrinsic and intrinsic value terms is key to the balance of exploration and exploitation that active inference agents evince. Despite its importance, the mathematical origins of this quantity and its relation to the variational free energy (VFE) remain unclear. In this letter, we investigate the origins of the EFE in detail and show that it is not simply "the free energy in the future." We present a functional that we argue is the natural extension of the VFE but actively discourages exploratory behavior, thus demonstrating that exploration does not directly follow from free energy minimization into the future. We then develop a novel objective, the free energy of the expected future (FEEF), which possesses both the epistemic component of the EFE and an intuitive mathematical grounding as the divergence between predicted and desired futures.This article proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the biophysical model to the modulation of parameters in the proposed integrate-and-fire model. The approach is illustrated on two well-documented examples of cellular neuromodulation the transition between type I and type II excitability and the transition between spiking and bursting.