We rely so much on vision that it is hard to imagine sensing the world differently. But most organisms primarily use other sensory information, even something as detached from our senses as electricity. Some fish, called weakly electric fish, generate electric pulses to sense their environment. Objects in their environment distort the electric pulses, and the fish use special receptors in their skin to process these distortions and identify the nearby objects. They detect the location, size, shape, and electric properties of nearby objects, enabling them to find preferred food. These fish use their discharges not only for sensing and foraging as described, but also for communication. Investigating this sensory system can provide insights into neural computations for sensory processing more broadly, and can expand our understanding of the complex stimuli present in our environment that we do not perceive.In the first half of this work, we investigated how the weakly electric fish Gnathonemus petersii processes the electric sensory information to interact with its environment. We also used the tools developed in this work to study social behavior in groups of freely swimming fish. Chapter 1 provides an in-depth introduction to this model organism and its prominent active electrolocation behavior. This introductory chapter is focused on the parts of the behavior that are relevant to the computational models developed in this work. We investigated the active electrolocation behavior using a comprehensive end-to-end model that contains multiple components, which will be detailed in the following chapters. Chapter 2 describes the physics model that simulates the fish and its environment to collect data. The physics model builds on previous work and extends it to a more general framework that can be used to simulate the fish in different environments. We developed and adequately documented an open code base that can be used to simulate various fish species and their interactions with nearby objects or electrical boundaries. Chapter 3, specifically Section 3.3, presents a data-based model of the electroreceptors that process the sensory input. We used machine learning techniques to develop a model that can predict the response of the receptors to distortions due to different objects. The model is based on local field potential data collected from the afferent layers of the electrosensory lobe, the first brain area that processes the sensory input. This data was collected by Abigail Zadina in Nathaniel Sawtell’s laboratory at Columbia University. Chapter 3, specifically Section 3.4, describes the neural network models that identify computations that help solve the behavior. We used data generated from the physics model as sensory input, we used our electroreceptor model to parse this data serving as first-stage input to down- stream brain areas, and we used neural network models to characterize the nearby objects’ spatial and electric properties based on the sensory input. Based on results from our neural network models, we set two hypotheses for how weakly electric fish sense their environment and motivate experiments on less studied brain areas to test these hypotheses. First, we suggest that decoding all spatial and electric properties of a nearby object distorting the electric discharge is very challenging due to interactions between these properties, but first decoding the spatial properties and then using the spatial properties as internal feedback to decode the electric properties helps solve the task by disentangling the interactions. Second, we suggest that the specialized Schnauzenorgan organ of the weakly electric G. petersii, previously described as an electric fovea due to the very high density of electroreceptors and believed to serve a primary role in close-range characterization, may also play a role in long-range detection of objects surrounding the fish. Chapter 4 explores social interactions in groups of freely swimming fish and starts to investigate how they use their electric discharges to navigate, interact and communicate. Here, we used our physics-based framework to accurately identify the fish that emitted each electric discharge in a group of fish. This work is currently in progress and we performed various preliminary analyses to investigate the social behavior and social rank of these fish, which we present here. Data for this project was collected by Federico Pedraja in Nathaniel Sawtell’s laboratory at Columbia University. The second half of this work addresses a variety of different research questions with loose connections in between them and in relation to the first half. The common factor present in all these projects can be generally described as investigating how computations may be used in neural circuits to produce successful behavior. We used a variety of computational models and tools to investigate these questions, and we present the results of these investigations in the following chapters. Chapter 5 provides a biologically plausible architecture alternative for the classical binary classification task. Typically, feed-forward models have been used to solve this task. However, neocortical circuits likely involved in decision making are recurrent and sparse. We used a recurrent neural network model with sparsity constraints to solve the binary classification task. We demonstrated that the sparse recurrent networks solve the task well, make use of dynamic computation similar to evidence accumulation, and distribute the information throughout the network despite the sparsity constraints. Chapter 6 explores syntactic differences of world languages and offers a potential neural computation mechanism that could account for those differences. We focused on differences in the basic word order of simple sentences because these have been extensively studied in the linguistic literature. These simple sentences only have three parts, subject, verb, and object, and the order of these parts varies across languages non-uniformly. We aimed to provide a possible language generation mechanism that could account for these differences. Chapter 7 investigates the computational journey from numerical cognition to arithmetic ability. This research direction was motivated by and based on experimental work that addressed whether bees (and later stingrays and cichlids) can learn simple arithmetic operations. This project was designed for introducing a Columbia SEAS undergraduate student, Katharyn Fatehi, to computational neuroscience research. I mentored Kat through the Women in Science at Columbia program, and provided detailed guidance, code base, tutorials and instructions for her to learn about computational neuroscience research and to contribute to this project. Chapter 8 represents my contribution to a large collaboration effort aimed at improving spike sorting techniques. This project quantified the impact on spike sorting quality of the geometry mis- match between typical recording probes (1D, or 2D at best) and the 3D structure of the brain. We leveraged the experimental setup, multi-electrode recording arrays with planar geometry recording the activity of 2D retinal tissue, to address this question. The work presented in this thesis is a collection of projects that investigate neural computations in different contexts. The first half of the work is focused on the weakly electric fish G. petersii and its active electrolocation behavior. The second half of the work explores a variety of different research questions related to computational mechanisms that could be implemented in neural circuits. The work presented here is a step towards understanding how computations in neural circuits can produce successful behavior in different contexts.