This thesis consists of three separate chapters, representing my journey from engineer to neuroscientist, and my PhD thesis. Two are completed papers, and each project is self-contained with relevant introductory material and context in the respective introductions, while the general introduction provides a brief orientation to my work in the general context of systems neuroscience. These projects span sensory systems neuroscience from spinal cord neurobiology to cortex and computation. In the first chapter I present a surgical technique to implant a cannula into the vertebral column of mice, allowing optogenetic access to spinal sensory neurons in the dorsal horn. In the second chapter, I analyze visual cortex calcium imaging data from the Allen Institute Brain observatory during free locomotion behavior. This analysis reveals that lower background noise during locomotion might be responsible for the increased encoding accuracy during locomotion (as opposed to increased firing rates). In the last chapter, I introduce a rodent decision-making task intended to allow parametric control both of the animals' expectation of the sensory stimuli as well as the noise in the stimuli

Several organisms often demonstrate the ability to produce highly adaptable and increasingly sophisticated movements. The computations required to produce even simple arm movements, e.g., reaching for a coffee cup, involve generating complex time varying patterns of neural activity. Learning poses an even greater challenge: the brain must somehow select a set of neural commands, from billions of possible activity patterns, that best help the organism achieve its movement objectives. Consider a common scenario where a subject learns a motor task in one context, and now wishes to perform the same task in a very different context. Certainly, in some cases this is possible. What are those cases? What is the neural mechanism that facilitates this transfer of learning? We developed a ``covert learning" paradigm whereby Rhesus monkeys can perform the same visuomotor learning task either overtly using arm movements, or covertly using a brain-machine interface. In the covert context, no overt movements can be made, and thus monkeys learn to generate patterns of neural activity that drive the brain-machine interface to perform the task. Using this paradigm, we demonstrated that learning can indeed transfer across contexts in order to improve overt behavior. We studied the neural activity in premotor and primary motor cortex during transfer learning at a population level. Intriguingly, we discovered that a key ingredient driving transfer is a shared neural substrate consisting of neural activity during motor preparation (this is known as preparatory activity or the preparatory state). Even on the single-trial level, behavioral improvements due to visuomotor learning are accompanied with systematic changes to the motor cortical preparatory state. Standard theories of visuomotor learning suggest that a trial-by-trial learning process performs computations based on an efference copy of the outgoing motor command, and sensory feedback during motor execution. These computations result in an update, which improves the behavior on subsequent trials. Our results suggest that this update occurs (at minimum) during motor preparation. Finally, through microstimulation experiments, we established the first causal link between motor preparation and visuomotor learning. Concretely, we found that neural activity during motor preparation causally interacts with the update computations of a trial-by-trial learning process. Disrupting preparatory activity does not affect the current trial, but instead influences the update computation in a fashion that manifests as disruption to learning on subsequent trials. More generally, these experiments reveal that the learning process (a) has access to the preparatory state, (b) the ability to assess how good the current preparatory state is, and (c) the ability to influence the preparatory state on both current and future trials. Taken together, this thesis reveals that neural activity before the onset of movement, or even in the absence of movement altogether, could play a fundamental role in the algorithm underlying the neural control of movement

Anatomical evidence suggests that planning and execution of adaptive behaviors in mammals may involve coordinated neuronal activity throughout the neocortex. To investigate this previously-unapproachable hypothesis, in collaboration with others, I developed a set of optical tools for probing fast neuronal activity across many cortical regions simultaneously. One of these methods—COSMOS—allows synchronous recording at 30 Hz from over a thousand near-cellular resolution neuronal sources distributed throughout the entire dorsal neocortex of awake mice. We applied these tools to make three discoveries. First, we found global cortical representations of goal-directed task engagement, with cell-type specific dynamics. Second, we identified neuronal population representations spanning dorsal neocortex that precisely encode ongoing and planned motor actions. Third, we discovered a localized neuronal rhythm underlying dissociation, a mysterious altered behavioral state in which normally-integrated cognitive processes—such as those linking the sense of self to body-position and action—become selectively disconnected. Together, these results illuminate how circuits throughout the brain of behaving mammals function as a coupled system—and the consequences that can arise when they decouple

Understanding what in the brain establishes specific motivational states, and how these states cause animals to pursue particular goal-directed behaviors, are central goals of behavioral neuroscience. Fully determining the mechanisms underlying these processes will require a comprehensive description of how the brain operates at different levels spanning multiple spatial and temporal scales, from the expression of individual genes within single cells to the coordinated activity of brain-wide networks of neurons. As a step towards this ultimate goal, this dissertation proposes several new approaches to map and understand the structural, functional, and molecular properties of neural circuits. These approaches are applied to study the circuits underlying motivated behavior, with an emphasis of thirst motivation. This work is divided into several parts. (1) I de-scribe the application of a method for labeling neural circuits defined by activity (TRAP) in combination with whole-brain clearing and imaging technology to map the location of neurons activated by a particular experience throughout the brain, and study their structural and molecular properties. (2) Extending the idea of brain-wide imaging to study dynamics, I introduce two new approaches to perform large-scale in vivo imaging of neural activity across the surface of the mouse brain, to study cell-type-specific cortical dynamics involved in production of a simple thirst-motivated choice behavior. (3) I dis-cuss an improved approach to TRAP, and apply this technique to measure and manipulate a crucial node in the neural circuit underlying the sensation of thirst to reveal how activity in this circuit induced by water deprivation produces an aversive drive that is diminished through water consumption. (4) I develop a new approach to spatially map the expression of up to 1,000 genes simultaneously in three dimensions within single cells in a tissue section, and show that this approach is compatible with activity measurement using activity regulated genes as a post hoc reporter of neural activity. (5) Finally, I develop an approach using large-scale electrophysiology to study spatially-localized activity dynamics from cells distributed throughout the entire mouse brain. I apply this technique to study brain-wide neural dynamics during thirst motivated choice behavior, revealing how thirst motivational state is represented throughout the brain and how this state gates the flow of information from sensory to motor regions.

Intracortical brain-computer interfaces (iBCIs) have largely built upon work investigating the neural representation of overt reaching movements in nonhuman primates (NHPs). However, in people with paralysis, iBCIs leverage neural features related to attempted movement of paralyzed limbs, which may differ substantially from that of overt movement of unparalyzed limbs. To understand how paralysis affects movement representation in the motor cortex, we first compared direction- and distance-related neural tuning of a human participant's attempted arm movements and overt head movements to that of NHP overt arm movements. The participant's neural activity during overt head movement was most similar to NHP overt arm movement with strongest tuning to distance. To further clarify how attempted movement-related neural activity translates into iBCI control, the participant controlled a cursor using a series of different attempted movement strategies. We found that neural activity changes during iBCI control, becoming more similar across different strategies. Applying these gained insights, we designed and demonstrated a discrete neural decoding system which leveraged the neural representation of both overt and attempted movements to enable classification of up to 32 discrete movements across the body. The attempt to move a paralyzed limb also differs from overt movement of an unparalyzed limb in that haptic feedback normally accompanying the movement is lost or diminished. To better understand how haptic stimulation affects motor cortical neurons and iBCI control, we integrated a haptic feedback device into our iBCI system, which provided skin-shear haptic stimulation at the back of the participant's neck. We found motor cortical units that exhibited sensory responses to the stimuli, some of which were significantly tuned to the stimuli and well modeled by cosine-shaped functions. We also demonstrated online iBCI cursor control with continuous skin-shear feedback driven by decoded command signals. Cursor control performance increased slightly but significantly when the participant was given haptic feedback as compared to the visual feedback condition. This work deepens our understanding of how paralysis affects movement representation, delivers a novel discrete neural decoding system leveraging the movement representation of both paralyzed and unparalyzed limbs, provides insight into how motor cortical units respond to haptic stimulation, and shows how this stimulation affects iBCI control performance. These results can help guide and inform the design of future neural prostheses.

Why do we do the things we do? Understanding cognition is a key step towards understanding our diverse perspectives and behaviors. Over the years, the study of decision-making in neuroscience has shed light on the black box of cognition. Decision-making is the process of arriving at one choice out of multiple alternatives, and correlates of this process have been found in many sensory- and motor-related brain structures. However, we do not have a full account of the way in which brain regions participate in this process, especially given the many potential forms that decision-making can take. Here, we focus in on the dorsal premotor cortex (PMd), a frontal brain region involved in motor preparation and execution, decision-making, and goal-oriented action. We use a perceptual decision-making task in which the subject reports the perceived dominant color of a red-and-green checkerboard by reaching to the corresponding colored target. Studies have previously found that the activity of PMd neurons correlate with the choice report, the evidence supporting that choice, and the time taken to deliberate upon the choice. We now ask: To what extent is PMd involved in the perceptual aspect of decision-making, and how do motor costs affect the decision-making process? First, we separate the perceptual process (whether the checkerboard is mostly red or green) from the motor process (to reach left or right) by presenting a checkerboard decision cue without providing information on how to report. We found that PMd neurons did not encode information about the perceptual color choice, but did exhibit decision-related activity when the subject was able to report the choice. We next randomly assign the positions of the target choices to be near or far relative to the hand's starting position. We found that performance was biased towards the choice that was closer to the animal, and that these target configurations were reflected in neural activity during the report epoch as well. These findings suggest that PMd involvement in the decision process is primarily in an action-decision space, and that relevant motor and perceptual information are combined at the same time. These results provide stepping stones towards understanding how brain regions drive our perception and behavior.

The activity of single neurons is stochastic: dissimilar spike patterns are often produced over nominally identical trials. This randomness has often limited the scope of neuroscience research to trial-averaged responses; however, advances in large-scale recording technologies are increasingly enabling statistical analyses with single-trial resolution. Nonetheless, single-trial dynamics are still poorly characterized in many cases, and approaches to characterizing these dynamics have not reached consensus. To meet this challenge, this thesis describes three statistical models that capture common forms of neural circuit activity and variability. First, single-trial variations in neural amplitude are statistically modeled through tensor decomposition. Second, an unsupervised time warping framework is developed to capture single-trial variations in temporal latency and duration. Finally, convolutional matrix factorization is used to extract recurring temporal motifs in the absence of human-annotated experimental trials. All methods are fit purely to neural data, and thus make few assumptions about the experimental design or behavioral task. Further, all methods flexibly model both linear and nonlinear dynamical behaviors in an interpretable and transparent manner. Practical results are shown on experimental data collected from diverse species (mice, rats, song birds, and nonhuman primates), behavioral contexts (olfaction, motor learning, decision-making, and motor production), and brain regions (olfactory bulb, premotor & motor cortex, and prefrontal cortex). These approaches revealed a wide variety of single-trial dynamical patterns including behavioral error detection and correction, incremental learning, spike-level oscillations, pulsatile responses to latent behavioral events, and neural ensembles that fire in sparse temporal sequences.

We provide an overview of neuromorphic engineering and describe two contributions to Braindrop, a state-of-the-art neuromorphic system. First, we describe a method for performing summing and weighting of spike trains by accumulative thinning, a deterministic procedure for merging and dropping spikes. Previous methods relied on probabilistic thinning, which results in Poissonian statistics. As a result, when the thinned spike-train is filtered with a first-order low-pass synapse, the signal-to-noise ratio (SNR) scales as the square-root of its rate. For our accumulative thinning method, the SNR depends on the weight w; it scales linearly in the best-case scenario (w-> 0) and as the square-root in the worst-case (w-> 1). We find that a three-quarter power scaling minimizes energy consumption. Second, we present a serial H-tree router for two-dimensional (2D) arrays. Existing routing mechanisms for 2D arrays either use low-overhead grids with one or two shared wires per row or column (e.g., RAM) or high-overhead meshes with many wires connecting neighboring clients (e.g., supercomputers). Neither is suitable for intermediate-complexity clients (e.g., small clusters of silicon neurons). We present a router tailored to 2D arrays of such clients. It uses a tree laid out in a fractal pattern (H-tree), which requires less wiring per signal than a grid, and adopts serial-signaling, which keeps link-width constant, regardless of payload size. To route from the tree's leaves to its root (or vise versa), each node prepends (consumes) a delay-insensitive 1-of-4 code that signals the route's previous (next) branch; additional codes carry payload. We employ this serial H-tree router to service a 16x16 array of silicon-neuron clusters, each with 16 spike-generating analog somas, 4 spike-consuming analog synapses, and one 128-bit SRAM. Fabricated in a 28-nm CMOS process, the router communicates 26.8M soma-generated and 18.3M synapse-targeted spikes per second while occupying 43% of the client's 35.1x36.1 sq.um.

A central goal of systems neuroscience is to relate an organism's neural activity to behavior. Current state of the art experimental methods are limited both in the capability of recording from large populations of neurons simultaneously, as well as in the complexity of the behaviors studied. In this work, I describe the development of new tools and methods for recording from large populations of neurons in rhesus macaque nonhuman primates (NHP). In addition, I describe the development of a haptic robotic interface to implement more complex motor tasks. I use this apparatus to study how short timescale adaptation to dynamic loads alters neural preparatory activity in premotor and primary motor cortices prior to movements. Chapter 1 provides an introduction and in-depth overview of the work covered in the remaining four chapters of this dissertation. Chapter 2 describes efforts to estimate neural population dynamics using multiunit threshold crossings in place of well isolated single units, which potentially eliminates a time consuming, difficult, and inexact portion of data analysis that serves as bottleneck for discovery. In Chapter 3, I describe the development of two-photon calcium imaging for rhesus macaque monkeys performing motor behaviors and the implementation of an optical brain machine interface (oBMI). In Chapter 4, I describe the development of techniques for using high-density silicon electrodes, such as the Neuropixels probe, in NHP. Lastly, in Chapter 5, I describe the development of a haptic experiment in which we introduce a simulated drag force and investigate the impact of short timescale adaptation to these dynamic loads on motor preparation.

Millions of people in the United States live with paralysis due to spinal cord injury or neurological diseases. The motor impairment limits the patients' independence and in some cases the ability to communicate. Brain-computer interfaces (BCIs) translate signals from the brain into useful control signals, manipulating end-effectors such as computer cursors or robotic arms. BCIs can help restore lost motor capabilities and improve the quality of life for people with paralysis. Intracortical BCIs (iBCIs) have shown promising results in clinical trials, making them the prime candidate as an assistive device for people with severe paralysis, such as tetraplegia. However, for most applications iBCIs need further improvements to be suitable for clinical use. In this dissertation, I aimed to advance the main three components of the iBCI system: the neural interface, the user estimation decoding algorithm, and the user interface. I advanced the three components using multidisciplinary tools from neuroscience, statistics, and engineering. I believe that the studies which comprise this dissertation are a step forward towards the goal of clinical viability of iBCIs.

The frontier challenges that must be solved before brain-machine interfaces (BMIs) can be used as clinically useful motor prostheses differ depending on the degree of function being restored. Two-dimensional cursor control (i.e., for communication) has recently reached high levels of peak performance in pre-clinical studies, but translation is hampered by less than reliable performance due to unstable neural signals. Meanwhile, control of robotic arms remains poor, despite some impressive glimpses at what the future could be, because we lack fundamental understanding of how the brain incorporates the BMI into its motor schema. This hampers our ability to accurately decode intended arm movements. My dissertation focused on both sets of problems in pre-clinical macaque BMI studies. Chapters 2 and 3 provide solutions for improving BMI robustness. I first describe a machine learning approach to building decoder algorithms that are robust to the changing neural-to-kinematic mappings that plague translational BMI efforts. We developed a multiplicative recurrent neural network decoder that could exploit the large quantities of data generated by a chronic BMI — data that has heretofore gone unused. I then describe a neural engineering approach for increasing the device lifespan by providing high performance control even after losing spike signals. I developed a method for decoding local field potentials (LFPs) as a longer-lasting alternative or complimentary BMI control signal. This led to the highest-performing LFP-driven BMI and the first 'hybrid' BMI which decoded kinematics from spikes and LFPs together. Chapter 4 looks ahead to challenges that will be encountered when BMI-controlled limbs operate in the physical world by describing how error signals impact ongoing BMI control. I perturbing the kinematics of monkeys performing a BMI cursor task and found that visual feedback drove responses starting 70 ms later in the same motor cortical population driving the BMI. However, this initial response did not cause unwanted BMI output because it was limited to a decoder null space in which activity does not affect the BMI. When activity changed in output-potent dimensions starting 115 ms after perturbation, it caused corrective BMI movement. This elegant arrangement may hint at a broader computational strategy by which error processing is separated from output.

Millions of people suffer from motor-related neurological injury or disease, which in some cases is so severe that even the ability to communicate is lost. For people with lost motor function, including paralysis and amyotrophic lateral sclerosis, neural prostheses are an emerging technology that has the potential to increase quality of life and enable greater communication with the world. Neural prostheses record neural signals from the brain and, through a decoder algorithm, translates these neural signals into control signals for actuating machines such as a computer cursor or a prosthetic arm. There are three important areas of development for neural prostheses to be clinically viable. Specifically, these systems must be (1) high-performance, (2) robust to perturbations and noise, and (3) usable for decades. My dissertation is focused on the design of decoder algorithms that achieve state-of-the-art performance in all three of these areas. These decoder algorithms rely on techniques and intuition from machine learning, statistical signal processing, and neuroscience. Together, these advances in decode algorithm design increase the clinical viability of neural prostheses.

This thesis consists of two main sections.The first is dedicated to the development of enabling technologies for optogenetic experimentation in rats. In this section, I provide an overview of opsin selection and targeting in rat models and review the state of the literature in terms of applying these technologies to neuroscientific questions in rats. In the second chapter, I discuss the development of the first cre-driver rat lines, allowing for genetic access to dopaminergic, cholinergic, and noradreneric neural populations in rats. Finally, in the third chapter of this section, I utilize the tyrosine hydroxlase cre-driver line to examine the effect of VTA dopamine neuron stimulation and inhibition, in combination with systemic pharamacological manipulations, on the brain-wide BOLD signal. This description of the BOLD response to dopamine neuron activity will, hopefully, inform human fMRI studies in behaviors where dopamine effects on the BOLD signal are suspected, including studies of reward, decision making, learning, and neuroeconomics. The second section of this thesis is devoted to my primary scientific project, examining the role of dopamine signaling in risk-preference. Risk aversion is fundamental to most human decision making and has been described in even evolutionarily-distant animals, including honeybees, stickleback fish, songbirds, and shrews. Such enduring evolutionary conservation implies both strong selection for this phenotype and the potential for conserved neural mechanism. Given this strong selection, it is interesting that variation persists; some individuals consistently prefer uncertainty. One fundamental and fascinating goal of neuroscience is to describe the neural basis for naturally-occurring individual variation, and I hope to address this goal in this work in the context of risk-preference. Dopamine neurons project to many areas of the brain, including nucleus accumbens, striatum, prefrontal cortex, and amygdala. Those neurons that project to the nucleus accumbens have been implicated in substance abuse and behavioral addictions. These cells fire in synchronized bursts in response to unexpected rewards and pause their firing in response to withheld rewards or unpredictable punishments. Postsynaptically, in the nucleus accumbens (NAc), this univariate signal is parsed into two distinct streams. The first pathway is reward-responsive. NAc cells expressing the D1-type dopamine receptor are excited by dopamine bursts and increase their firing in response to reward. The second pathway is loss-responsive. Cells expressing D2-type receptors are inhibited by dopamine and are thought to increase their firing when dopamine neurons pause in response to losses. Evidence from clinical populations suggests that disruption of encoding in the loss pathway may contribute to problem gambling behavior. In the first segment of this section, I describe a novel behavioral model for risk-preference in rats, in which rats repeatedly chose between a ``safe" lever, which yields the same volume of sucrose reward on every trial, and a ``risky" lever, which yields a small reward on 75\% of trials (a ``loss") and a large reward on 25\% of trials (a ``win"). The expected value of choosing either lever was the same. I found that most rats exhibit stable risk-averse behavior, but some smaller subset of rats are consistently risk-seeking. This long-term behavioral difference seems to be driven by a highly-local behavioral phenomenon: if a risk-averse rat ``loses" on the risky lever, they are much more likely to switch to the safe lever, as compared to risk-seeking rats. They are more ``loss sensitive". In the next segment, I discuss a pharmacological investigation of neural populations that might be driving individual variability in risk-preference. Concordant with human clinical literature, I find that a D2-agonist drug (loss pathway) but not a D1 agonist drug (win pathway) dramatically and reversibly increases risk-seeking choices in rats. By infusing the drug directly into the brain through permanently-implanted cannulas, I found that I could recapitulate this effect by administering the drug only into the nucleus accumbens (NAc), but not into other likely targets, such as the orbitofrontal cortex. This experiment strongly implicated dopamine D2 receptor (D2R) expressing cells in the NAc in driving risk preference. I then optically recorded from these cells during the behavior. I found that the D2R cells are more active during the decision period following a loss than following other trial types. This ``loss sensitivity" signal was largest in the most risk-averse animals. A correlation between the size of this effect and the degree of risk-aversion explains the vast majority of the rat-by-rat variance in risk-preference. Finally, I used optogenetic manipulation of D2R NAc cells to determine whether this increased activity was sufficient to drive risk-preference. By driving increased activity in those cells during the decision period of the task, I reasoned I could mimic the ``loss sensitivity" effect observed in the recordings, and attempt to decrease risk-seeking behavior. I found that driving firing in D2R cells during the decision period does, in fact, decrease risk-seeking choices, both on a trial-by-trial basis and on average, across an entire session of behavior. These findings together suggest that natural individual variation in risk preference can be largely explained by loss-related activity of D2R-expressing NAc cells during decision-making.

I present the design and implementation of a manual dexterity assessment system that can measure hand movement data using Inertial Measurement Unit (IMU) sensors. These wireless sensors consist of a 3-axis accelerometer, a 3-axis gyroscope, and a 3-axis magnetometer; and record at the rate of 30 data samples per second. The Purdue Pegboard test and the O'Connor Tweezer Dexterity test are timed manual dexterity assessment tests with accomplishment measured by a single outcome metric -- speed. However, accuracy is often more important than speed in surgical tasks. I have modified both of these standardized tests to incorporate an assessment of accuracy. For the integrated system, I show the results of two validation studies: (1) Construct validity and (2) Concurrent validity. I also propose a new method to interpret hand movement data for objective assessment of manual dexterity, called EDGE (ElectroDextroGramExam). The EDGE model derives analogies from the gait analysis and the ECG (ElectroCardioGram). By dividing each cycle of a repetitive task into discrete phases, we can better understand the differences between the motion characteristics of a novice versus an expert surgeon. This would help in providing a meaningful feedback to the learners for improving their manual skills.

Despite the apparent effortlessness with which we control our limbs, the physics of the skeletal muscle system that allows you to move and interact with the world are complex. Consequently, executing crisp and precise movements presents a complex control problem to the nervous system. In this thesis, we probe the neural computations in primary motor cortex (M1) and dorsal premotor cortex (PMd) that subserve reaching movements. We record neural activity using electrodes during highly controlled reaching movements performed by rhesus macaques. These neuronal population data were analyzed and modeled using techniques borrowed from the theories of dynamical systems and of dimensionality reduction. We employ both direct neuronal perturbations delivered via optogenetic activation or electrical microstimulation and mechanical perturbations of the arm facilitated by a novel, haptic reaching paradigm. We used engineered tools for observing and perturbing the neural circuits of the primate motor system, enabling dynamical models of neuronal computation to be formulated, validated, and refined. We present three major scientific results, enabled by several technical advances. First, we develop an extended array of optogenetic tools in squirrel monkeys for optical activation and inhibition of genetically and anatomically-targeted neuronal populations. Second, we utilize optogenetic activation in motor cortex of reaching macaques and analyze the robust, local neuronal dynamics which facilitate rapid recovery from this perturbation. Third, we develop an artifact rejection method which we use to directly observe the cortical response to electrical microstimulation, which we then contrast with optogenetic perturbation. Fourth, we apply ideas from optimal feedback control theory to demonstrate that the selection of task-appropriate control policies during reaching is strongly reflected in motor cortical preparatory activity. Lastly, we discuss the need for two-photon calcium imaging in awake, behaving non-human primates and report significant progress towards translating these tools from rodent models.

Rapid technology developments in neuroscience are enabling us to record from an ever increasing number of neurons from the brain. However, with the deluge of experimental data, our ability to extract simple yet fundamental understandings of the neural mechanisms underlying behavior and cognition is hampered by a lack of theoretically principled data analytics procedures. In the present work, we outline a set of theoretical frameworks that begins to address this challenge. First, we focus on the analysis of trial-averaged data obtained over experimental repetitions of tightly controlled behaviors. We start by developing a theory of neural dimensionality, which explains the prevalence of low-dimensional dynamic portraits observed in system neuroscience. We then connect the experimental act of recording a random subset of neurons to the mathematical theories of random projection, and illustrate how we might understand anything about the brain given the infinitesimal fractional of behaviorally relevant neurons observed. The second part of the thesis addresses the analyses of single-trial neural data collected during potentially more complex or naturalistic behaviors that may not be repeatable. We explore the effects of trial-to-trial variability and neuronal noise in the context of several analytically tractable generative data models covering linear and nonlinear stimulus-response mappings as well as static and dynamic latent states. We derive exhaustively the functional dependencies of commonly applied analytics procedures' performances on the number of recorded neurons, the number of trials and other model specific parameters. For each of the theoretical puzzles addressed in this thesis, we formulate the question with mathematical precision, derive quantitative predictions testable against simulations and/or neural data, and provide guidelines for the interpretation of past results as well as the design of future experiments.

Humans and other organisms show an incredibly sophisticated ability to learn about their environments during their lifetimes. This learning is thought to alter the strength of connections between neurons in the brain, but we still do not understand the principles linking synaptic changes at the neural level to behavioral changes at the psychological level. Part of the difficulty stems from depth: the brain has a deep, many-layered structure that substantially complicates the learning process. To understand the specific impact of depth, I develop the theory of gradient descent learning in deep linear neural networks. Despite their linearity, the learning problem in these networks remains nonconvex and exhibits rich nonlinear learning dynamics. I give new exact solutions to the dynamics that quantitatively answer fundamental theoretical questions such as how learning speed scales with depth. These solutions revise the basic conceptual picture underlying deep learning systems--both engineered and biological--with ramifications for a variety of phenomena. I highlight three consequences at different levels of detail. First, the theory shows that layerwise unsupervised learning is a domain general strategy for speeding up subsequent learning, which I link to critical period plasticity in sensory cortices. Second, the theory suggests that depth influences the size and timing of receptive field changes in visual perceptual learning. And third, by considering data drawn from structured probabilistic graphical models, the theory reveals that only deep (and not shallow) networks undergo quasi stage-like transitions during learning reminiscent of those found in infant semantic development. These applications span levels of analysis from single neurons to cognitive psychology, demonstrating the potential of deep linear networks to connect detailed changes in neuronal networks to changes in high-level behavior and cognition.

While it is accepted that coordinated activity among populations of neurons in three-dimensional brain structures is critical to animal behavior, our understanding of such systems and their dynamics is circumscribed by available recording and intervention technologies. In particular, the ability to optically record and perturb dynamics in long-range, connectivity- and genetically-specified projections is needed to understand the roles that such inter-regional projections play in behavior, and fast methods to record and perturb population dynamics at cellular resolution across brain volumes are necessary to understand how cell assemblies coordinate across areas to encode and generate behavior. Finally, interpretable statistical techniques able to accurately capture the trends and dynamics in these complex data are required to turn observations into comprehensible descriptions, models, and theories. This work seeks to address these needs by developing (1) fiber photometry, a minimally-invasive method for recording bulk activity in connectivity-targeted and genetically-targeted cell bodies and projections during behavior, (2) SWIFT volume imaging, a method for synchronous recording and identification of cell assemblies across large volumes of tissue at high frame rates during behavior, and (3) interpretable statistical methods appropriate for high dimensional, potentially nonlinear neuroimaging data including those that are produced by SWIFT but also applicable to other whole-brain imaging data such as those generated by functional magnetic resonance imaging (fMRI). These approaches are applied and validated in several examples of motivated behavior including social approach behavior in mice, prey approach behavior in zebrafish, reward-based learning in mice, modulation of reward-seeking behavior by prefrontal cortex in rats, and incentivized decision making in humans.

Voluntary movement is such an integral part of common tasks that the loss of this ability is detrimental to quality of life. Effective functional restoration for patients with a limited ability to move requires deep understanding of movement control. However, despite decades of motor system research, the mechanism by which motor cortex controls movement is still unclear. Although technological advances such as electrical microstimulation have been used to investigate this mechanism, its limitations in simultaneous recording and perturbation have prevented us from obtaining more informative measurements. To address this challenge, a multidisciplinary approach was taken to further examine the underlying mechanism of motor control. Specifically, we used optogenetics along with the analytical framework of dynamical systems theory to probe the dynamics of motor preparation. Three major results are presented in this work. Firstly, we characterized and assessed the functionality of optogenetics electrophysiologically and histologically in non-human primates. Although optogenetics has been used extensively in rodents, it is still in a developmental state in primates. Hence, the efficiency of virus transfection, the reliability of neural responses to optical stimulation, the pattern of opsin expression and the safety to animals were investigated to minimize any potential risk and to aid future experimental designs. We also discovered that, in contrast to electrical microstimulation, optical stimulation in cortical motor and premotor areas did not evoke overt skeletal movements. Secondly, we continued the characterization process by injecting a red-shifted opsin, C1V1(TT), in dorsal premotor cortex (PMd) and optically perturbed the neural activity while the animals were actively engaged in an instructed-delay reach task. We found that the optical perturbation in PMd resulted in increased reach reaction times. Moreover, using the dynamical systems perspective, we discovered that, post-perturbation, the neural state did not return to its pre-perturbed state. Instead, it proceeded directly to re-join the normal neural trajectory path to execute the movement. We also observed that optical stimulation did not obliterate task-related activity in light-responsive neurons. In fact, the relationship between task-related and optically-evoked activities appeared to be linearly additive. Lastly, we developed a decoding algorithm to extract kinematics information from optogenetically-perturbed data. We trained a Kalman filter based on a mixture of perturbed and unperturbed data, and found that it provided us with an effective decoder. This decoding performance was achieved despite the fact that the decoder made no attempt to detect whether or not the neural activity was perturbed.

Motor neuroscience and brain-machine interface (BMI) design is based on examining how the brain controls voluntary movement, typically by recording neural activity and behavior from animal models. Recording technologies used with these animal models have traditionally limited the range of behaviors that can be studied, and thus the generality of science and engineering research. In this dissertation, I present a freely-moving animal model using neural and behavioral recording technologies that do not constrain movement. The freely-moving rhesus monkey model employs technology that transmits neural activity from an intracortical array using a head-mounted device and records behavior through computer vision using markerless motion capture. This dissertation demonstrates the flexibility and utility of this new monkey model, including the first recordings from motor cortex while rhesus monkeys walk quadrupedally on a treadmill. Using this monkey model, it is shown that multi-unit threshold-crossing neural activity encodes the phase of walking and that the average firing rate of the threshold crossings covaries with the speed of individual steps. On a population level, neural state-space trajectories of walking at different speeds have similar rotational dynamics in some dimensions that evolve at the step rate of walking, yet robustly separate by speed in other state-space dimensions. Freely-moving animal models may allow neuroscientists to examine a wider range of behaviors and can provide a flexible experimental paradigm for examining the neural mechanisms that underlie movement generation across behaviors and environments. For BMIs, freely-moving animal models have the potential to aid prosthetic design by examining how neural encoding changes with posture, environment, and other real-world context changes. Understanding this new realm of behavior in more naturalistic settings is essential for overall progress of basic motor neuroscience and for the successful translation of BMIs to people with paralysis.