Gaussian Process Factor Analysis (GPFA) is a powerful latent variable model for extracting low-dimensional manifolds underlying population neural activities. However, one limitation of standard GPFA models is that the number of latent factors needs to be pre-specified or selected through heuristic-based processes, and that all factors contribute at all times. We propose the infinite GPFA model, a fully Bayesian non-parametric extension of the classical GPFA by incorporating an Indian Buffet Process (IBP) prior over the factor loading process, such that it is possible to infer a potentially infinite set of latent factors, and the identity of those factors that contribute to neural firings in a compositional manner at \textit{each} time point. Learning and inference in the infinite GPFA model is performed through variational expectation-maximisation, and we additionally propose scalable extensions based on sparse variational Gaussian Process methods. We empirically demonstrate that the infinite GPFA model correctly infers dynamically changing activations of latent factors on a synthetic dataset. By fitting the infinite GPFA model to population activities of hippocampal place cells during spatial tasks with alternating random foraging and spatial memory phases, we identify novel non-trivial and behaviourally meaningful dynamics in the neural encoding process.

Recent advancements in bionic prosthetic technology offer transformative opportunities to restore mobility and functionality for individuals with missing limbs. Users of bionic limbs, or bionic humans, learn to seamlessly integrate prosthetic extensions into their motor repertoire, regaining critical motor abilities. The remarkable movement generalization and environmental adaptability demonstrated by these individuals highlight motor intelligence capabilities unmatched by current artificial intelligence systems. Addressing these limitations, MyoChallenge '24 at NeurIPS 2024 established a benchmark for human-robot coordination with an emphasis on joint control of both biological and mechanical limbs. The competition featured two distinct tracks: a manipulation task utilizing the myoMPL model, integrating a virtual biological arm and the Modular Prosthetic Limb (MPL) for a passover task; and a locomotion task using the novel myoOSL model, combining a bilateral virtual biological leg with a trans-femoral amputation and the Open Source Leg (OSL) to navigate varied terrains. Marking the third iteration of the MyoChallenge, the event attracted over 50 teams with more than 290 submissions all around the globe, with diverse participants ranging from independent researchers to high school students. The competition facilitated the development of several state-of-the-art control algorithms for bionic musculoskeletal systems, leveraging techniques such as imitation learning, muscle synergy, and model-based reinforcement learning that significantly surpassed our proposed baseline performance by a factor of 10. By providing the open-source simulation framework of MyoSuite, standardized tasks, and physiologically realistic models, MyoChallenge serves as a reproducible testbed and benchmark for bridging ML and biomechanics. The competition website is featured here: https://sites.google.com/view/myosuite/myochallenge/myochallenge-2024.

Neural networks are most often trained under the assumption that data come from a stationary distribution. However, settings in which this assumption is violated are of increasing importance; examples include supervised learning with distributional shifts, reinforcement learning, continual learning and non-stationary contextual bandits. Here, we introduce a novel learning approach that automatically models and adapts to non-stationarity by linking parameters through an Ornstein-Uhlenbeck process with an adaptive drift parameter. The adaptive drift draws the parameters towards the distribution used at initialisation, so the approach can be understood as a form of soft parameter reset. We show empirically that our approach performs well in non-stationary supervised, and off-policy reinforcement learning settings.

Dual-process theories play a central role in both psychology and neuroscience, figuring prominently in domains ranging from executive control to reward-based learning to judgment and decision making. In each of these domains, two mechanisms appear to operate concurrently, one relatively high in computational complexity, the other relatively simple. Why is neural information processing organized in this way? We propose an answer to this question based on the notion of compression. The key insight is that dual-process structure can enhance adaptive behavior by allowing an agent to minimize the description length of its own behavior. We apply a single model based on this observation to findings from research on executive control, reward-based learning, and judgment and decision making, showing that seemingly diverse dual-process phenomena can be understood as domain-specific consequences of a single underlying set of computational principles.

We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key assumption that observations are conditionally independent given latents, the RPM combines parametric prior and observation-conditioned latent distributions with non-parametric observation marginals. This approach leads to a flexible learnt recognition model capturing latent dependence between observations, without the need for an explicit, parametric generative model. The RPM admits exact maximum-likelihood learning for discrete latents, even for powerful neural network-based recognition. We develop effective approximations applicable in the continuous latent case. Experiments demonstrate the effectiveness of the RPM on high-dimensional data, learning image classification from weak indirect supervision; direct image-level latent Dirichlet allocation; and Recognition-Parametrised Gaussian Process Factor Analysis (RP-GPFA) applied to multi-factorial spatiotemporal datasets. The RPM provides a powerful framework to discover meaningful latent structure underlying observational data, a function critical to both animal and artificial intelligence.

A common setting in multitask reinforcement learning (RL) demands that an agent rapidly adapt to various stationary reward functions randomly sampled from a fixed distribution. In such situations, the successor representation (SR) is a popular framework which supports rapid policy evaluation by decoupling a policy's expected discounted, cumulative state occupancies from a specific reward function. However, in the natural world, sequential tasks are rarely independent, and instead reflect shifting priorities based on the availability and subjective perception of rewarding stimuli. Reflecting this disjunction, in this paper we study the phenomenon of diminishing marginal utility and introduce a novel state representation, the $\lambda$ representation ($\lambda$R) which, surprisingly, is required for policy evaluation in this setting and which generalizes the SR as well as several other state representations from the literature. We establish the $\lambda$R's formal properties and examine its normative advantages in the context of machine learning, as well as its usefulness for studying natural behaviors, particularly foraging.

Exploration is essential in reinforcement learning, particularly in environments where external rewards are sparse. Here we focus on exploration with intrinsic rewards, where the agent transiently augments the external rewards with self-generated intrinsic rewards. Although the study of intrinsic rewards has a long history, existing methods focus on composing the intrinsic reward based on measures of future prospects of states, ignoring the information contained in the retrospective structure of transition sequences. Here we argue that the agent can utilise retrospective information to generate explorative behaviour with structure-awareness, facilitating efficient exploration based on global instead of local information. We propose Successor-Predecessor Intrinsic Exploration (SPIE), an exploration algorithm based on a novel intrinsic reward combining prospective and retrospective information. We show that SPIE yields more efficient and ethologically plausible exploratory behaviour in environments with sparse rewards and bottleneck states than competing methods. We also implement SPIE in deep reinforcement learning agents, and show that the resulting agent achieves stronger empirical performance than existing methods on sparse-reward Atari games.

Perception is an inferential process, in which the state of the immediate environment must be estimated from sensory input. Inference in the face of noise and ambiguity requires reasoning with uncertainty, and much animal behaviour appears close to Bayes optimal. This observation has inspired hypotheses for how the activity of neurons in the brain might represent the distributional beliefs necessary to implement explicit Bayesian computation. While previous work has focused on the sufficiency of these hypothesised codes for computation, relatively little consideration has been given to optimality in the representation itself. Here, we adopt an encoder-decoder approach to study representational optimisation within one hypothesised belief encoding framework: the distributed distributional code (DDC). We consider a setting in which typical belief distribution functions take the form of a sparse combination of an underlying set of basis functions, and the corresponding DDC signals are corrupted by neural variability. We estimate the conditional entropy over beliefs induced by these DDC signals using an appropriate decoder. Like other hypothesised frameworks, a DDC representation of a belief depends on a set of fixed encoding functions that are usually set arbitrarily. Our approach allows us to seek the encoding functions that minimise the decoder conditional entropy and thus optimise representational accuracy in an information theoretic sense. We apply the approach to show how optimal encoding properties may adapt to represent beliefs in new environments, relating the results to experimentally reported neural responses.

A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent variables captured through a probabilistic graphical model. Although the learning of structured graphical models has a long history, much recent work in unsupervised modelling has instead emphasised flexible deep-network-based generation, either transforming independent latent generators to model complex data or assuming that distinct observed variables are derived from different latent nodes. Here, we extend amortised variational inference to incorporate structured factors over multiple variables, able to capture the observation-induced posterior dependence between latents that results from “explaining away” and thus allow complex observations to depend on multiple nodes of a structured graph. We show that appropriately parametrised factors can be combined efficiently with variational message passing in rich graphical structures. We instantiate the framework in nonlinear Gaussian Process Factor Analysis, evaluating the structured recognition framework using synthetic data from known generative processes. We fit the GPFA model to high-dimensional neural spike data from the hippocampus of freely moving rodents, where the model successfully identifies latent signals that correlate with behavioural covariates.

Deep learning (DL) and reinforcement learning (RL) methods seem to be a part of indispensable factors to achieve human-level or super-human AI systems. On the other hand, both DL and RL have strong connections with our brain functions and with neuroscientific findings. In this review, we summarize talks and discussions in the "Deep Learning and Reinforcement Learning" session of the symposium, International Symposium on Artificial Intelligence and Brain Science. In this session, we discussed whether we can achieve comprehensive understanding of human intelligence based on the recent advances of deep learning and reinforcement learning algorithms. Speakers contributed to provide talks about their recent studies that can be key technologies to achieve human-level intelligence.

The firing of neural populations is coordinated across cells, in time, and across experimentalconditions or repeated experimental trials; and so a full understanding of the computationalsignificance of neural responses must be based on a separation of these different contributions tostructured activity.Tensor decomposition is an approach to untangling the influence of multiple factors in data that iscommon in many fields. However, despite some recent interest in neuroscience, wider applicabilityof the approach is hampered by the lack of a full probabilistic treatment allowing principledinference of a decomposition from non-Gaussian spike-count data.Here, we extend the Pólya-Gamma (PG) augmentation, previously used in sampling-based Bayesianinference, to implement scalable variational inference in non-conjugate spike-count models.Using this new approach, we develop techniques related to automatic relevance determination to inferthe most appropriate tensor rank, as well as to incorporate priors based on known brain anatomy suchas the segregation of cell response properties by brain area.We apply the model to neural recordings taken under conditions of visual-vestibular sensoryintegration, revealing how the encoding of self- and visual-motion signals is modulated by thesensory information available to the animal.

Models that employ latent variables to capture structure in observed data lie at the heart of many current unsupervised learning algorithms, but exact maximum-likelihood learning for powerful and flexible latent-variable models is almost always intractable. Thus, state-of-the-art approaches either abandon the maximum-likelihood framework entirely, or else rely on a variety of variational approximations to the posterior distribution over the latents. Here, we propose an alternative approach that we call amortised learning. Rather than computing an approximation to the posterior over latents, we use a wake-sleep Monte-Carlo strategy to learn a function that directly estimates the maximum-likelihood parameter updates. Amortised learning is possible whenever samples of latents and observations can be simulated from the generative model, treating the model as a “black box”. We demonstrate its effectiveness on a wide range of complex models, including those with latents that are discrete or supported on non-Euclidean spaces.

Biological systems face dynamic environments that require continual learning. It is not well understood how these systems balance the tension between flexibility for learning and robustness for memory of previous behaviors. Continual learning without catastrophic interference also remains a challenging problem in machine learning. Here, we develop a novel learning rule designed to minimize interference between sequentially learned tasks in recurrent networks. Our learning rule preserves network dynamics within activity-defined subspaces used for previously learned tasks. It encourages dynamics associated with new tasks that might otherwise interfere to instead explore orthogonal subspaces, and it allows for reuse of previously established dynamical motifs where possible. Employing a set of tasks used in neuroscience, we demonstrate that our approach successfully eliminates catastrophic interference and offers a substantial improvement over previous continual learning algorithms. Using dynamical systems analysis, we show that networks trained using our approach can reuse similar dynamical structures across similar tasks. This possibility for shared computation allows for faster learning during sequential training. Finally, we identify organizational differences that emerge when training tasks sequentially versus simultaneously.

A common goal in the analysis of neural data is to compress large population recordings into sets of interpretable, low-dimensional latent trajectories. This problem can be approached using Gaussian process (GP)-based methods which provide uncertainty quantification and principled model selection. However, standard GP priors do not distinguish between underlying dynamical processes and other forms of temporal autocorrelation. Here, we propose a new family of “dynamical” priors over trajectories, in the form of GP covariance functions that express a property shared by most dynamical systems: temporal non-reversibility. Non-reversibility is a universal signature of autonomous dynamical systems whose state trajectories follow consistent flow fields, such that any observed trajectory could not occur in reverse. Our new multi-output GP kernels can be used as drop-in replacements for standard kernels in multivariate regression, but also in latent variable models such as Gaussian process factor analysis (GPFA). We therefore introduce GPFADS (Gaussian Process Factor Analysis with Dynamical Structure), which models single-trial neural population activity using low-dimensional, non-reversible latent processes. Unlike previously proposed non-reversible multi-output kernels, ours admits a Kronecker factorization enabling fast and memory-efficient learning and inference. We apply GPFADS to synthetic data and show that it correctly recovers ground truth phase portraits. GPFADS also provides a probabilistic generalization of jPCA, a method originally developed for identifying latent rotational dynamics in neural data. When applied to monkey M1 neural recordings, GPFADS discovers latent trajectories with strong dynamical structure in the form of rotations.

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolution function drawn from a Gaussian process (GP) conditioned on a set of learnt fixed points and corresponding local Jacobian matrices. This form yields a flexible nonparametric model of the dynamics, with a representation corresponding directly to the interpretable portraits routinely employed in the study of nonlinear dynamical systems. The learning algorithm combines inference of continuous latent paths underlying observed data with a sparse variational description of the dynamical process. We demonstrate our approach on simulated data from different nonlinear dynamical systems.

Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X and the unmeasured confounder. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which convergence occurs at the minimax optimal rate for unconfounded, single-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric IV regression.

Animals need to devise strategies to maximize returns while interacting with their environment based on incoming noisy sensory observations. Task-relevant states, such as the agent's location within an environment or the presence of a predator, are often not directly observable but must be inferred using available sensory information. Successor representations (SR) have been proposed as a middle-ground between model-based and model-free reinforcement learning strategies, allowing for fast value computation and rapid adaptation to changes in the reward function or goal locations. Indeed, recent studies suggest that features of neural responses are consistent with the SR framework. However, it is not clear how such representations might be learned and computed in partially observed, noisy environments. Here, we introduce a neurally plausible model using \emph{distributional successor features}, which builds on the distributed distributional code for the representation and computation of uncertainty, and which allows for efficient value function computation in partially observed environments via the successor representation. We show that distributional successor features can support reinforcement learning in noisy environments in which direct learning of successful policies is infeasible.

Humans and other animals are frequently near-optimal in their ability to integrate noisy and ambiguous sensory data to form robust percepts---which are informed both by sensory evidence and by prior expectations about the structure of the environment. It is suggested that the brain does so using the statistical structure provided by an internal model of how latent, causal factors produce the observed patterns. In dynamic environments, such integration often takes the form of \emph{postdiction}, wherein later sensory evidence affects inferences about earlier percepts. As the brain must operate in current time, without the luxury of acausal propagation of information, how does such postdictive inference come about? Here, we propose a general framework for neural probabilistic inference in dynamic models based on the distributed distributional code (DDC) representation of uncertainty, naturally extending the underlying encoding to incorporate implicit probabilistic beliefs about both present and past. We show that, as in other uses of the DDC, an inferential model can be learnt efficiently using samples from an internal model of the world. Applied to stimuli used in the context of psychophysics experiments, the framework provides an online and plausible mechanism for inference, including postdictive effects.

We introduce a novel scalable approach to identifying common latent structure in neural population spike-trains, which allows for variability both in the trajectory and in the rate of progression of the underlying computation. Our approach is based on shared latent Gaussian processes (GPs) which are combined linearly, as in the Gaussian Process Factor Analysis (GPFA) algorithm. We extend GPFA to handle unbinned spike-train data by incorporating a continuous time point-process likelihood model, achieving scalability with a sparse variational approximation. Shared variability is separated into terms that express condition dependence, as well as trial-to-trial variation in trajectories. Finally, we introduce a nested GP formulation to capture variability in the rate of evolution along the trajectory. We show that the new method learns to recover latent trajectories in synthetic data, and can accurately identify the trial-to-trial timing of movement-related parameters from motor cortical data without any supervision.

We introduce a new approach to learning in hierarchical latent-variable generative models called the “distributed distributional code Helmholtz machine”, which emphasises flexibility and accuracy in the inferential process. Like the original Helmholtz machine and later variational autoencoder algorithms (but unlike adver- sarial methods) our approach learns an explicit inference or “recognition” model to approximate the posterior distribution over the latent variables. Unlike these earlier methods, it employs a posterior representation that is not limited to a narrow tractable parametrised form (nor is it represented by samples). To train the genera- tive and recognition models we develop an extended wake-sleep algorithm inspired by the original Helmholtz machine. This makes it possible to learn hierarchical latent models with both discrete and continuous variables, where an accurate poste- rior representation is essential. We demonstrate that the new algorithm outperforms current state-of-the-art methods on synthetic, natural image patch and the MNIST data sets.

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variational optimisation of the posterior distribution on coordinates and locally linear maps from the latent space to the observation space given the data. Thus, the LL-LVM encapsulates the local-geometry preserving intuitions that underlie non-probabilistic methods such as locally linear embedding (LLE). Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, select the intrinsic dimensionality of the manifold, construct out-of-sample extensions and to combine the manifold model with additional probabilistic models that capture the structure of coordinates within the manifold.

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex.

Biological tissue is often composed of cells with similar morphologies replicated throughout large volumes and many biological applications rely on the accurate identification of these cells and their locations from image data. Here we develop a generative model that captures the regularities present in images composed of repeating elements of a few different types. Formally, the model can be described as convolutional sparse block coding. For inference we use a variant of convolutional matching pursuit adapted to block-based representations. We extend the K-SVD learning algorithm to subspaces by retaining several principal vectors from the SVD decomposition instead of just one. Good models with little cross-talk between subspaces can be obtained by learning the blocks incrementally. We perform extensive experiments on simulated images and the inference algorithm consistently recovers a large proportion of the cells with a small number of false positives. We fit the convolutional model to noisy GCaMP6 two-photon images of spiking neurons and to Nissl-stained slices of cortical tissue and show that it recovers cell body locations without supervision. The flexibility of the block-based representation is reflected in the variability of the recovered cell shapes.

Population neural recordings with long-range temporal structure are often best understood in terms of a shared underlying low-dimensional dynamical process. Advances in recording technology provide access to an ever larger fraction of the population, but the standard computational approaches available to identify the collective dynamics scale poorly with the size of the dataset. Here we describe a new, scalable approach to discovering the low-dimensional dynamics that underlie simultaneously recorded spike trains from a neural population. Our method is based on recurrent linear models (RLMs), and relates closely to timeseries models based on recurrent neural networks. We formulate RLMs for neural data by generalising the Kalman-filter-based likelihood calculation for latent linear dynamical systems (LDS) models to incorporate a generalised-linear observation process. We show that RLMs describe motor-cortical population data better than either directly-coupled generalised-linear models or latent linear dynamical system models with generalised-linear observations. We also introduce the cascaded linear model (CLM) to capture low-dimensional instantaneous correlations in neural populations. The CLM describes the cortical recordings better than either Ising or Gaussian models and, like the RLM, can be fit exactly and quickly. The CLM can also be seen as a generalization of a low-rank Gaussian model, in this case factor analysis. The computational tractability of the RLM and CLM allow both to scale to very high-dimensional neural data.

We constantly look for patterns in the environment that allow us to learn its key regularities. These regularities are fundamental in enabling us to make predictions about what is likely to happen next. The physiological study of regularity extraction has focused primarily on repetitive sequence-based rules within the sensory environment, or on stimulus-outcome associations in the context of reward-based decision-making. Here we ask whether we implicitly encode non-sequential stochastic regularities, and detect violations therein. We addressed this question using a novel experimental design and both behavioural and magnetoencephalographic (MEG) metrics associated with responses to pure-tone sounds with frequencies sampled from a Gaussian distribution. We observed that sounds in the tail of the distribution evoked a larger response than those that fell at the centre. This response resembled the mismatch negativity (MMN) evoked by surprising or unlikely events in traditional oddball paradigms. Crucially, responses to physically identical outliers were greater when the distribution was narrower. These results show that humans implicitly keep track of the uncertainty induced by apparently random distributions of sensory events. Source reconstruction suggested that the statistical-context-sensitive responses arose in a temporo-parietal network, areas that have been associated with attention orientation to unexpected events. Our results demonstrate a very early neurophysiological marker of the brain's ability to implicitly encode complex statistical structure in the environment. We suggest that this sensitivity provides a computational basis for our ability to make perceptual inferences in noisy environments and to make decisions in an uncertain world.

There are many methods for decomposing signals into a sum of amplitude and frequency modulated sinusoids. In this paper we take a new estimation based approach. Identifying the problem as ill-posed, we show how to regularize the solution by imposing soft constraints on the amplitude and phase variables of the sinusoids. Estimation proceeds using a version of Kalman smoothing. We evaluate the method on synthetic and natural, clean and noisy signals, showing that it outperforms previous decompositions, but at a higher computational cost.

Latent linear dynamical systems with generalised-linear observation models arise in a variety of applications, for example when modelling the spiking activity of populations of neurons. Here, we show how spectral learning methods for linear systems with Gaussian observations (usually called subspace identification in this context) can be extended to estimate the parameters of dynamical system models observed through non-Gaussian noise models. We use this approach to obtain estimates of parameters for a dynamical model of neural population data, where the observed spike-counts are Poisson-distributed with log-rates determined by the latent dynamical process, possibly driven by external inputs. We show that the extended system identification algorithm is consistent and accurately recovers the correct parameters on large simulated data sets with much smaller computational cost than approximate expectation-maximisation (EM) due to the non-iterative nature of subspace identification. Even on smaller data sets, it provides an effective initialization for EM, leading to more robust performance and faster convergence. These benefits are shown to extend to real neural data.

We present a dynamic nonlinear generative model for visual motion based on a latent representation of binary-gated Gaussian variables. Trained on sequences of images, the model learns to represent different movement directions in different variables. We use an online approximate-inference scheme that can be mapped to the dynamics of networks of neurons. Probed with drifting grating stimuli and moving bars of light, neurons in the model show patterns of responses analogous to those of direction-selective simple cells in primary visual cortex. Most model neurons also show speed tuning and respond equally well to a range of motion directions and speeds aligned to the constraint line of their respective preferred speed. We show how these computations are enabled by a specific pattern of recurrent connections learned by the model.

Neurons in the neocortex code and compute as part of a locally interconnected population. Large-scale multi-electrode recording makes it possible to access these population processes empirically by fitting statistical models to unaveraged data. What statistical structure best describes the concurrent spiking of cells within a local network? We argue that in the cortex, where firing exhibits extensive correlations in both time and space and where a typical sample of neurons still reflects only a very small fraction of the local population, the most appropriate model captures shared variability by a low-dimensional latent process evolving with smooth dynamics, rather than by putative direct coupling. We test this claim by comparing a latent dynamical model with realistic spiking observations to coupled generalised linear spike-response models (GLMs) using cortical recordings. We find that the latent dynamical approach outperforms the GLM in terms of goodness-of-fit, and reproduces the temporal correlations in the data more accurately. We also compare models whose observations models are either derived from a Gaussian or point-process models, finding that the non-Gaussian model provides slightly better goodness-of-fit and more realistic population spike counts.

Simultaneous recordings of many neurons embedded within a recurrently-connected cortical network may provide concurrent views into the dynamical processes of that network, and thus its computational function. In principle, these dynamics might be identified by purely unsupervised, statistical means. Here, we show that a Hidden Switching Linear Dynamical Systems (HSLDS) model---in which multiple linear dynamical laws approximate a nonlinear and potentially non-stationary dynamical process---is able to distinguish different dynamical regimes within single-trial motor cortical activity associated with the preparation and initiation of hand movements. The regimes are identified without reference to behavioural or experimental epochs, but nonetheless transitions between them correlate strongly with external events whose timing may vary from trial to trial. The HSLDS model also performs better than recent comparable models in predicting the firing rate of an isolated neuron based on the firing rates of others, suggesting that it captures more of the "shared variance" of the data. Thus, the method is able to trace the dynamical processes underlying the coordinated evolution of network activity in a way that appears to reflect its computational role.

A number of recent scientific and engineering problems require signals to be decomposed into a product of a slowly varying positive envelope and a quickly varying carrier whose instantaneous frequency also varies slowly over time. Although signal processing provides algorithms for so-called amplitude- and frequency-demodulation (AFD), there are well known problems with all of the existing methods. Motivated by the fact that AFD is ill-posed, we approach the problem using probabilistic inference. The new approach, called probabilistic amplitude and frequency demodulation (PAFD), models instantaneous frequency using an auto-regressive generalization of the von Mises distribution, and the envelopes using Gaussian auto-regressive dynamics with a positivity constraint. A novel form of expectation propagation is used for inference. We demonstrate that although PAFD is computationally demanding, it outperforms previous approaches on synthetic and real signals in clean, noisy and missing data settings.

Demodulation is an ill-posed problem whenever both carrier and envelope signals are broadband and unknown. Here, we approach this problem using the methods of probabilistic inference. The new approach, called Probabilistic Amplitude Demodulation (PAD), is computationally challenging but improves on existing methods in a number of ways. By contrast to previous approaches to demodulation, it satisfies five key desiderata: PAD has soft constraints because it is probabilistic; PAD is able to automatically adjust to the signal because it learns parameters; PAD is user-steerable because the solution can be shaped by user-specific prior information; PAD is robust to broad-band noise because this is modeled explicitly; and PAD's solution is self-consistent, empirically satisfying a Carrier Identity property. Furthermore, the probabilistic view naturally encompasses noise and uncertainty, allowing PAD to cope with missing data and return error bars on carrier and envelope estimates. Finally, we show that when PAD is applied to a bandpass-filtered signal, the stop-band energy of the inferred carrier is minimal, making PAD well-suited to sub-band demodulation.

Amplitude demodulation is an ill-posed problem and so it is natural to treat it from a Bayesian viewpoint, inferring the most likely carrier and envelope under probabilistic constraints. One such treatment is Probabilistic Amplitude Demodulation (PAD), which, whilst computationally more intensive than traditional approaches, offers several advantages. Here we provide methods for estimating the uncertainty in the PAD-derived envelopes and carriers, and for learning free parameters like the time-scale of the envelope. We show how the probabilistic approach can naturally handle noisy and missing data. Finally, we indicate how to extend the model to signals which contain multiple modulators and carriers.

We study unsupervised learning in a probabilistic generative model for occlusion. The model uses two types of latent variables: one indicates which objects are present in the image, and the other how they are ordered in depth. This depth order then determines how the positions and appearances of the objects present, specified in the model parameters, combine to form the image. We show that the object parameters can be learnt from an unlabelled set of images in which objects occlude one another. Exact maximum-likelihood learning is intractable. However, we show that tractable approximations to Expectation Maximization (EM) can be found if the training images each contain only a small number of objects on average. In numerical experiments it is shown that these approximations recover the correct set of object parameters. Experiments on a novel version of the bars test using colored bars, and experiments on more realistic data, show that the algorithm performs well in extracting the generating causes. Experiments based on the standard bars benchmark test for object learning show that the algorithm performs well in comparison to other recent component extraction approaches. The model and the learning algorithm thus connect research on occlusion with the research field of multiple-cause component extraction methods.

The visual system must learn to infer the presence of objects and features in the world from the images it encounters, and as such it must, either implicitly or explicitly, model the way these elements interact to create the image. Do the response properties of cells in the mammalian visual system reflect this constraint? To address this question, we constructed a probabilistic model in which the identity and attributes of simple visual elements were represented explicitly and learnt the parameters of this model from unparsed, natural video sequences. After learning, the behaviour and grouping of variables in the probabilistic model corresponded closely to functional and anatomical properties of simple and complex cells in the primary visual cortex (V1). In particular, feature identity variables were activated in a way that resembled the activity of complex cells, while feature attribute variables responded much like simple cells. Furthermore, the grouping of the attributes within the model closely parallelled the reported anatomical grouping of simple cells in cat V1. Thus, this generative model makes explicit an interpretation of complex and simple cells as elements in the segmentation of a visual scene into basic independent features, along with a parametrisation of their moment-by-moment appearances. We speculate that such a segmentation may form the initial stage of a hierarchical system that progressively separates the identity and appearance of more articulated visual elements, culminating in view-invariant object recognition.

Increasing the performance of neural prostheses is necessary for assuring their clinical viability. One performance limitation is the presence of correlated trial-to-trial variability that can cause neural responses to wax and wane in concert as the subject is, for example, more attentive or more fatigued. We report here the design and characterization of a Factor- Analysis-based decoding algorithm that is able to contend with this confound. We characterize the decoder (classifier) on a previously reported dataset where monkeys performed both a real reach task and a prosthetic cursor movement task while we recorded from 96 electrodes implanted in dorsal pre- motor cortex. In principle, the decoder infers the underlying factors that co-modulate the neurons' responses and can use this information to function with reduced error rates (1 of 8 reach target prediction) of up to ~75% (~20% total prediction error using independent Gaussian or Poisson models became ~5%). Such Factor-Analysis based methods appear to be effective when attempting to combat directly unobserved trial-by-trial neural variabiliy.

Point processes are difficult to analyze because they provide only a sparse and noisy observation of the intensity function driving the process. Gaussian Processes offer an attractive framework within which to infer underlying intensity functions. The result of this inference is a continuous function defined across time that is typically more amenable to analytical efforts. However, a naive implementation will become computationally infeasible in any problem of reasonable size, both in memory and run time requirements. We demonstrate problem specific methods for a class of renewal processes that eliminate the memory burden and reduce the solve time by orders of magnitude.

We consider the problem of extracting smooth low-dimensional neural trajectories'' that summarize the activity recorded simultaneously from tens to hundreds of neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional noisy spiking activity in a compact denoised form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the data are firstdenoised'' by smoothing over time, then a static dimensionality reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way, and account for spiking variability that may vary both across neurons and across time. We then present a novel method for extracting neural trajectories, Gaussian-process factor analysis (GPFA), which unifies the smoothing and dimensionality reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that GPFA provided a better characterization of the population activity than the two-stage methods. From the extracted single-trial neural trajectories, we directly observed a convergence in neural state during motor planning, an effect suggestive of attractor dynamics that was shown indirectly by previous studies.

Many perceptual processes and neural computations, such as speech recognition, motor control and learning, depend on the ability to measure and mark the passage of time. However, the processes that make such temporal judgements possible are unknown. A number of different hypothetical mechanisms have been advanced, all of which depend on the known, temporally predictable evolution of a neural or psychological state, possibly through oscillations or the gradual decay of a memory trace. Alternatively, judgements of elapsed time might be based on observations of temporally structured, but stochastic processes. Such processes need not be specific to the sense of time; typical neural and sensory processes contain at least some statistical structure across a range of time scales. Here, we investigate the statistical properties of an estimator of elapsed time which is based on a simple family of stochastic process.

Computational models of visual cortex, and in particular those based on sparse coding, have enjoyed much recent attention. Despite this currency, the question of how sparse or how over-complete a sparse representation should be, has gone without principled answer. Here, we use Bayesian model-selection methods to address these questions for a sparse-coding model based on a Student-t prior. Having validated our methods on toy data, we find that natural images are indeed best modelled by extremely sparse distributions; although for the Student-t prior, the associated optimal basis size is only modestly overcomplete.

Neural spike trains present challenges to analytical efforts due to their noisy, spiking nature. Many studies of neuroscienti(cid:2)c and neural prosthetic importance rely on a smoothed, denoised estimate of the spike train’s underlying (cid:2)ring rate. Current techniques to (cid:2)nd time-varying (cid:2)ring rates require ad hoc choices of parameters, offer no con(cid:2)dence intervals on their estimates, and can obscure potentially important single trial variability. We present a new method, based on a Gaussian Process prior, for inferring probabilistically optimal estimates of (cid:2)ring rate functions underlying single or multiple neural spike trains. We test the performance of the method on simulated data and experimentally gathered neural spike trains, and we demonstrate improvements over conventional estimators.

Natural sounds are structured on many time-scales. A typical segment of speech, for example, contains features that span four orders of magnitude: Sentences (~1s); phonemes (~0.1s); glottal pulses (~0.01s); and formants (<0.001s). The auditory system uses information from each of these time-scales to solve complicated tasks such as auditory scene analysis. One route toward understanding how auditory processing accomplishes this analysis is to build neuroscience-inspired algorithms which solve similar tasks and to compare the properties of these algorithms with properties of auditory processing. There is however a discord: Current machine-audition algorithms largely concentrate on the shorter time-scale structures in sounds, and the longer structures are ignored. The reason for this is two-fold. Firstly, it is a difficult technical problem to construct an algorithm that utilises both sorts of information. Secondly, it is computationally demanding to simultaneously process data both at high resolution (to extract short temporal information) and for long duration (to extract long temporal information). The contribution of this work is to develop a new statistical model for natural sounds that captures structure across a wide range of time-scales, and to provide efficient learning and inference algorithms. We demonstrate the success of this approach on a missing data task.

The brain extracts useful features from a maelstrom of sensory information, and a fundamental goal of theoretical neuroscience is to work out how it does so. One proposed feature extraction strategy is motivated by the observation that the meaning of sensory data, such as the identity of a moving visual object, is often more persistent than the activation of any single sensory receptor. This notion is embodied in the slow feature analysis (SFA) algorithm, which uses "slowness" as a heuristic by which to extract semantic information from multidimensional time series. Here, we develop a probabilistic interpretation of this algorithm, showing that inference and learning in the limiting case of a suitable probabilistic model yield exactly the results of SFA. Similar equivalences have proved useful in interpreting and extending comparable algorithms such as independent component analysis. For SFA, we use the equivalent probabilistic model as a conceptual springboard with which to motivate several novel extensions to the algorithm.

Spiking activity from neurophysiological experiments often exhibits dy- namics beyond that driven by external stimulation, presumably reflect- ing the extensive recurrence of neural circuitry. Characterizing these dynamics may reveal important features of neural computation, par- ticularly during internally-driven cognitive operations. For example, the activity of premotor cortex (PMd) neurons during an instructed de- lay period separating movement-target specification and a movement- initiation cue is believed to be involved in motor planning. We show that the dynamics underlying this activity can be captured by a low- dimensional non-linear dynamical systems model, with underlying re- current structure and stochastic point-process output. We present and validate latent variable methods that simultaneously estimate the system parameters and the trial-by-trial dynamical trajectories. These meth- ods are applied to characterize the dynamics in PMd data recorded from a chronically-implanted 96-electrode array while monkeys perform delayed-reach tasks.

Significant plasticity in sensory cortical representations can be driven in mature animals either by behavioural tasks that pair sensory stimuli with reinforcement, or by electrophysiological experiments that pair sensory input with direct stimulation of neuromodulatory nuclei, but usually not by sensory stimuli presented alone. Biologically motivated theories of representational learning, however, have tended to focus on unsupervised mechanisms, which may play a significant role on evolutionary or devel- opmental timescales, but which neglect this essential role of reinforce- ment in adult plasticity. By contrast, theoretical reinforcement learning has generally dealt with the acquisition of optimal policies for action in an uncertain world, rather than with the concurrent shaping of sensory representations. This paper develops a framework for representational learning which builds on the relative success of unsupervised generative- modelling accounts of cortical encodings to incorporate the effects of reinforcement in a biologically plausible way.

Existing source location and recovery algorithms used in magnetoen- cephalographic imaging generally assume that the source activity at dif- ferent brain locations is independent or that the correlation structure is known. However, electrophysiological recordings of local field poten- tials show strong correlations in aggregate activity over significant dis- tances. Indeed, it seems very likely that stimulus-evoked activity would follow strongly correlated time-courses in different brain areas. Here, we present, and validate through simulations, a new approach to source reconstruction in which the correlation between sources is modelled and estimated explicitly by variational Bayesian methods, facilitating accu- rate recovery of source locations and the time-courses of their activation.

Perceptual inference fundamentally involves uncertainty, arising from noise in sensation and the ill-posed nature of many perceptual problems. Accurate perception requires that this uncertainty be correctly represented, manipulated, and learned about. The choices subjects make in various psychophysical experiments suggest that they do indeed take such uncertainty into account when making perceptual inferences, posing the question as to how uncertainty is represented in the activities of neuronal populations. Most theoretical investigations of population coding have ignored this issue altogether; the few existing proposals that address it do so in such a way that it is fatally conflated with another facet of perceptual problems that also needs correct handling: multiplicity (that is, the simultaneous presence of multiple distinct stimuli). We present and validate a more powerful proposal for the way that population activity may encode uncertainty, both distinctly from and simultaneously with multiplicity.

Adaptation is a ubiquitous neural and psychological phenomenon, with a wealth of instantiations and implications. Although a basic form of plasticity, it has, bar some notable exceptions, attracted computational theory of only one main variety. In this paper, we study adaptation from the perspective of factor analysis, a paradigmatic technique of unsuper- vised learning. We use factor analysis to re-interpret a standard view of adaptation, and apply our new model to some recent data on adaptation in the domain of face discrimination.

By comparison to some other sensory cortices, the functional proper- ties of cells in the primary auditory cortex are not yet well understood. Recent attempts to obtain a generalized description of auditory cortical responses have often relied upon characterization of the spectrotempo- ral receptive field (STRF), which amounts to a model of the stimulus- response function (SRF) that is linear in the spectrogram of the stimulus. How well can such a model account for neural responses at the very first stages of auditory cortical processing? To answer this question, we de- velop a novel methodology for evaluating the fraction of stimulus-related response power in a population that can be captured by a given type of SRF model. We use this technique to show that, in the thalamo-recipient layers of primary auditory cortex, STRF models account for no more than 40% of the stimulus-related power in neural responses.

An essential step in understanding the function of sensory nervous sys- tems is to characterize as accurately as possible the stimulus-response function (SRF) of the neurons that relay and process sensory informa- tion. One increasingly common experimental approach is to present a rapidly varying complex stimulus to the animal while recording the re- sponses of one or more neurons, and then to directly estimate a func- tional transformation of the input that accounts for the neuronal firing. The estimation techniques usually employed, such as Wiener filtering or other correlation-based estimation of the Wiener or Volterra kernels, are equivalent to maximum likelihood estimation in a Gaussian-output-noise regression model. We explore the use of Bayesian evidence-optimization techniques to condition these estimates. We show that by learning hyper- parameters that control the smoothness and sparsity of the transfer func- tion it is possible to improve dramatically the quality of SRF estimates, as measured by their success in predicting responses to novel input.