Recurrent sampling models for the Helmholtz machine

Coding accuracy on the psychophysical scale

Sensory neurons are often reported to adjust their coding accuracy to the stimulus statistics. The observed match is not always perfect and the maximal accuracy does not align with the most frequent stimuli. As an alternative to a physiological explanation we show that the match critically depends on the chosen stimulus measurement scale. More generally, we argue that if we measure the stimulus intensity on the scale which is proportional to the perception intensity, an improved adjustment in the coding accuracy is revealed. The unique feature of stimulus units based on the psychophysical scale is that the coding accuracy can be meaningfully compared for different stimuli intensities, unlike in the standard case of a metric scale.

Performance breakdown in optimal stimulus decoding

OBJECTIVE

One of the primary goals of neuroscience is to understand how neurons encode and process information about their environment. The problem is often approached indirectly by examining the degree to which the neuronal response reflects the stimulus feature of interest.

APPROACH

In this context, the methods of signal estimation and detection theory provide the theoretical limits on the decoding accuracy with which the stimulus can be identified. The Cramér-Rao lower bound on the decoding precision is widely used, since it can be evaluated easily once the mathematical model of the stimulus-response relationship is determined. However, little is known about the behavior of different decoding schemes with respect to the bound if the neuronal population size is limited.

MAIN RESULTS

We show that under broad conditions the optimal decoding displays a threshold-like shift in performance in dependence on the population size. The onset of the threshold determines a critical range where a small increment in size, signal-to-noise ratio or observation time yields a dramatic gain in the decoding precision.

SIGNIFICANCE

We demonstrate the existence of such threshold regions in early auditory and olfactory information coding. We discuss the origin of the threshold effect and its impact on the design of effective coding approaches in terms of relevant population size.

Spiking neuron network Helmholtz machine

An increasing amount of behavioral and neurophysiological data suggests that the brain performs optimal (or near-optimal) probabilistic inference and learning during perception and other tasks. Although many machine learning algorithms exist that perform inference and learning in an optimal way, the complete description of how one of those algorithms (or a novel algorithm) can be implemented in the brain is currently incomplete. There have been many proposed solutions that address how neurons can perform optimal inference but the question of how synaptic plasticity can implement optimal learning is rarely addressed. This paper aims to unify the two fields of probabilistic inference and synaptic plasticity by using a neuronal network of realistic model spiking neurons to implement a well-studied computational model called the Helmholtz Machine. The Helmholtz Machine is amenable to neural implementation as the algorithm it uses to learn its parameters, called the wake-sleep algorithm, uses a local delta learning rule. Our spiking-neuron network implements both the delta rule and a small example of a Helmholtz machine. This neuronal network can learn an internal model of continuous-valued training data sets without supervision. The network can also perform inference on the learned internal models. We show how various biophysical features of the neural implementation constrain the parameters of the wake-sleep algorithm, such as the duration of the wake and sleep phases of learning and the minimal sample duration. We examine the deviations from optimal performance and tie them to the properties of the synaptic plasticity rule.

Statistically optimal perception and learning: from behavior to neural representations

Human perception has recently been characterized as statistical inference based on noisy and ambiguous sensory inputs. Moreover, suitable neural representations of uncertainty have been identified that could underlie such probabilistic computations. In this review, we argue that learning an internal model of the sensory environment is another key aspect of the same statistical inference procedure and thus perception and learning need to be treated jointly. We review evidence for statistically optimal learning in humans and animals, and re-evaluate possible neural representations of uncertainty based on their potential to support statistically optimal learning. We propose that spontaneous activity can have a functional role in such representations leading to a new, sampling-based, framework of how the cortex represents information and uncertainty.

Goal-directed control and its antipodes

In instrumental conditioning, there is a rather precise definition of goal-directed control, and therefore an acute boundary between it and the somewhat more amorphous category comprising its opposites. Here, we review this division in terms of the various distinctions that accompany it in the fields of reinforcement learning and cognitive architectures, considering issues such as declarative and procedural control, the effect of prior distributions over environments, the neural substrates involved, and the differing views about the relative rationality of the various forms of control. Our overall aim is to reconnect some presently far-flung relations.

Bayesian representation learning in the cortex regulated by acetylcholine

A brain needs to detect an environmental change and to quickly learn internal representations necessary in a new environment. This paper presents a theoretical model of cortical representation learning that can adapt to dynamic environments, incorporating the results by previous studies on the functional role of acetylcholine (ACh). We adopt the probabilistic principal component analysis (PPCA) as a functional model of cortical representation learning, and present an on-line learning method for PPCA according to Bayesian inference, including a heuristic criterion for model selection. Our approach is examined in two types of simulations with synthesized and realistic data sets, in which our model is able to re-learn new representation bases after the environment changes. Our model implies the possibility that a higher-level recognition regulates the cortical ACh release in the lower-level, and that the ACh level alters the learning dynamics of a local circuit in order to continuously acquire appropriate representations in a dynamic environment.

Acetylcholine in cortical inference

Acetylcholine (ACh) plays an important role in a wide variety of cognitive tasks, such as perception, selective attention, associative learning, and memory. Extensive experimental and theoretical work in tasks involving learning and memory has suggested that ACh reports on unfamiliarity and controls plasticity and effective network connectivity. Based on these computational and implementational insights, we develop a theory of cholinergic modulation in perceptual inference. We propose that ACh levels reflect the uncertainty associated with top-down information, and have the effect of modulating the interaction between top-down and bottom-up processing in determining the appropriate neural representations for inputs. We illustrate our proposal by means of an hierarchical hidden Markov model, showing that cholinergic modulation of contextual information leads to appropriate perceptual inference.