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Bayesian parameter estimation and Shannon’s theory of information provide tools for analysing and understanding data from behavioural and neurobiological experiments on interval timing—and from experiments on Pavlovian and operant conditioning, because timing plays a fundamental role in associative learning. In this tutorial, we explain basic concepts behind these tools and show how to apply them to estimating, on a trial-by-trial, reinforcement-by-reinforcement and response-by-response basis, important parameters of timing behaviour and of the neurobiological manifestations of timing in the brain. These tools enable quantification of relevant variables in the trade-off between acting as an ideal observer should act and acting as an ideal agent should act, which is also known as the trade-off between exploration (information gathering) and exploitation (information utilization) in reinforcement learning. They enable comparing the strength of the evidence for a measurable association to the strength of the behavioural evidence that the association has been perceived. A GitHub site and an OSF site give public access to well-documented Matlab and Python code and to raw data to which these tools have been applied.

Learning, especially rapid learning, is critical for survival. However, learning is hard; a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of probability distributions over weights is the optimal strategy. Here we hypothesize that synapses take that strategy; in essence, when they estimate weights, they include error bars. They then use that uncertainty to adjust their learning rates, with more uncertain weights having higher learning rates. We also make a second, independent, hypothesis: synapses communicate their uncertainty by linking it to variability in postsynaptic potential size, with more uncertainty leading to more variability. These two hypotheses cast synaptic plasticity as a problem of Bayesian inference, and thus provide a normative view of learning. They generalize known learning rules, offer an explanation for the large variability in the size of postsynaptic potentials and make falsifiable experimental predictions.

The dominant view in neuroscience is that changes in synaptic weights underlie learning. It is unclear, however, how the brain is able to determine which synapses should change, and by how much. This uncertainty stands in sharp contrast to deep learning, where changes in weights are explicitly engineered to optimize performance. However, the main tool for that, backpropagation, has two problems. One is neuro-science related: it is not biologically plausible. The other is inherent: networks trained with this rule tend to forget old tasks when learning new ones. Here we introduce the Dendritic Gated Network (DGN), a variant of the Gated Linear Network, which offers a biologically plausible alternative to backpropagation. DGNs combine dendritic ‘gating’ (whereby interneurons target dendrites to shape neuronal responses) with local learning rules to yield provably efficient performance. They are significantly more data efficient than conventional artificial networks, and are highly resistant to forgetting. Consequently, they perform well on a variety of tasks, in some cases better than backpropagation. Importantly, DGNs have structural and functional similarities to the cerebellum, a link that we strengthen by usingin vivotwo-photon calcium imaging to show that single interneurons suppress activity in individual dendritic branches of Purkinje cells, a key feature of the model. Thus, DGNs leverage targeted dendritic inhibition and local learning – two features ubiquitous in the brain – to achieve fast and efficient learning.

Learning, especially rapid learning, is critical for survival. However, learning is hard; a large number of synaptic weights must be set based on noisy, often ambiguous, sensory information. In such a high-noise regime, keeping track of probability distributions over weights is the optimal strategy. Here we hypothesize that synapses take that strategy; in essence, when they estimate weights, they include error bars. They then use that uncertainty to adjust their learning rates, with more uncertain weights having higher learning rates. We also make a second, independent, hypothesis: synapses communicate their uncertainty by linking it to variability in postsynaptic potential size, with more uncertainty leading to more variability. These two hypotheses cast synaptic plasticity as a problem of Bayesian inference, and thus provide a normative view of learning. They generalize known learning rules, offer an explanation for the large variability in the size of postsynaptic potentials and make falsifiable experimental predictions.

The two basic processes underlying perceptual decisions – how neural responses encode stimuli, and how they inform behavioral choices – have mainly been studied separately. Thus, although many spatiotemporal features of neural population activity, or “neural codes,” have been shown to carry sensory information, it is often unknown whether the brain uses these features for perception. To address this issue, we propose a new framework centered on redefining the neural code as the neural features that carry sensory information used by the animal to drive appropriate behavior; that is, the features that have an intersection between sensory and choice information. We show how this framework leads to a new statistical analysis of neural activity recorded during behavior that can identify such neural codes, and we discuss how to combine intersection-based analysis of neural recordings with intervention on neural activity to determine definitively whether specific neural activity features are involved in a task.

More often than not, action potentials fail to trigger neurotransmitter release. And even when neurotransmitter is released, the resulting change in synaptic conductance is highly variable. Given the energetic cost of generating and propagating action potentials, and the importance of information transmission across synapses, this seems both wasteful and inefficient. However, synaptic noise arising from variable transmission can improve, in certain restricted conditions, information transmission. Under broader conditions, it can improve information transmission per release, a quantity that is relevant given the energetic constraints on computing in the brain. Here we discuss the role, both positive and negative, synaptic noise plays in information transmission and computation in the brain., Highlights Synaptic transmission is noisy, partially because neurotransmitter release is unreliable but also because synaptic receptor current varies stochastically. When synaptic input is below the cell spike threshold, adding noise may push it above the threshold, thus improving information transmission. Synaptic noise can widen the dynamic range of transmission. Synaptic noise allows synapses to communicate their degree of uncertainty. Noise is a ubiquitous feature of brain activity and is likely to be a critical element in any theory of how the brain works.

If the brain processes incoming data efficiently, information should degrade little between early and later neural processing stages, and so information in early stages should match behavioral performance. For instance, if there is enough information in a visual cortical area to determine the orientation of a grating to within 1 degree, and the code is simple enough to be read out by downstream circuits, then animals should be able to achieve that performance behaviourally. Despite over 30 years of research, it is still not known how efficient the brain is. For tasks involving a large number of neurons, the amount of information encoded by neural circuits is limited by differential correlations. Therefore, determining how much information is encoded requires quantifying the strength of differential correlations. Detecting them, however, is difficult. We report here a new method, which requires on the order of 100s of neurons and trials. This method relies on computing the alignment of the neural stimulus encoding direction, f′, with the eigenvectors of the noise covariance matrix, Σ. In the presence of strong differential correlations, f′ must be spanned by a small number of the eigenvectors with largest eigenvalues. Using simulations with a leaky-integrate-and-fire neuron model of the LGN-V1 circuit, we confirmed that this method can indeed detect differential correlations consistent with those that would limit orientation discrimination thresholds to 0.5-3 degrees. We applied this technique to V1 recordings in awake monkeys and found signatures of differential correlations, consistent with a discrimination threshold of 0.47-1.20 degrees, which is not far from typical discrimination thresholds (1-2 deg). These results suggest that, at least in macaque monkeys, V1 contains about as much information as is seen in behaviour, implying that downstream circuits are efficient at extracting the information available in V1.

Systems neuroscience seeks explanations for how the brain implements a wide variety of perceptual, cognitive and motor tasks. Conversely, artificial intelligence attempts to design computational systems based on the tasks they will have to solve. In the case of artificial neural networks, the three components specified by design are the objective functions, the learning rules, and architectures. With the growing success of deep learning, which utilizes brain-inspired architectures, these three designed components have increasingly become central to how we model, engineer and optimize complex artificial learning systems. Here we argue that a greater focus on these components would also benefit systems neuroscience. We give examples of how this optimization-based framework can drive theoretical and experimental progress in neuroscience. We contend that this principled perspective on systems neuroscience will help to generate more rapid progress.

This package contains data, in NWB (Neurodata Without Borders) format, from the 4 mice included in "Farzaneh Najafi, Gamaleldin F Elsayed, Robin Cao, Eftychios Pnevmatikakis, Peter E. Latham, John P Cunningham, Anne K Churchland (bioRxiv, 2018); Excitatory and inhibitory subnetworks are equally selective during decision-making and emerge simultaneously during learning.” The "FN_dataSharing/nwb' folder contains NWB files for all recorded sessions for four mice discussed in the paper. Each NWB file represents the data and metadata associated with one recording session. In each NWB file, the metadata related to the session (mouse name, session date/time, lab/institution name, etc.) can be found under "general". Information related to ROI-segmentation such as ROI mask, ROI type (excitatory or inhibitory), poor or good quality, etc. can be found under "modules/Image-Segmentation/pln-seg". Trial information (e.g. start, end times, trial types, trial outcomes, etc.) can be found under "trials". Recorded trial-segmented neuronal responses aligned to different time event (e.g. stimulus start, animal choice, etc.) can be found under "modules/ Trial-based-Segmentation". A jupyter notebook presenting in detail how to work with NWB files is provided at https://github.com/ttngu207/najafi-2018-nwb/blob/master/notebooks/Najafi-2018_example.ipynb.

Most models of decision-making suggest that confidence, the ‘feeling of knowing’ that accompanies our choices, is constructed as the decision unfolds. However, more recent studies have noted that processes occurring after we commit to a particular choice also affect this subjective belief. This leads to the following question: when are we better judges of ourselves? If, after a decision, evidence continues to accumulate in an unbiased manner, then our confidence judgements should improve. Conversely, if post-decisional information processing is biased, our sense of confidence could be distorted, and so our confidence judgements should degrade with time. We briefly discuss recently proposed models of post-decisional evidence accumulation, and explore whether, and how, biases in confidence could arise.

SummaryInhibitory neurons, which play a critical role in decision-making models, are often simplified as a single pool of non-selective neurons lacking connection specificity. This assumption is supported by observations in primary visual cortex: inhibitory neurons are broadly tuned in vivo, and show non-specific connectivity in slice. Selectivity of excitatory and inhibitory neurons within decision circuits, and hence the validity of decision-making models, is unknown. We simultaneously measured excitatory and inhibitory neurons in posterior parietal cortex of mice judging multisensory stimuli. Surprisingly, excitatory and inhibitory neurons were equally selective for the animal’s choice, both at the single cell and population level. Further, both cell types exhibited similar changes in selectivity and temporal dynamics during learning, paralleling behavioral improvements. These observations, combined with modeling, argue against circuit architectures assuming non-selective inhibitory neurons. Instead, they argue for selective subnetworks of inhibitory and excitatory neurons that are shaped by experience to support expert decision-making.

Bang et al. use behavioural data in culturally distinct settings (United Kingdom and Iran) and computational modelling to show that, when making decisions in pairs, people adopt a confidence-matching heuristic to combine their opinions.

Confidence is the 'feeling of knowing' that accompanies decision-making. Bayesian theory proposes that confidence is a function solely of the perceived probability of being correct. Empirical research has suggested, however, that different individuals may perform different computations to estimate confidence from uncertain evidence. To test this hypothesis, we collected confidence reports in a task in which subjects made categorical decisions about the mean of a sequence. We found that for most individuals, confidence did indeed reflect the perceived probability of being correct. However, in approximately half of them, confidence also reflected a different probabilistic quantity: the perceived uncertainty in the estimated variable. We found that the contribution of both quantities was stable over weeks. We also observed that the influence of the perceived probability of being correct was stable across two tasks, one perceptual and one cognitive. Overall, our findings provide a computational interpretation of individual differences in human confidence. Fil: Navajas Ahumada, Joaquin Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. University College London; Estados Unidos. Universidad Torcuato Di Tella; Argentina Fil: Hindocha, Chandni. University College London; Estados Unidos Fil: Foda, Hebah. University College London; Estados Unidos Fil: Keramati, Mehdi. University College London; Estados Unidos Fil: Latham, Peter E.. University College London; Estados Unidos Fil: Bahrami, Bahador. University College London; Estados Unidos

The olfactory system faces a hard problem: on the basis of noisy information from olfactory receptor neurons (the neurons that transduce chemicals to neural activity), it must figure out which odors are present in the world. Odors almost never occur in isolation, and different odors excite overlapping populations of olfactory receptor neurons, so the central challenge of the olfactory system is to demix its input. Because of noise and the large number of possible odors, demixing is fundamentally a probabilistic inference task. We propose that the early olfactory system uses approximate Bayesian inference to solve it. The computations involve a dynamical loop between the olfactory bulb and the piriform cortex, with cortex explaining incoming activity from the olfactory receptor neurons in terms of a mixture of odors. The model is compatible with known anatomy and physiology, including pattern decorrelation, and it performs better than other models at demixing odors.

A wide range of computations performed by the nervous system involves a type of probabilistic inference known as marginalization. This computation comes up in seemingly unrelated tasks, including causal reasoning, odor recognition, motor control, visual tracking, coordinate transformations, visual search, decision making, and object recognition, to name just a few. The question we address here is: how could neural circuits implement such marginalizations? We show that when spike trains exhibit a particular type of statistics—associated with constant Fano factors and gain-invariant tuning curves, as is often reportedin vivo—some of the more common marginalizations can be achieved with networks that implement a quadratic nonlinearity and divisive normalization, the latter being a type of nonlinear lateral inhibition that has been widely reported in neural circuits. Previous studies have implicated divisive normalization in contrast gain control and attentional modulation. Our results raise the possibility that it is involved in yet another, highly critical, computation: near optimal marginalization in a remarkably wide range of tasks.

It is well known that neural activity exhibits variability, in the sense that identical sensory stimuli produce different responses, but it has been difficult to determine what this variability means. Is it noise, or does it carry important information-about, for example, the internal state of the organism? Here we address this issue from the bottom up, by asking whether small perturbations to activity in cortical networks are amplified. Based on in vivo whole-cell patch-clamp recordings in rat barrel cortex, we find that a perturbation consisting of a single extra spike in one neuron produces approximately 28 additional spikes in its postsynaptic targets. We also show, using simultaneous intra- and extracellular recordings, that a single spike in a neuron produces a detectable increase in firing rate in the local network. Theoretical analysis indicates that this amplification leads to intrinsic, stimulus-independent variations in membrane potential of the order of +/-2.2-4.5 mV-variations that are pure noise, and so carry no information at all. Therefore, for the brain to perform reliable computations, it must either use a rate code, or generate very large, fast depolarizing events, such as those proposed by the theory of synfire chains. However, in our in vivo recordings, we found that such events were very rare. Our findings are thus consistent with the idea that cortex is likely to use primarily a rate code.