Efficient coding has served as a guiding principle in understanding the neural code. To date, however, it has been explored mainly in the context of peripheral sensory cells with simple tuning curves. By contrast, ‘deeper’ neurons such as grid cells come with more complex tuning properties which imply a different, yet highly efficient, strategy for representing information. I will show that a highly efficient code is not specific to a population of neurons with finely tuned response properties: it emerges robustly in a shallow network with random synapses. Here, the geometry of population responses implies that optimality obtains from a tradeoff between two qualitatively different types of error: ‘local’ errors (common to classical neural population codes) and ‘global’ (or ‘catastrophic’) errors. This tradeoff leads to efficient compression of information from a high-dimensional representation to a low-dimensional one. After describing the theoretical framework, I will use it to re-interpret recordings of motor cortex in behaving monkey. Our framework addresses the encoding of (sensory) information; if time allows, I will comment on ongoing work that focuses on decoding from the perspective of efficient coding.

Excitatory and inhibitory (E & I) inputs to cortical neurons remain balanced across different conditions. The balanced network model provides a self-consistent account of this observation: population rates dynamically adjust to yield a state in which all neurons are active at biological levels, with their E & I inputs tightly balanced. But global tight E/I balance predicts population responses with linear stimulus-dependence and does not account for systematic cortical response nonlinearities such as divisive normalization, a canonical brain computation. However, when necessary connectivity conditions for global balance fail, states arise in which only a localized subset of neurons are active and have balanced inputs. We analytically show that in networks of neurons with different stimulus selectivities, the emergence of such localized balance states robustly leads to normalization, including sublinear integration and winner-take-all behavior. An alternative model that exhibits normalization is the Stabilized Supralinear Network (SSN), which predicts a regime of loose, rather than tight, E/I balance. However, an understanding of the causal relationship between E/I balance and normalization in SSN and conditions under which SSN yields significant sublinear integration are lacking. For weak inputs, SSN integrates inputs supralinearly, while for very strong inputs it approaches a regime of tight balance. We show that when this latter regime is globally balanced, SSN cannot exhibit strong normalization for any input strength; thus, in SSN too, significant normalization requires localized balance. In summary, we causally and quantitatively connect a fundamental feature of cortical dynamics with a canonical brain computation. Time allowing I will also cover our work extending a normative theoretical account of normalization which explains it as an example of efficient coding of natural stimuli. We show that when biological noise is accounted for, this theory makes the same prediction as the SSN: a transition to supralinear integration for weak stimuli.

Low-dimensional population dynamics can be observed in neural activity recorded from the prefrontal cortex (PFC) of subjects performing simple cognitive tasks. Many studies have shown that recurrent neural networks (RNNs) trained on the same tasks can reproduce qualitatively these state space trajectories, and have used them as models of how neuronal dynamics implement task computations. The PFC is also viewed as a conductor that organizes the communication between cortical areas and provides contextual information. It is then not clear what is its role in solving simple cognitive tasks. Do the low-dimensional trajectories observed in the PFC really correspond to the computations that it performs? Or do they indirectly reflect the computations occurring within the cortical areas projecting to the PFC? To address these questions, we modelled cortical areas with a modular RNN and equipped it with a PFC-like cognitive system. When trained on cognitive tasks, this multi-system brain model can reproduce the low-dimensional population responses observed in neuronal activity as well as classical RNNs. Qualitatively different mechanisms can emerge from the training process when varying some details of the architecture such as the time constants. In particular, there is one class of models where it is the dynamics of the cognitive system that is implementing the task computations, and another where the cognitive system is only necessary to provide contextual information about the task rule as task performance is not impaired when preventing the system from accessing the task inputs. These constitute two different hypotheses about the causal role of the PFC in solving simple cognitive tasks, which could motivate further experiments on the brain.

To prevail in a dynamic and noisy environment, the brain must create reliable and meaningful representations from sensory inputs that are often ambiguous or corrupt. Since only information that permeates the cortical hierarchy can influence sensory perception and decision-making, it is critical that noisy external stimuli are encoded and propagated through different processing stages with minimal signal degradation. Here we hypothesize that stimulus-specific pathways akin to cortical topographic maps may provide the structural scaffold for such signal routing. We investigate whether the feature-specific pathways within such maps, characterized by the preservation of the relative organization of cells between distinct populations, can guide and route stimulus information throughout the system while retaining representational fidelity. We demonstrate that, in a large modular circuit of spiking neurons comprising multiple sub-networks, topographic projections are not only necessary for accurate propagation of stimulus representations, but can also help the system reduce sensory and intrinsic noise. Moreover, by regulating the effective connectivity and local E/I balance, modular topographic precision enables the system to gradually improve its internal representations and increase signal-to-noise ratio as the input signal passes through the network. Such a denoising function arises beyond a critical transition point in the sharpness of the feed-forward projections, and is characterized by the emergence of inhibition-dominated regimes where population responses along stimulated maps are amplified and others are weakened. Our results indicate that this is a generalizable and robust structural effect, largely independent of the underlying model specificities. Using mean-field approximations, we gain deeper insight into the mechanisms responsible for the qualitative changes in the system’s behavior and show that these depend only on the modular topographic connectivity and stimulus intensity. The general dynamical principle revealed by the theoretical predictions suggest that such a denoising property may be a universal, system-agnostic feature of topographic maps, and may lead to a wide range of behaviorally relevant regimes observed under various experimental conditions: maintaining stable representations of multiple stimuli across cortical circuits; amplifying certain features while suppressing others (winner-take-all circuits); and endow circuits with metastable dynamics (winnerless competition), assumed to be fundamental in a variety of tasks.

Neural responses are variable: even under identical experimental conditions, single neuron and population responses typically differ from trial to trial and across time. Recent work has demonstrated that this variability has predictable structure, can be modulated by sensory input and behaviour, and bears critical signatures of the underlying network dynamics and computations. However, current methods for characterising neural variability are primarily geared towards sensory coding in the laboratory: they require trials with repeatable experimental stimuli and behavioural covariates. In addition, they make strong assumptions about the parametric form of variability, rely on assumption-free but data-inefficient histogram-based approaches, or are altogether ill-suited for capturing variability modulation by covariates. Here we present a universal probabilistic spike count model that eliminates these shortcomings. Our method uses scalable Bayesian machine learning techniques to model arbitrary spike count distributions (SCDs) with flexible dependence on observed as well as latent covariates. Without requiring repeatable trials, it can flexibly capture covariate-dependent joint SCDs, and provide interpretable latent causes underlying the statistical dependencies between neurons. We apply the model to recordings from a canonical non-sensory neural population: head direction cells in the mouse. We find that variability in these cells defies a simple parametric relationship with mean spike count as assumed in standard models, its modulation by external covariates can be comparably strong to that of the mean firing rate, and slow low-dimensional latent factors explain away neural correlations. Our approach paves the way to understanding the mechanisms and computations underlying neural variability under naturalistic conditions, beyond the realm of sensory coding with repeatable stimuli.

In this lecture, I will present our recent progress on three aspects of population responses in the primary visual cortex: encoding local stimulus attributes, electrical microstimulation and higher visual function. In the first part I will focus on population encoding and reconstruction of contour shapes in V1 and the comparison between monkey and mouse visual responses. In the second part of the talk I will present the effects of microstimulation on neural population in V1 and the relation to evoked saccades. In the final part of the talk I will discuss top-down influences in V1 and their relation to higher visual functions.