Optimal plasticity for memory maintenance during ongoing synaptic change.

Synaptic connections in many brain circuits fluctuate, exhibiting substantial turnover and remodelling over hours to days. Surprisingly, experiments show that most of this flux in connectivity persists in the absence of learning or known plasticity signals. How can neural circuits retain learned information despite a large proportion of ongoing and potentially disruptive synaptic changes? We address this question from first principles by analysing how much compensatory plasticity would be required to optimally counteract ongoing fluctuations, regardless of whether fluctuations are random or systematic. Remarkably, we find that the answer is largely independent of plasticity mechanisms and circuit architectures: compensatory plasticity should be at most equal in magnitude to fluctuations, and often less, in direct agreement with previously unexplained experimental observations. Moreover, our analysis shows that a high proportion of learning-independent synaptic change is consistent with plasticity mechanisms that accurately compute error gradients.

Frozen algorithms: how the brain's wiring facilitates learning.

Synapses and neural connectivity are plastic and shaped by experience. But to what extent does connectivity itself influence the ability of a neural circuit to learn? Insights from optimization theory and AI shed light on how learning can be implemented in neural circuits. Though abstract in their nature, learning algorithms provide a principled set of hypotheses on the necessary ingredients for learning in neural circuits. These include the kinds of signals and circuit motifs that enable learning from experience, as well as an appreciation of the constraints that make learning challenging in a biological setting. Remarkably, some simple connectivity patterns can boost the efficiency of relatively crude learning rules, showing how the brain can use anatomy to compensate for the biological constraints of known synaptic plasticity mechanisms. Modern connectomics provides rich data for exploring this principle, and may reveal how brain connectivity is constrained by the requirement to learn efficiently.

Stable task information from an unstable neural population.

Over days and weeks, neural activity representing an animal's position and movement in sensorimotor cortex has been found to continually reconfigure or 'drift' during repeated trials of learned tasks, with no obvious change in behavior. This challenges classical theories, which assume stable engrams underlie stable behavior. However, it is not known whether this drift occurs systematically, allowing downstream circuits to extract consistent information. Analyzing long-term calcium imaging recordings from posterior parietal cortex in mice (Mus musculus), we show that drift is systematically constrained far above chance, facilitating a linear weighted readout of behavioral variables. However, a significant component of drift continually degrades a fixed readout, implying that drift is not confined to a null coding space. We calculate the amount of plasticity required to compensate drift independently of any learning rule, and find that this is within physiologically achievable bounds. We demonstrate that a simple, biologically plausible local learning rule can achieve these bounds, accurately decoding behavior over many days.

Delineating parameter unidentifiabilities in complex models.

Scientists use mathematical modeling as a tool for understanding and predicting the properties of complex physical systems. In highly parametrized models there often exist relationships between parameters over which model predictions are identical, or nearly identical. These are known as structural or practical unidentifiabilities, respectively. They are hard to diagnose and make reliable parameter estimation from data impossible. They furthermore imply the existence of an underlying model simplification. We describe a scalable method for detecting unidentifiabilities, as well as the functional relations defining them, for generic models. This allows for model simplification, and appreciation of which parameters (or functions thereof) cannot be estimated from data. Our algorithm can identify features such as redundant mechanisms and fast time-scale subsystems, as well as the regimes in parameter space over which such approximations are valid. We base our algorithm on a quantification of regional parametric sensitivity that we call 'multiscale sloppiness'. Traditionally, the link between parametric sensitivity and the conditioning of the parameter estimation problem is made locally, through the Fisher information matrix. This is valid in the regime of infinitesimal measurement uncertainty. We demonstrate the duality between multiscale sloppiness and the geometry of confidence regions surrounding parameter estimates made where measurement uncertainty is non-negligible. Further theoretical relationships are provided linking multiscale sloppiness to the likelihood-ratio test. From this, we show that a local sensitivity analysis (as typically done) is insufficient for determining the reliability of parameter estimation, even with simple (non)linear systems. Our algorithm can provide a tractable alternative. We finally apply our methods to a large-scale, benchmark systems biology model of necrosis factor (NF)-κB, uncovering unidentifiabilities.