Rarely categorical, always high-dimensional: how the neural code changes along the cortical hierarchy.

The brain is highly structured both at anatomical and functional levels. However, within individual brain areas, neurons often exhibit very diverse and seemingly disorganized responses. A more careful analysis shows that these neurons can sometimes be grouped together into specialized subpopulations (categorical representations).

Task-dependent optimal representations for cerebellar learning.

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli.

Optimal routing to cerebellum-like structures.

The vast expansion from mossy fibers to cerebellar granule cells (GrC) produces a neural representation that supports functions including associative and internal model learning. This motif is shared by other cerebellum-like structures and has inspired numerous theoretical models. Less attention has been paid to structures immediately presynaptic to GrC layers, whose architecture can be described as a 'bottleneck' and whose function is not understood.

Rapid suppression and sustained activation of distinct cortical regions for a delayed sensory-triggered motor response.

The neuronal mechanisms generating a delayed motor response initiated by a sensory cue remain elusive. Here, we tracked the precise sequence of cortical activity in mice transforming a brief whisker stimulus into delayed licking using wide-field calcium imaging, multiregion high-density electrophysiology, and time-resolved optogenetic manipulation. Rapid activity evoked by whisker deflection acquired two prominent features for task performance: (1) an enhanced excitation of secondary whisker motor cortex, suggesting its important role connecting whisker sensory processing to lick motor planning; and (2) a transient reduction of activity in orofacial sensorimotor cortex, which contributed to suppressing premature licking.

Optimal Stimulation Protocol in a Bistable Synaptic Consolidation Model.

Synaptic changes induced by neural activity need to be consolidated to maintain memory over a timescale of hours. In experiments, synaptic consolidation can be induced by repeating a stimulation protocol several times and the effectiveness of consolidation depends crucially on the repetition frequency of the stimulations. We address the question: is there an understandable reason why induction protocols with repetitions at some frequency work better than sustained protocols-even though the accumulated stimulation strength might be exactly the same in both cases? In real synapses, plasticity occurs on multiple time scales from seconds (induction), to several minutes (early phase of long-term potentiation) to hours and days (late phase of synaptic consolidation).

How single neuron properties shape chaotic dynamics and signal transmission in random neural networks.

While most models of randomly connected neural networks assume single-neuron models with simple dynamics, neurons in the brain exhibit complex intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of single neurons and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate neurons shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single neurons.

Exponentially Long Orbits in Hopfield Neural Networks.

We show that Hopfield neural networks with synchronous dynamics and asymmetric weights admit stable orbits that form sequences of maximal length. For [Formula: see text] units, these sequences have length [Formula: see text]; that is, they cover the full state space. We present a mathematical proof that maximal-length orbits exist for all [Formula: see text], and we provide a method to construct both the sequence and the weight matrix that allow its production.