Backpropagation through space, time, and the brain

Effective learning in neuronal networks requires the adaptation of individual synapses given their relative contribution to solving a task. However, physical neuronal systems -- whether biological or artificial -- are constrained by spatio-temporal locality. How such networks can perform efficient credit assignment, remains, to a large extent, an open question. In Machine Learning, the answer is almost universally given by the error backpropagation algorithm, through both space (BP) and time (BPTT). However, BP(TT) is well-known to rely on biologically implausible assumptions, in particular with respect to spatiotemporal (non-)locality, while forward-propagation models such as real-time recurrent learning (RTRL) suffer from prohibitive memory constraints. We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. We start by defining an energy based on neuron-local mismatches, from which we derive both neuronal dynamics via stationarity and parameter dynamics via gradient descent. The resulting dynamics can be interpreted as a real-time, biologically plausible approximation of BPTT in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the ability of biological neurons to phase-shift their output rate with respect to their membrane potential, which is essential in both directions of information propagation. For the forward computation, it enables the mapping of time-continuous inputs to neuronal space, performing an effective spatiotemporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint states necessary for useful parameter updates.

Learning beyond sensations: how dreams organize neuronal representations

Semantic representations in higher sensory cortices form the basis for robust, yet flexible behavior. These representations are acquired over the course of development in an unsupervised fashion and continuously maintained over an organism's lifespan. Predictive learning theories propose that these representations emerge from predicting or reconstructing sensory inputs. However, brains are known to generate virtual experiences, such as during imagination and dreaming, that go beyond previously experienced inputs. Here, we suggest that virtual experiences may be just as relevant as actual sensory inputs in shaping cortical representations. In particular, we discuss two complementary learning principles that organize representations through the generation of virtual experiences. First, "adversarial dreaming" proposes that creative dreams support a cortical implementation of adversarial learning in which feedback and feedforward pathways engage in a productive game of trying to fool each other. Second, "contrastive dreaming" proposes that the invariance of neuronal representations to irrelevant factors of variation is acquired by trying to map similar virtual experiences together via a contrastive learning process. These principles are compatible with known cortical structure and dynamics and the phenomenology of sleep thus providing promising directions to explain cortical learning beyond the classical predictive learning paradigm.

Three-Dimensional Coherent Diffractive Imaging of Isolated Faceted Nanostructures

The structure and dynamics of isolated nanosamples in free flight can be directly visualized via single-shot coherent diffractive imaging using the intense and short pulses of X-ray free-electron lasers. Wide-angle scattering images even encode three-dimensional morphological information of the samples, but the retrieval of this information remains a challenge. Up to now, effective three-dimensional morphology reconstructions from single shots were only achieved via fitting with highly constrained models, requiring a priori knowledge about possible geometrical shapes. Here we present a much more generic imaging approach. Relying on a model that allows for any sample morphology described by a convex polyhedron, we reconstruct wide-angle diffraction patterns from individual silver nanoparticles. In addition to known structural motives with high symmetries, we retrieve imperfect shapes and agglomerates which were not accessible previously. Our results open new routes towards true 3D structure determination of single nanoparticles and, ultimately, 3D movies of ultrafast nanoscale dynamics.

DELAUNAY: a dataset of abstract art for psychophysical and machine learning research

Image datasets are commonly used in psychophysical experiments and in machine learning research. Most publicly available datasets are comprised of images of realistic and natural objects. However, while typical machine learning models lack any domain specific knowledge about natural objects, humans can leverage prior experience for such data, making comparisons between artificial and natural learning challenging. Here, we introduce DELAUNAY, a dataset of abstract paintings and non-figurative art objects labelled by the artists' names. This dataset provides a middle ground between natural images and artificial patterns and can thus be used in a variety of contexts, for example to investigate the sample efficiency of humans and artificial neural networks. Finally, we train an off-the-shelf convolutional neural network on DELAUNAY, highlighting several of its intriguing features.

Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons

The response time of physical computational elements is finite, and neurons are no exception. In hierarchical models of cortical networks each layer thus introduces a response lag. This inherent property of physical dynamical systems results in delayed processing of stimuli and causes a timing mismatch between network output and instructive signals, thus afflicting not only inference, but also learning. We introduce Latent Equilibrium, a new framework for inference and learning in networks of slow components which avoids these issues by harnessing the ability of biological neurons to phase-advance their output with respect to their membrane potential. This principle enables quasi-instantaneous inference independent of network depth and avoids the need for phased plasticity or computationally expensive network relaxation phases. We jointly derive disentangled neuron and synapse dynamics from a prospective energy function that depends on a network's generalized position and momentum. The resulting model can be interpreted as a biologically plausible approximation of error backpropagation in deep cortical networks with continuous-time, leaky neuronal dynamics and continuously active, local plasticity. We demonstrate successful learning of standard benchmark datasets, achieving competitive performance using both fully-connected and convolutional architectures, and show how our principle can be applied to detailed models of cortical microcircuitry. Furthermore, we study the robustness of our model to spatio-temporal substrate imperfections to demonstrate its feasibility for physical realization, be it in vivo or in silico.

Memory semantization through perturbed and adversarial dreaming

Classical theories of memory consolidation emphasize the importance of replay in extracting semantic information from episodic memories. However, the characteristic creative nature of dreams suggests that memory semantization may go beyond merely replaying previous experiences. We propose that rapid-eye-movement (REM) dreaming is essential for efficient memory semantization by randomly combining episodic memories to create new, virtual sensory experiences. We support this hypothesis by implementing a cortical architecture with hierarchically organized feedforward and feedback pathways, inspired by generative adversarial networks (GANs). Learning in our model is organized across three different global brain states mimicking wakefulness, non-REM (NREM) and REM sleep, optimizing different, but complementary objective functions. We train the model in an unsupervised fashion on standard datasets of natural images and evaluate the quality of the learned representations. Our results suggest that adversarial dreaming during REM sleep is essential for extracting memory contents, while perturbed dreaming during NREM sleep improves robustness of the latent representation to noisy sensory inputs. The model provides a new computational perspective on sleep states, memory replay and dreams and suggests a cortical implementation of GANs.

Evolving Neuronal Plasticity Rules using Cartesian Genetic Programming

We formulate the search for phenomenological models of synaptic plasticity as an optimization problem. We employ Cartesian genetic programming to evolve biologically plausible human-interpretable plasticity rules that allow a given network to successfully solve tasks from specific task families. While our evolving-to-learn approach can be applied to various learning paradigms, here we illustrate its power by evolving plasticity rules that allow a network to efficiently determine the first principal component of its input distribution. We demonstrate that the evolved rules perform competitively with known hand-designed solutions. We explore how the statistical properties of the datasets used during the evolutionary search influences the form of the plasticity rules and discover new rules which are adapted to the structure of the corresponding datasets.