Gradient
gradient
Why age-related macular degeneration is a mathematically tractable disease
Among all prevalent diseases with a central neurodegeneration, AMD can be considered the most promising in terms of prevention and early intervention, due to several factors surrounding the neural geometry of the foveal singularity. • Steep gradients of cell density, deployed in a radially symmetric fashion, can be modeled with a difference of Gaussian curves. • These steep gradients give rise to huge, spatially aligned biologic effects, summarized as the Center of Cone Resilience, Surround of Rod Vulnerability. • Widely used clinical imaging technology provides cellular and subcellular level information. • Data are now available at all timelines: clinical, lifespan, evolutionary • Snapshots are available from tissues (histology, analytic chemistry, gene expression) • A viable biogenesis model exists for drusen, the largest population-level intraocular risk factor for progression. • The biogenesis model shares molecular commonality with atherosclerotic cardiovascular disease, for which there has been decades of public health success. • Animal and cell model systems are emerging to test these ideas.
Learning produces a hippocampal cognitive map in the form of an orthogonalized state machine
Cognitive maps confer animals with flexible intelligence by representing spatial, temporal, and abstract relationships that can be used to shape thought, planning, and behavior. Cognitive maps have been observed in the hippocampus, but their algorithmic form and the processes by which they are learned remain obscure. Here, we employed large-scale, longitudinal two-photon calcium imaging to record activity from thousands of neurons in the CA1 region of the hippocampus while mice learned to efficiently collect rewards from two subtly different versions of linear tracks in virtual reality. The results provide a detailed view of the formation of a cognitive map in the hippocampus. Throughout learning, both the animal behavior and hippocampal neural activity progressed through multiple intermediate stages, gradually revealing improved task representation that mirrored improved behavioral efficiency. The learning process led to progressive decorrelations in initially similar hippocampal neural activity within and across tracks, ultimately resulting in orthogonalized representations resembling a state machine capturing the inherent struture of the task. We show that a Hidden Markov Model (HMM) and a biologically plausible recurrent neural network trained using Hebbian learning can both capture core aspects of the learning dynamics and the orthogonalized representational structure in neural activity. In contrast, we show that gradient-based learning of sequence models such as Long Short-Term Memory networks (LSTMs) and Transformers do not naturally produce such orthogonalized representations. We further demonstrate that mice exhibited adaptive behavior in novel task settings, with neural activity reflecting flexible deployment of the state machine. These findings shed light on the mathematical form of cognitive maps, the learning rules that sculpt them, and the algorithms that promote adaptive behavior in animals. The work thus charts a course toward a deeper understanding of biological intelligence and offers insights toward developing more robust learning algorithms in artificial intelligence.
Loss shaping enhances exact gradient learning with EventProp in Spiking Neural Networks
Behavioral Timescale Synaptic Plasticity (BTSP) for biologically plausible credit assignment across multiple layers via top-down gating of dendritic plasticity
A central problem in biological learning is how information about the outcome of a decision or behavior can be used to reliably guide learning across distributed neural circuits while obeying biological constraints. This “credit assignment” problem is commonly solved in artificial neural networks through supervised gradient descent and the backpropagation algorithm. In contrast, biological learning is typically modelled using unsupervised Hebbian learning rules. While these rules only use local information to update synaptic weights, and are sometimes combined with weight constraints to reflect a diversity of excitatory (only positive weights) and inhibitory (only negative weights) cell types, they do not prescribe a clear mechanism for how to coordinate learning across multiple layers and propagate error information accurately across the network. In recent years, several groups have drawn inspiration from the known dendritic non-linearities of pyramidal neurons to propose new learning rules and network architectures that enable biologically plausible multi-layer learning by processing error information in segregated dendrites. Meanwhile, recent experimental results from the hippocampus have revealed a new form of plasticity—Behavioral Timescale Synaptic Plasticity (BTSP)—in which large dendritic depolarizations rapidly reshape synaptic weights and stimulus selectivity with as little as a single stimulus presentation (“one-shot learning”). Here we explore the implications of this new learning rule through a biologically plausible implementation in a rate neuron network. We demonstrate that regulation of dendritic spiking and BTSP by top-down feedback signals can effectively coordinate plasticity across multiple network layers in a simple pattern recognition task. By analyzing hidden feature representations and weight trajectories during learning, we show the differences between networks trained with standard backpropagation, Hebbian learning rules, and BTSP.
A parsimonious description of global functional brain organization in three spatiotemporal patterns
Resting-state functional magnetic resonance imaging (MRI) has yielded seemingly disparate insights into large-scale organization of the human brain. The brain’s large-scale organization can be divided into two broad categories: zero-lag representations of functional connectivity structure and time-lag representations of traveling wave or propagation structure. In this study, we sought to unify observed phenomena across these two categories in the form of three low-frequency spatiotemporal patterns composed of a mixture of standing and traveling wave dynamics. We showed that a range of empirical phenomena, including functional connectivity gradients, the task-positive/task-negative anti-correlation pattern, the global signal, time-lag propagation patterns, the quasiperiodic pattern and the functional connectome network structure, are manifestations of these three spatiotemporal patterns. These patterns account for much of the global spatial structure that underlies functional connectivity analyses and unifies phenomena in resting-state functional MRI previously thought distinct.
Online Training of Spiking Recurrent Neural Networks With Memristive Synapses
Spiking recurrent neural networks (RNNs) are a promising tool for solving a wide variety of complex cognitive and motor tasks, due to their rich temporal dynamics and sparse processing. However training spiking RNNs on dedicated neuromorphic hardware is still an open challenge. This is due mainly to the lack of local, hardware-friendly learning mechanisms that can solve the temporal credit assignment problem and ensure stable network dynamics, even when the weight resolution is limited. These challenges are further accentuated, if one resorts to using memristive devices for in-memory computing to resolve the von-Neumann bottleneck problem, at the expense of a substantial increase in variability in both the computation and the working memory of the spiking RNNs. In this talk, I will present our recent work where we introduced a PyTorch simulation framework of memristive crossbar arrays that enables accurate investigation of such challenges. I will show that recently proposed e-prop learning rule can be used to train spiking RNNs whose weights are emulated in the presented simulation framework. Although e-prop locally approximates the ideal synaptic updates, it is difficult to implement the updates on the memristive substrate due to substantial device non-idealities. I will mention several widely adapted weight update schemes that primarily aim to cope with these device non-idealities and demonstrate that accumulating gradients can enable online and efficient training of spiking RNN on memristive substrates.
The neural basis of flexible semantic cognition (BACN Mid-career Prize Lecture 2022)
Semantic cognition brings meaning to our world – it allows us to make sense of what we see and hear, and to produce adaptive thoughts and behaviour. Since we have a wealth of information about any given concept, our store of knowledge is not sufficient for successful semantic cognition; we also need mechanisms that can steer the information that we retrieve so it suits the context or our current goals. This talk traces the neural networks that underpin this flexibility in semantic cognition. It draws on evidence from multiple methods (neuropsychology, neuroimaging, neural stimulation) to show that two interacting heteromodal networks underpin different aspects of flexibility. Regions including anterior temporal cortex and left angular gyrus respond more strongly when semantic retrieval follows highly-related concepts or multiple convergent cues; the multivariate responses in these regions correspond to context-dependent aspects of meaning. A second network centred on left inferior frontal gyrus and left posterior middle temporal gyrus is associated with controlled semantic retrieval, responding more strongly when weak associations are required or there is more competition between concepts. This semantic control network is linked to creativity and also captures context-dependent aspects of meaning; however, this network specifically shows more similar multivariate responses across trials when association strength is weak, reflecting a common controlled retrieval state when more unusual associations are the focus. Evidence from neuropsychology, fMRI and TMS suggests that this semantic control network is distinct from multiple-demand cortex which supports executive control across domains, although challenging semantic tasks recruit both networks. The semantic control network is juxtaposed between regions of default mode network that might be sufficient for the retrieval of strong semantic relationships and multiple-demand regions in the left hemisphere, suggesting that the large-scale organisation of flexible semantic cognition can be understood in terms of cortical gradients that capture systematic functional transitions that are repeated in temporal, parietal and frontal cortex.
Towards a Theory of Microbial Ecosystems
A major unresolved question in microbiome research is whether the complex ecological patterns observed in surveys of natural communities can be explained and predicted by fundamental, quantitative principles. Bridging theory and experiment is hampered by the multiplicity of ecological processes that simultaneously affect community assembly and a lack of theoretical tools for modeling diverse ecosystems. Here, I will present a simple ecological model of microbial communities that reproduces large-scale ecological patterns observed across multiple natural and experimental settings including compositional gradients, clustering by environment, diversity/harshness correlations, and nestedness. Surprisingly, our model works despite having a “random metabolisms” and “random consumer preferences”. This raises the natural of question of why random ecosystems can describe real-world experimental data. In the second, more theoretical part of the talk, I will answer this question by showing that when a community becomes diverse enough, it will always self-organize into a stable state whose properties are well captured by a “typical random ecosystems”.
NMC4 Short Talk: What can deep reinforcement learning tell us about human motor learning and vice-versa ?
In the deep reinforcement learning (RL) community, motor control problems are usually approached from a reward-based learning perspective. However, humans are often believed to learn motor control through directed error-based learning. Within this learning setting, the control system is assumed to have access to exact error signals and their gradients with respect to the control signal. This is unlike reward-based learning, in which errors are assumed to be unsigned, encoding relative successes and failures. Here, we try to understand the relation between these two approaches, reward- and error- based learning, and ballistic arm reaches. To do so, we test canonical (deep) RL algorithms on a well-known sensorimotor perturbation in neuroscience: mirror-reversal of visual feedback during arm reaching. This test leads us to propose a potentially novel RL algorithm, denoted as model-based deterministic policy gradient (MB-DPG). This RL algorithm draws inspiration from error-based learning to qualitatively reproduce human reaching performance under mirror-reversal. Next, we show MB-DPG outperforms the other canonical (deep) RL algorithms on a single- and a multi- target ballistic reaching task, based on a biomechanical model of the human arm. Finally, we propose MB-DPG may provide an efficient computational framework to help explain error-based learning in neuroscience.
Norse: A library for gradient-based learning in Spiking Neural Networks
We introduce Norse: An open-source library for gradient-based training of spiking neural networks. In contrast to neuron simulators which mainly target computational neuroscientists, our library seamlessly integrates with the existing PyTorch ecosystem using abstractions familiar to the machine learning community. This has immediate benefits in that it provides a familiar interface, hardware accelerator support and, most importantly, the ability to use gradient-based optimization. While many parallel efforts in this direction exist, Norse emphasizes flexibility and usability in three ways. Users can conveniently specify feed-forward (convolutional) architectures, as well as arbitrarily connected recurrent networks. We strictly adhere to a functional and class-based API such that neuron primitives and, for example, plasticity rules composes. Finally, the functional core API ensures compatibility with the PyTorch JIT and ONNX infrastructure. We have made progress to support network execution on the SpiNNaker platform and plan to support other neuromorphic architectures in the future. While the library is useful in its present state, it also has limitations we will address in ongoing work. In particular, we aim to implement event-based gradient computation, using the EventProp algorithm, which will allow us to support sparse event-based data efficiently, as well as work towards support of more complex neuron models. With this library, we hope to contribute to a joint future of computational neuroscience and neuromorphic computing.
Self-organized formation of discrete grid cell modules from smooth gradients
Modular structures in myriad forms — genetic, structural, functional — are ubiquitous in the brain. While modularization may be shaped by genetic instruction or extensive learning, the mechanisms of module emergence are poorly understood. Here, we explore complementary mechanisms in the form of bottom-up dynamics that push systems spontaneously toward modularization. As a paradigmatic example of modularity in the brain, we focus on the grid cell system. Grid cells of the mammalian medial entorhinal cortex (mEC) exhibit periodic lattice-like tuning curves in their encoding of space as animals navigate the world. Nearby grid cells have identical lattice periods, but at larger separations along the long axis of mEC the period jumps in discrete steps so that the full set of periods cluster into 5-7 discrete modules. These modules endow the grid code with many striking properties such as an exponential capacity to represent space and unprecedented robustness to noise. However, the formation of discrete modules is puzzling given that biophysical properties of mEC stellate cells (including inhibitory inputs from PV interneurons, time constants of EPSPs, intrinsic resonance frequency and differences in gene expression) vary smoothly in continuous topographic gradients along the mEC. How does discreteness in grid modules arise from continuous gradients? We propose a novel mechanism involving two simple types of lateral interaction that leads a continuous network to robustly decompose into discrete functional modules. We show analytically that this mechanism is a generic multi-scale linear instability that converts smooth gradients into discrete modules via a topological “peak selection” process. Further, this model generates detailed predictions about the sequence of adjacent period ratios, and explains existing grid cell data better than existing models. Thus, we contribute a robust new principle for bottom-up module formation in biology, and show that it might be leveraged by grid cells in the brain.
Norse: A library for gradient-based learning in Spiking Neural Networks
Norse aims to exploit the advantages of bio-inspired neural components, which are sparse and event-driven - a fundamental difference from artificial neural networks. Norse expands PyTorch with primitives for bio-inspired neural components, bringing you two advantages: a modern and proven infrastructure based on PyTorch and deep learning-compatible spiking neural network components.
Event-based Backpropagation for Exact Gradients in Spiking Neural Networks
Gradient-based optimization powered by the backpropagation algorithm proved to be the pivotal method in the training of non-spiking artificial neural networks. At the same time, spiking neural networks hold the promise for efficient processing of real-world sensory data by communicating using discrete events in continuous time. We derive the backpropagation algorithm for a recurrent network of spiking (leaky integrate-and-fire) neurons with hard thresholds and show that the backward dynamics amount to an event-based backpropagation of errors through time. Our derivation uses the jump conditions for partial derivatives at state discontinuities found by applying the implicit function theorem, allowing us to avoid approximations or substitutions. We find that the gradient exists and is finite almost everywhere in weight space, up to the null set where a membrane potential is precisely tangent to the threshold. Our presented algorithm, EventProp, computes the exact gradient with respect to a general loss function based on spike times and membrane potentials. Crucially, the algorithm allows for an event-based communication scheme in the backward phase, retaining the potential advantages of temporal sparsity afforded by spiking neural networks. We demonstrate the optimization of spiking networks using gradients computed via EventProp and the Yin-Yang and MNIST datasets with either a spike time-based or voltage-based loss function and report competitive performance. Our work supports the rigorous study of gradient-based optimization in spiking neural networks as well as the development of event-based neuromorphic architectures for the efficient training of spiking neural networks. While we consider the leaky integrate-and-fire model in this work, our methodology generalises to any neuron model defined as a hybrid dynamical system.
Optimal initialization strategies for Deep Spiking Neural Networks
Recent advances in neuromorphic hardware and Surrogate Gradient (SG) learning highlight the potential of Spiking Neural Networks (SNNs) for energy-efficient signal processing and learning. Like in Artificial Neural Networks (ANNs), training performance in SNNs strongly depends on the initialization of synaptic and neuronal parameters. While there are established methods of initializing deep ANNs for high performance, effective strategies for optimal SNN initialization are lacking. Here, we address this gap and propose flexible data-dependent initialization strategies for SNNs.
Optimising spiking interneuron circuits for compartment-specific feedback
Cortical circuits process information by rich recurrent interactions between excitatory neurons and inhibitory interneurons. One of the prime functions of interneurons is to stabilize the circuit by feedback inhibition, but the level of specificity on which inhibitory feedback operates is not fully resolved. We hypothesized that inhibitory circuits could enable separate feedback control loops for different synaptic input streams, by means of specific feedback inhibition to different neuronal compartments. To investigate this hypothesis, we adopted an optimization approach. Leveraging recent advances in training spiking network models, we optimized the connectivity and short-term plasticity of interneuron circuits for compartment-specific feedback inhibition onto pyramidal neurons. Over the course of the optimization, the interneurons diversified into two classes that resembled parvalbumin (PV) and somatostatin (SST) expressing interneurons. The resulting circuit can be understood as a neural decoder that inverts the nonlinear biophysical computations performed within the pyramidal cells. Our model provides a proof of concept for studying structure-function relations in cortical circuits by a combination of gradient-based optimization and biologically plausible phenomenological models
StereoSpike: Depth Learning with a Spiking Neural Network
Depth estimation is an important computer vision task, useful in particular for navigation in autonomous vehicles, or for object manipulation in robotics. Here we solved it using an end-to-end neuromorphic approach, combining two event-based cameras and a Spiking Neural Network (SNN) with a slightly modified U-Net-like encoder-decoder architecture, that we named StereoSpike. More specifically, we used the Multi Vehicle Stereo Event Camera Dataset (MVSEC). It provides a depth ground-truth, which was used to train StereoSpike in a supervised manner, using surrogate gradient descent. We propose a novel readout paradigm to obtain a dense analog prediction –the depth of each pixel– from the spikes of the decoder. We demonstrate that this architecture generalizes very well, even better than its non-spiking counterparts, leading to state-of-the-art test accuracy. To the best of our knowledge, it is the first time that such a large-scale regression problem is solved by a fully spiking network. Finally, we show that low firing rates (<10%) can be obtained via regularization, with a minimal cost in accuracy. This means that StereoSpike could be implemented efficiently on neuromorphic chips, opening the door for low power real time embedded systems.
On the implicit bias of SGD in deep learning
Tali's work emphasized the tradeoff between compression and information preservation. In this talk I will explore this theme in the context of deep learning. Artificial neural networks have recently revolutionized the field of machine learning. However, we still do not have sufficient theoretical understanding of how such models can be successfully learned. Two specific questions in this context are: how can neural nets be learned despite the non-convexity of the learning problem, and how can they generalize well despite often having more parameters than training data. I will describe our recent work showing that gradient-descent optimization indeed leads to 'simpler' models, where simplicity is captured by lower weight norm and in some cases clustering of weight vectors. We demonstrate this for several teacher and student architectures, including learning linear teachers with ReLU networks, learning boolean functions and learning convolutional pattern detection architectures.
PiVR: An affordable and versatile closed-loop platform to study unrestrained sensorimotor behavior
PiVR is a system that allows experimenters to immerse small animals into virtual realities. The system tracks the position of the animal and presents light stimulation according to predefined rules, thus creating a virtual landscape in which the animal can behave. By using optogenetics, we have used PiVR to present fruit fly larvae with virtual olfactory realities, adult fruit flies with a virtual gustatory reality and zebrafish larvae with a virtual light gradient. PiVR operates at high temporal resolution (70Hz) with low latencies (<30 milliseconds) while being affordable (<US$500) and easy to build (<6 hours). Through extensive documentation (www.PiVR.org), this tool was designed to be accessible to a wide public, from high school students to professional researchers studying systems neuroscience in academia.
Do leader cells drive collective behavior in Dictyostelium Discoideum amoeba colonies?
Dictyostelium Discoideum (DD) are a fascinating single-cellular organism. When nutrients are plentiful, the DD cells act as autonomous individuals foraging their local vicinity. At the onset of starvation, a few (<0.1%) cells begin communicating with others by emitting a spike in the chemoattractant protein cyclic-AMP. Nearby cells sense the chemical gradient and respond by moving toward it and emitting a cyclic-AMP spike of their own. Cyclic-AMP activity increases over time, and eventually a spiral wave emerges, attracting hundreds of thousands of cells to an aggregation center. How DD cells go from autonomous individuals to a collective entity remains an open question for more than 60 years--a question whose answer would shed light on the emergence of multi-cellular life. Recently, trans-scale imaging has allowed the ability to sense the cyclic-AMP activity at both cell and colony levels. Using both the images as well as toy simulation models, this research aims to clarify whether the activity at the colony level is in fact initiated by a few cells, which may be deemed "leader" or "pacemaker" cells. In this talk, I will demonstrate the use of information-theoretic techniques to classify leaders and followers based on trajectory data, as well as to infer the domain of interaction of leader cells. We validate the techniques on toy models where leaders and followers are known, and then try to answer the question in real data--do leader cells drive collective behavior in DD colonies?
Zero-shot visual reasoning with probabilistic analogical mapping
There has been a recent surge of interest in the question of whether and how deep learning algorithms might be capable of abstract reasoning, much of which has centered around datasets based on Raven’s Progressive Matrices (RPM), a visual analogy problem set commonly employed to assess fluid intelligence. This has led to the development of algorithms that are capable of solving RPM-like problems directly from pixel-level inputs. However, these algorithms require extensive direct training on analogy problems, and typically generalize poorly to novel problem types. This is in stark contrast to human reasoners, who are capable of solving RPM and other analogy problems zero-shot — that is, with no direct training on those problems. Indeed, it’s this capacity for zero-shot reasoning about novel problem types, i.e. fluid intelligence, that RPM was originally designed to measure. I will present some results from our recent efforts to model this capacity for zero-shot reasoning, based on an extension of a recently proposed approach to analogical mapping we refer to as Probabilistic Analogical Mapping (PAM). Our RPM model uses deep learning to extract attributed graph representations from pixel-level inputs, and then performs alignment of objects between source and target analogs using gradient descent to optimize a graph-matching objective. This extended version of PAM features a number of new capabilities that underscore the flexibility of the overall approach, including 1) the capacity to discover solutions that emphasize either object similarity or relation similarity, based on the demands of a given problem, 2) the ability to extract a schema representing the overall abstract pattern that characterizes a problem, and 3) the ability to directly infer the answer to a problem, rather than relying on a set of possible answer choices. This work suggests that PAM is a promising framework for modeling human zero-shot reasoning.
Agency through Physical Lenses
I will offer a broad-brush account of what explains the emergence of agents from a physics perspective, what sorts of conditions have to be in place for them to arise, and the essential features of agents when they are viewed through the lenses of physics. One implication will be a tight link to informational asymmetries associated with the thermodynamic gradient. Another will be a reversal of the direction of explanation from the one that is usually assumed in physical discussions. In in an evolved system, while it is true in some sense that the macroscopic behavior is the way it is because of the low-level dynamics, there is another sense in which the low-level dynamics is the way that it is because of the high-level behavior it supports. (More precisely and accurately, the constraints on the configuration of its components that define system as the kind of system it is are the way they are to exploit the low-level dynamics to produce the emergent behavior.) Another will be some insight into what might make human agency special.
3D Printing Cellular Communities: Mammalian Cells, Bacteria, And Beyond
While the motion and collective behavior of cells are well-studied on flat surfaces or in unconfined liquid media, in most natural settings, cells thrive in complex 3D environments. Bioprinting processes are capable of structuring cells in 3D and conventional bioprinting approaches address this challenge by embedding cells in bio-degradable polymer networks. However, heterogeneity in network structure and biodegradation often preclude quantitative studies of cell behavior in specified 3D architectures. Here, I will present a new approach to 3D bioprinting of cellular communities that utilizes jammed, granular polyelectrolyte microgels as a support medium. The self-healing nature of this medium allows the creation of highly precise cellular communities and tissue-like structures by direct injection of cells inside the 3D medium. Further, the transparent nature of this medium enables precise characterization of cellular behavior. I will describe two examples of my work using this platform to study the behavior of two different classes of cells in 3D. First, I will describe how we interrogate the growth, viability, and migration of mammalian cells—ranging from epithelial cells, cancer cells, and T cells—in the 3D pore space. Second, I will describe how we interrogate the migration of E. coli bacteria through the 3D pore space. Direct visualization enables us to reveal a new mode of motility exhibited by individual cells, in stark contrast to the paradigm of run-and-tumble motility, in which cells are intermittently and transiently trapped as they navigate the pore space; further, analysis of these dynamics enables prediction of single-cell transport over large length and time scales. Moreover, we show that concentrated populations of E. coli can collectively migrate through a porous medium—despite being strongly confined—by chemotactically “surfing” a self-generated nutrient gradient. Together, these studies highlight how the jammed microgel medium provides a powerful platform to design and interrogate complex cellular communities in 3D—with implications for tissue engineering, microtissue mechanics, studies of cellular interactions, and biophysical studies of active matter.
Traffic jams and U-turns: motility of swimming cells in viscosity gradients
Recurrent network dynamics lead to interference in sequential learning
Learning in real life is often sequential: A learner first learns task A, then task B. If the tasks are related, the learner may adapt the previously learned representation instead of generating a new one from scratch. Adaptation may ease learning task B but may also decrease the performance on task A. Such interference has been observed in experimental and machine learning studies. In the latter case, it is mediated by correlations between weight updates for the different tasks. In typical applications, like image classification with feed-forward networks, these correlated weight updates can be traced back to input correlations. For many neuroscience tasks, however, networks need to not only transform the input, but also generate substantial internal dynamics. Here we illuminate the role of internal dynamics for interference in recurrent neural networks (RNNs). We analyze RNNs trained sequentially on neuroscience tasks with gradient descent and observe forgetting even for orthogonal tasks. We find that the degree of interference changes systematically with tasks properties, especially with emphasis on input-driven over autonomously generated dynamics. To better understand our numerical observations, we thoroughly analyze a simple model of working memory: For task A, a network is presented with an input pattern and trained to generate a fixed point aligned with this pattern. For task B, the network has to memorize a second, orthogonal pattern. Adapting an existing representation corresponds to the rotation of the fixed point in phase space, as opposed to the emergence of a new one. We show that the two modes of learning – rotation vs. new formation – are directly linked to recurrent vs. input-driven dynamics. We make this notion precise in a further simplified, analytically tractable model, where learning is restricted to a 2x2 matrix. In our analysis of trained RNNs, we also make the surprising observation that, across different tasks, larger random initial connectivity reduces interference. Analyzing the fixed point task reveals the underlying mechanism: The random connectivity strongly accelerates the learning mode of new formation, and has less effect on rotation. The prior thus wins the race to zero loss, and interference is reduced. Altogether, our work offers a new perspective on sequential learning in recurrent networks, and the emphasis on internally generated dynamics allows us to take the history of individual learners into account.
Research talk: Is Escherichia coli information limited when navigating chemical gradients?
Exploring the evolution of motile curved bacteria using a regularized Stokeslet Boundary Element Method and Pareto optimality theory
Bacteria exhibit a bewildering diversity of morphologies, but despite their impact on nearly all aspects of life, they are frequently classified into a few general categories, usually just “spheres” and “rods.” Curved-rod bacteria are one simple variation observed in many environments, particularly the ocean. However, why so many species have evolved this shape is unknown. We used a regularized Stokeslet Boundary Element Method to model the motility of flagellated, curved bacteria. We show that curvature can increase swimming efficiency, revealing a widely applicable selective advantage. Furthermore, we show that the distribution of cell lengths and curvatures observed across bacteria in nature is predicted by evolutionary trade-offs between three tasks influenced by shape: efficient swimming, the ability to detect chemical gradients, and reduced cost of cell construction. We therefore reveal shape as an important component of microbial fitness.
Global AND Scale-Free? Spontaneous cortical dynamics between functional networks and cortico-hippocampal communication
Recent advancements in anatomical and functional imaging emphasize the presence of whole-brain networks organized according to functional and connectivity gradients, but how such structure shapes activity propagation and memory processes still lacks asatisfactory model. We analyse the fine-grained spatiotemporal dynamics of spontaneous activity in the entire dorsal cortex. through simultaneous recordings of wide-field voltage sensitive dye transients (VS), cortical ECoG, and hippocampal LFP in anesthetized mice. Both VS and ECoG show cortical avalanches. When measuring avalanches from the VS signal, we find a major deviation of the size scaling from the power-law distribution predicted by the criticality hypothesis and well approximated by the results from the ECoG. Breaking from scale-invariance, avalanches can thus be grouped in two regimes. Small avalanches consists of a limited number of co-activation modes involving a sub-set of cortical networks (related to the Default Mode Network), while larger avalanches involve a substantial portion of the cortical surface and can be clustered into two families: one immediately preceded by Retrosplenial Cortex activation and mostly involving medial-posterior networks, the other initiated by Somatosensory Cortex and extending preferentially along the lateral-anterior region. Rather than only differing in terms of size, these two set of events appear to be associated with markedly different brain-wide dynamical states: they are accompaniedby a shift in the hippocampal LFP, from the ripple band (smaller) to the gamma band (larger avalanches), and correspond to opposite directionality in the cortex-to-hippocampus causal relationship. These results provide a concrete description of global cortical dynamics, and shows how cortex in its entirety is involved in bi-directional communication in the hippocampus even in sleep-like states.
Molecular Biology of the Fragile X Syndrome
Silencing of FMR1 and loss of its gene product, FMRP, results in fragile X syndrome (FXS). FMRP binds brain mRNAs and inhibits polypeptide elongation. Using ribosome profiling of the hippocampus, we find that ribosome footprint levels in Fmr1-deficient tissue mostly reflect changes in RNA abundance. Profiling over a time course of ribosome runoff in wild-type tissue reveals a wide range of ribosome translocation rates; on many mRNAs, the ribosomes are stalled. Sucrose gradient ultracentrifugation of hippocampal slices after ribosome runoff reveals that FMRP co-sediments with stalled ribosomes, and its loss results in decline of ribosome stalling on specific mRNAs. One such mRNA encodes SETD2, a lysine methyltransferase that catalyzes H3K36me3. Chromatin immunoprecipitation sequencing (ChIP-seq) demonstrates that loss of FMRP alters the deployment of this histone mark. H3K36me3 is associated with alternative pre-RNA processing, which we find occurs in an FMRP-dependent manner on transcripts linked to neural function and autism spectrum disorders.
“DNA sensing in Bacillus subtilis”
Chemotaxis is the process where cells move in response to external chemical gradients. It has mainly been viewed as a foraging and defense mechanism, enabling bacteria to move towards nutrients or away from toxins. We recently found that the Gram-positive bacterium Bacillus subtilis performs chemotaxis towards DNA. While DNA can serve as a nutrient for B. subtilis, our results suggest that the response is not to DNA itself but rather to the information encoded within the DNA. In particular, we found that B. subtilis prefers DNA from more closely related species. These results suggest that B. subtilis seeks out specific DNA sequences that are more abundant in its own and related chromosomes. In this talk, I will discuss the mechanism of DNA sensing and chemotaxis in B. subtilis. I will conclude by discussing the physiological significance of DNA chemotaxis with regards to natural competence and kin identification.
Theory of gating in recurrent neural networks
Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data, and also in neuroscience, to understand the emergent properties of networks of real neurons. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating i.e. multiplicative interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we develop a dynamical mean-field theory (DMFT) to study the consequences of gating in RNNs. We use random matrix theory to show how gating robustly produces marginal stability and line attractors – important mechanisms for biologically-relevant computations requiring long memory. The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation-time of the dynamics. Gating is also shown to give rise to a novel, discontinuous transition to chaos, where the proliferation of critical points (topological complexity) is decoupled from the appearance of chaotic dynamics (dynamical complexity), contrary to a seminal result for additive RNNs. Critical surfaces and regions of marginal stability in the parameter space are indicated in phase diagrams, thus providing a map for principled parameter choices for ML practitioners. Finally, we develop a field-theory for gradients that arise in training, by incorporating the adjoint sensitivity framework from control theory in the DMFT. This paves the way for the use of powerful field-theoretic techniques to study training/gradients in large RNNs.
Synthetic swimmers: microorganism swimming without microorganisms
The effect of non Newtonian liquid rheology on the swimming performance of microorganisms is still poorly understood, despite numerous recent studies. In our effort to clarify some aspects of this problem, we have developed a series of magnetic synthetic swimmers that self-propel immersed in a fluid by emulating the swimming strategy of flagellated microorganisms. With these devices, it is possible to control some aspects of the motion with the objective to isolate specific effects. In this talk, recent results on the effects of shear-thinning viscosity and viscoelasticity on the motion of helical swimmers will presented and discussed. Also, a number of other new uses of the synthetic swimmers will be presented including swimming across gradients, swimming in sand, interactions and rheometry.
Back-propagation in spiking neural networks
Back-propagation is a powerful supervised learning algorithm in artificial neural networks, because it solves the credit assignment problem (essentially: what should the hidden layers do?). This algorithm has led to the deep learning revolution. But unfortunately, back-propagation cannot be used directly in spiking neural networks (SNN). Indeed, it requires differentiable activation functions, whereas spikes are all-or-none events which cause discontinuities. Here we present two strategies to overcome this problem. The first one is to use a so-called 'surrogate gradient', that is to approximate the derivative of the threshold function with the derivative of a sigmoid. We will present some applications of this method for time series processing (audio, internet traffic, EEG). The second one concerns a specific class of SNNs, which process static inputs using latency coding with at most one spike per neuron. Using approximations, we derived a latency-based back-propagation rule for this sort of networks, called S4NN, and applied it to image classification.
E-prop: A biologically inspired paradigm for learning in recurrent networks of spiking neurons
Transformative advances in deep learning, such as deep reinforcement learning, usually rely on gradient-based learning methods such as backpropagation through time (BPTT) as a core learning algorithm. However, BPTT is not argued to be biologically plausible, since it requires to a propagate gradients backwards in time and across neurons. Here, we propose e-prop, a novel gradient-based learning method with local and online weight update rules for recurrent neural networks, and in particular recurrent spiking neural networks (RSNNs). As a result, e-prop has the potential to provide a substantial fraction of the power of deep learning to RSNNs. In this presentation, we will motivate e-prop from the perspective of recent insights in neuroscience and show how these have to be combined to form an algorithm for online gradient descent. The mathematical results will be supported by empirical evidence in supervised and reinforcement learning tasks. We will also discuss how limitations that are inherited from gradient-based learning methods, such as sample-efficiency, can be addressed by considering an evolution-like optimization that enhances learning on particular task families. The emerging learning architecture can be used to learn tasks by a single demonstration, hence enabling one-shot learning.
Swimming in the third domain: archaeal extremophiles
Archaea have evolved to survive in some of the most extreme environments on earth. Life in extreme, nutrient-poor conditions gives the opportunity to probe fundamental energy limitations on movement and response to stimuli, two essential markers of living systems. Here we use three-dimensional holographic microscopy and computer simulations to show that halophilic archaea achieve chemotaxis with power requirements one hundred-fold lower than common eubacterial model systems. Their swimming direction is stabilised by their flagella (archaella), enhancing directional persistence in a manner similar to that displayed by eubacteria, albeit with a different motility apparatus. Our experiments and simulations reveal that the cells are capable of slow but deterministic chemotaxis up a chemical gradient, in a biased random walk at the thermodynamic limit.
Inferring Brain Rhythm Circuitry and Burstiness
Bursts in gamma and other frequency ranges are thought to contribute to the efficiency of working memory or communication tasks. Abnormalities in bursts have also been associated with motor and psychiatric disorders. The determinants of burst generation are not known, specifically how single cell and connectivity parameters influence burst statistics and the corresponding brain states. We first present a generic mathematical model for burst generation in an excitatory-inhibitory (EI) network with self-couplings. The resulting equations for the stochastic phase and envelope of the rhythm’s fluctuations are shown to depend on only two meta-parameters that combine all the network parameters. They allow us to identify different regimes of amplitude excursions, and to highlight the supportive role that network finite-size effects and noisy inputs to the EI network can have. We discuss how burst attributes, such as their durations and peak frequency content, depend on the network parameters. In practice, the problem above follows the a priori challenge of fitting such E-I spiking networks to single neuron or population data. Thus, the second part of the talk will discuss a novel method to fit mesoscale dynamics using single neuron data along with a low-dimensional, and hence statistically tractable, single neuron model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous ‘pools’ of neurons, and modelling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to either optimize parameters by gradient ascent on the log-likelihood, or to perform Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this approach using an E-I network of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived. We show that both single-neuron and connectivity parameters can be adequately recovered from simulated data.
DelGrad: Exact gradients in spiking networks for learning transmission delays and weights
Bernstein Conference 2024
Gradient and network~structure of lagged correlations\\in band-limited cortical dynamics
Bernstein Conference 2024
Smooth exact gradient descent learning in spiking neural networks
Bernstein Conference 2024
Approximate gradient descent and the brain: the role of bias and variance
COSYNE 2022
Mind the gradient: context-dependent selectivity to natural images in the retina revealed with a novel perturbative approach
COSYNE 2022
Mind the gradient: context-dependent selectivity to natural images in the retina revealed with a novel perturbative approach
COSYNE 2022
Traveling UP states in the post-subiculum reveal an anatomical gradient of intrinsic properties
COSYNE 2023
Brain-like learning with exponentiated gradients
COSYNE 2025
Controlling Gradient Dynamics for Improved Temporal Learning in Neural Circuits
COSYNE 2025
Reach-to-grasp activity is organized along an abstract-to-detailed gradient in mouse sensorimotor cortex
COSYNE 2025
Three-factor gradient-ascent approximation explains local-circuit plasticity during BCI learning
COSYNE 2025
Fast gradient-free activation maximization for neurons in spiking neural networks
FENS Forum 2024
Timing-dependent LTP at Schaffer collateral-CA1 synapses exhibits a dorso-ventral gradient of GABAergic modulation in the mouse hippocampus
FENS Forum 2024