Publications

We report the first ab initio, non-relativistic QED method that couples light and matter self-consistently beyond the electric dipole approximation and without multipolar truncations. This method is based on an extension of the Maxwell-Pauli-Kohn-Sham approach to a full minimal coupling Hamiltonian, where the space- and time-dependent vector potential is coupled to the matter system, and its back-reaction to the radiated fields is generated by the full current density. The implementation in the open-source Octopus code is designed for massively-parallel multiscale simulations considering different grid spacings for the Maxwell and matter subsystems. Here, we show the first applications of this framework to simulate renormalized Cherenkov radiation of an electronic wavepacket, magnetooptical effects with non-chiral light in non-chiral molecular systems, and renormalized plasmonic modes in a nanoplasmonic dimer. We show that in some cases the beyond-dipole effects can not be captured by a multipolar expansion Hamiltonian in the length gauge. Finally, we discuss further opportunities enabled by the framework in the field of twisted light and orbital angular momentum, inelastic light scattering and strong field physics.

Multi-scale non-Gaussian time-series having stationary increments appear in a wide range of applications, particularly in finance and physics. We introduce stochastic models that capture intermittency phenomena such as crises or bursts of activity, time reversal asymmetries, and that can be estimated from a single realization of size N. Variations at multiple scales are separated with a wavelet transform. Non-Gaussian properties appear through dependencies of wavelet coefficients across scales. We define maximum entropy models from the joint correlation across time and scales of wavelet coefficients and their modulus. Diagonal matrix approximations are estimated with a wavelet representation of this joint correlation. The resulting diagonals define O(log3⁡N) moments that are called scattering spectra. A notion of wide-sense self-similarity is defined from the invariance of scattering spectra to scaling, which can be tested numerically on a single realization. We study the accuracy of maximum entropy scattering spectra models for fractional Brownian motions, Hawkes processes, multifractal random walks, as well as financial and turbulent time-series.

In this work, we introduce the No-Underrun Sampler (NURS), a locally-adaptive, gradient-free Markov chain Monte Carlo method that blends ideas from Hit-and-Run and the No-U-Turn Sampler. NURS dynamically adapts to the local scale of the target distribution without requiring gradient evaluations, making it especially suitable for applications where gradients are unavailable or costly. We establish key theoretical properties, including reversibility, formal connections to Hit-and-Run and Random Walk Metropolis, Wasserstein contraction comparable to Hit-and-Run in Gaussian targets, and bounds on the total variation distance between the transition kernels of Hit-and-Run and NURS. Empirical experiments, supported by theoretical insights, illustrate the ability of NURS to sample from Neal's funnel, a challenging multi-scale distribution from Bayesian hierarchical inference.

We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes or the fast Fourier transform can efficiently treat the volumetric inhomogeneity, but require care to be taken near the boundary to ensure that the volume data is globally smooth. We avoid function extension or cut-cell quadratures near the boundary by dividing the domain into two regions: a bulk region away from the boundary that is efficiently treated with a truncated free-space box code, and a variable-width boundary-conforming strip region that is treated with a spectral collocation method and accompanying fast direct solver. Particular solutions in each region are then combined with Laplace layer potentials to yield the global solution. The resulting solver has an optimal computational complexity of O(N) for an adaptive discretization with N degrees of freedom. With an efficient two-dimensional (2D) implementation we demonstrate adaptive resolution of volumetric data, boundary data, and geometric features across a wide range of length scales, to typically 10-digit accuracy. The cost of all boundary corrections remains small relative to that of the bulk box code. The extension to 3D is expected to be straightforward in many cases because the strip

Apical and basal dendrites of pyramidal neurons receive anatomically and functionally distinct inputs, implying compartment-level functional diversity during behavior. To test this, we imaged in vivo calcium signals from soma, apical dendrites, and basal dendrites in mouse hippocampal CA3 pyramidal neurons during head-fixed navigation. To capture compartment-specific population dynamics, we developed computational tools to automatically segment dendrites and extract accurate fluorescence traces from densely labeled neurons. We validated the method on sparsely labeled preparations and synthetic data, predicting an optimal labeling density for high experimental throughput and analytical accuracy. Our method detected rapid, local dendritic activity. Dendrites showed robust spatial tuning, similar to soma but with higher activity rates. Across days, apical dendrites remained more stable and outperformed in decoding of the animal’s position. Thus, population-level apical and basal dendritic differences may reflect distinct compartment-specific input-output functions and computations in CA3. These tools will facilitate future studies mapping sub-cellular activity and their relation to behavior.

Optimization in deep learning remains poorly understood. A key difficulty is that optimizers exhibit complex oscillatory dynamics, referred to as "edge of stability," which cannot be captured by traditional optimization theory. In this paper, we show that the path taken by an oscillatory optimizer can often be captured by a central flow: a differential equation which directly models the time-averaged (i.e. smoothed) optimization trajectory. We empirically show that these central flows can predict long-term optimization trajectories for generic neural networks with a high degree of numerical accuracy. By interpreting these flows, we are able to understand how gradient descent makes progress even as the loss sometimes goes up; how adaptive optimizers ``adapt'' to the local loss landscape; and how adaptive optimizers implicitly seek out regions of weight space where they can take larger steps. These insights (and others) are not apparent from the optimizers' update rules, but are revealed by the central flows. Therefore, we believe that central flows constitute a promising tool for reasoning about optimization in deep learning.

Prediction is a fundamental capability of all living organisms, and has been proposed as an objective for learning sensory representations. Recent work demonstrates that in primate visual systems, prediction is facilitated by neural representations that follow straighter temporal trajectories than their initial photoreceptor encoding, which allows for prediction by linear extrapolation. Inspired by these experimental findings, we develop a self-supervised learning (SSL) objective that explicitly quantifies and promotes straightening. We demonstrate the power of his objective in training deep feedforward neural networks on smoothly-rendered synthetic image sequences that mimic commonly-occurring properties of natural videos. The learned model contains neural embeddings that are predictive, but also factorize the geometric, photometric, and semantic attributes of objects. The representations also prove more robust to noise and adversarial attacks compared to previous SSL methods that optimize for invariance to random augmentations. Moreover, these beneficial properties can be transferred to other training procedures by using the straightening objective as a regularizer, suggesting a broader utility of straightening as a principle for robust unsupervised learning.

Neurons early in the primate visual cortical pathway generate responses by combining signals from other neurons: some from downstream areas, some from within the same area, and others from areas upstream. Here we develop a model that selectively combines afferents derived from a population model of V1 cells. We use this model to account for responses we recorded of both V1 and V2 neurons in awake fixating macaque monkeys to stimuli composed of a sparse collection of locally oriented features ("droplets") designed to drive subsets of V1 neurons. The first stage computes the rectified responses of a fixed population of oriented filters at different scales that cover the visual field. The second stage computes a weighted combination of these first-stage responses, followed by a final nonlinearity, with parameters optimized to fit data from physiological recordings and constrained to encourage sparsity and locality. The fitted model accounts for the responses of both V1 and V2 neurons, capturing an average of 43% of the explainable variance for V1 and 38% for V2. The models fitted to droplet recordings predict responses to classical stimuli, such as gratings of different orientations and spatial frequencies, as well as to textures of different spectral content, which are known to be especially effective in driving V2. The models are less effective, however, at capturing the selectivity of responses to textures that include naturalistic image statistics. The pattern of afferents {\textemdash} defined by their weights over the 4 dimensions of spatial position, orientation, and spatial frequency {\textemdash} provides a common and interpretable characterization of the origin of many neuronal response properties in the early visual cortex.Competing Interest StatementThe authors have declared no competing interest.

Efficient coding theory posits that sensory circuits transform natural signals into neural representations that maximize information transmission subject to resource constraints. Local interneurons are thought to play an important role in these transformations, dynamically shaping patterns of local circuit activity to facilitate and direct information flow. However, the relationship between these coordinated, nonlinear, circuit-level transformations and the properties of interneurons (e.g., connectivity, activation functions, response dynamics) remains unknown. Here, we propose a normative computational model that establishes such a relationship. Our model is derived from an optimal transport objective that conceptualizes the circuit’s input-response function as transforming the inputs to achieve an efficient target response distribution. The circuit, which is comprised of primary neurons that are recurrently connected to a set of local interneurons, continuously optimizes this objective by dynamically adjusting both the synaptic connections between neurons as well as the interneuron activation functions. In an example application motivated by redundancy reduction, we construct a circuit that learns a dynamical nonlinear transformation that maps natural image data to a spherical Gaussian, significantly reducing statistical dependencies in neural responses. Overall, our results provide a framework in which the distribution of circuit responses is systematically and nonlinearly controlled by adjustment of interneuron connectivity and activation functions.

We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint.