Publications

A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may affect task precision. Using methods from statistical mechanics, we study the average-case learning curves for ε-insensitive Support Vector Regression (ε-SVR) and discuss its capacity as a measure of linear decodability. Our analysis reveals a phase transition in the training error at a critical load, capturing the interplay between the tolerance parameter ε and neural variability. We uncover a double-descent phenomenon in the generalization error, showing that ε acts as a regularizer, both suppressing and shifting these peaks. Theoretical predictions are validated both on toy models and deep neural networks, extending the theory of Support Vector Machines to continuous tasks with inherent neural variability.

Cells modified outside of the body and then reintroduced provide an advantage over most small-molecule therapeutics in that cells can be designed to recognize target molecules in specific tissues and then act locally. Two studies now demonstrate advances in cell engineering for treating human disease (see the Perspective by Davila and Brentjens). Reddy et al. engineered human T cells to make a synthetic receptor that recognized overactive T cells such as those causing autoimmune disease and organ rejection. The most effective modified cells tested were ones in which the synthetic receptor initiated a program causing the production of both an anti-inflammatory cytokine and a receptor that acted as sink for a locally produced proinflammatory cytokine. In mouse models, such cells could be designed with logic programs that protect the desired tissues without detrimental systemic immunosuppression. Simic et al. modified T cells to produce a synthetic receptor that recognized an antigen localized to the extracellular matrix of the brain. The synthetic receptor activated a circuit stimulating the production of chimeric antigen receptors that targeted and killed cancer cells in the brain but not those implanted elsewhere in the mouse. A mouse model of neuroinflammatory brain disease could be treated with cells engineered to locally produce an anti-inflammatory cytokine.

Extracellular-signal-regulated kinase (ERK) signaling controls development and homeostasis and is genetically deregulated in human diseases, including neurocognitive disorders and cancers. Although the list of ERK functions is vast and steadily growing, the full spectrum of processes controlled by any specific ERK activation event remains unknown. Here, we show how ERK functions can be systematically identified using targeted perturbations and global readouts of ERK activation. Our experimental model is the Drosophila embryo, where ERK signaling at the embryonic poles has thus far only been associated with the transcriptional patterning of the future larva. Through a combination of live imaging and phosphoproteomics, we demonstrated that ERK activation at the poles is also critical for maintaining the speed and synchrony of embryonic cleavages. The presented approach to interrogating phosphorylation networks identifies a hidden function of a well-studied signaling event and sets the stage for similar studies in other organisms.

Neurons in primate visual cortex (area V1) are tuned for spatial frequency, in a manner that depends on their position in the visual field. Several studies have examined this dependency using fMRI, reporting preferred spatial frequencies (tuning curve peaks) of V1 voxels as a function of eccentricity, but their results differ by as much as two octaves, presumably due to differences in stimuli, measurements, and analysis methodology. Here, we characterize spatial frequency tuning at a millimeter resolution within human primary visual cortex, across stimulus orientation and visual field locations. We measured fMRI responses to a novel set of stimuli, constructed as sinusoidal gratings in log-polar coordinates, which include circular, radial, and spiral geometries. For each individual stimulus, the local spatial frequency varies inversely with eccentricity, and for any given location in the visual field, the full set of stimuli span a broad range of spatial frequencies and orientations. Over the measured range of eccentricities, the preferred spatial frequency is well-fit by a function that varies as the inverse of the eccentricity plus a small constant. We also find small but systematic effects of local stimulus orientation, defined in both absolute coordinates and relative to visual field location. Specifically, peak spatial frequency is higher for tangential than radial orientations and for horizontal than vertical orientations.

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from this http URL to the overcompleteness, we achieve only qualitative agreement.

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different ansatze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs = 37 +/- 1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.

The exploration of quantum phases in moiré systems has drawn intense experimental and theoretical efforts. The realization of honeycomb symmetry has been a recent focus. The combination of strong interaction and honeycomb symmetry can lead to exotic electronic states such as fractional Chern insulator, unconventional superconductor, and quantum spin liquid. Accurate computations in such systems, with reliable treatment of strong long-ranged Coulomb interaction and approaching the large system sizes to extract thermodynamic phases, are mostly missing. We study the two-dimensional electron gas on a honeycomb moiré lattice at quarter filling, using fixed-phase diffusion Monte Carlo. The ground state phases of this important model are determined in the parameter regime relevant to current experiments. With increasing moiré potential, the systems transitions from a paramagnetic metal to an itinerant ferromagnetic semimetal and then a charge-density-wave insulator.

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from this http URL to the overcompleteness, we achieve only qualitative agreement.

The exploration of quantum phases in moiré systems has drawn intense experimental and theoretical efforts. The realization of honeycomb symmetry has been a recent focus. The combination of strong interaction and honeycomb symmetry can lead to exotic electronic states such as fractional Chern insulator, unconventional superconductor, and quantum spin liquid. Accurate computations in such systems, with reliable treatment of strong long-ranged Coulomb interaction and approaching the large system sizes to extract thermodynamic phases, are mostly missing. We study the two-dimensional electron gas on a honeycomb moiré lattice at quarter filling, using fixed-phase diffusion Monte Carlo. The ground state phases of this important model are determined in the parameter regime relevant to current experiments. With increasing moiré potential, the systems transitions from a paramagnetic metal to an itinerant ferromagnetic semimetal and then a charge-density-wave insulator.