Publications

The efficient coding hypothesis posits that sensory systems are adapted to the statistics of their inputs, maximizing mutual information between environmental signals and their representations, subject to biological constraints. While elegant, information theoretic quantities are notoriously difficult to measure or optimize, and most research on the hypothesis employs approximations, bounds, or substitutes (e.g., reconstruction error). A recently developed measure of coding efficiency, the "manifold capacity", quantifies the number of object categories that may be represented in a linearly separable fashion, but its calculation relies on a computationally intensive iterative procedure that precludes its use as an objective. Here, we simplify this measure to a form that facilitates direct optimization, use it to learn Maximum Manifold Capacity Representations (MMCRs), and demonstrate that these are competitive with state-of-the-art results on current self-supervised learning (SSL) recognition benchmarks. Empirical analyses reveal important differences between MMCRs and the representations learned by other SSL frameworks, and suggest a mechanism by which manifold compression gives rise to class separability. Finally, we evaluate a set of SSL methods on a suite of neural predictivity benchmarks, and find MMCRs are highly competitive as models of the primate ventral stream.

Internal representations are not uniquely identifiable from perceptual measurements: different representations can generate identical perceptual predictions, and similar representations may predict dissimilar percepts. Here, we generalize a previous method (``Eigendistortions'' -- Berardino et al., 2017) to enable comparison of models based on their metric tensors, which can be verified perceptually. Metric tensors characterize sensitivity to stimulus perturbations, reflecting both the geometric and stochastic properties of the representation, and providing an explicit prediction of perceptual discriminability. Brute force comparison of model-predicted metric tensors would require estimation of human perceptual thresholds along an infeasibly large set of stimulus directions. To circumvent this ``perceptual curse of dimensionality'', we compute and measure discrimination capabilities for a small set of most-informative perturbations, reducing the measurement cost from thousands of hours (a conservative estimate) to a single trial. We show that this single measurement, made for a variety of different test stimuli, is sufficient to differentiate models, select models that better match human perception, or generate new models that combine the advantages of existing models. We demonstrate the power of this method in comparison of (1) two models for trichromatic color representation, with differing internal noise; and (2) two autoencoders trained with different regularizers.

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.

We study the temperature evolution of quasiparticles in the correlated metal Sr

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.

We use state-of-the-art numerical techniques to compute ground state correlations in the two-dimensional SU(3) Fermi Hubbard model at 1/3-filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We find clear evidence of a quantum critical point separating a non-magnetic uniform metallic phase from a regime where long-range `spin' order is present. In particular, there are multiple successive transitions to states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N) physics.