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Higher uniformity of bounded multiplicative functions in short intervals on average
No full textLet λ denote the Liouville function. We show that, as X → ∞, ∫^(2X)_X sup_(P(Y)∈R[Y]degP≤k) ∣∣∣ ∑_(x≤n≤x+H) λ(n)e(−P(n))∣∣∣∣ dx = o(XH)
for all fixed k and X^θ ≤ H ≤ X with 0 < θ < 1 fixed but arbitrarily small. Previously this was only established for
k ≤ 1. We obtain this result as a special case of the corresponding statement for (non-pretentious) 1-bounded multiplicative functions that we prove.
In fact, we are able to replace the polynomial phases
e(−P(n)) by degree k nilsequences F̅(g(n)Γ). By the inverse theory for the Gowers norms this implies the higher order asymptotic uniformity result ∫^(2X)_X ∥λ∥_(U^(k+1))([x,x+H]) dx = o(X)in the same range of H.
We present applications of this result to patterns of various types in the Liouville sequence. Firstly, we show that the number of sign patterns of the Liouville function is superpolynomial, making progress on a conjecture of Sarnak about the Liouville sequence having positive entropy. Secondly, we obtain cancellation in averages of λ over short polynomial progressions (n+P₁(m),…,n+Pₖ(m)), which in the case of linear polynomials yields a new averaged version of Chowla's conjecture.
We are in fact able to prove our results on polynomial phases in the wider range H ≥ exp((log X)^(5/(8+ε))), thus strengthening also previous work on the Fourier uniformity of the Liouville function
MimicPlay: Long-Horizon Imitation Learning by Watching Human Play
No full textImitation Learning from human demonstrations is a promising paradigm to teach robots manipulation skills in the real world, but learning complex long-horizon tasks often requires an unattainable amount of demonstrations. To reduce the high data requirement, we resort to human play data - video sequences of people freely interacting with the environment using their hands. We hypothesize that even with different morphologies, human play data contain rich and salient information about physical interactions that can readily facilitate robot policy learning. Motivated by this, we introduce a hierarchical learning framework named MimicPlay that learns latent plans from human play data to guide low-level visuomotor control trained on a small number of teleoperated demonstrations. With systematic evaluations of 14 long-horizon manipulation tasks in the real world, we show that MimicPlay dramatically outperforms state-of-the-art imitation learning methods in task success rate, generalization ability, and robustness to disturbances. More details and video results could be found at https://mimic-play.github.io/
I²SB: Image-to-Image Schrödinger Bridge
No full textWe propose Image-to-Image Schrödinger Bridge (I²SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for image restoration, as the degraded images are structurally informative priors for reconstructing the clean images. I²SB belongs to a tractable class of Schrödinger bridge, the nonlinear extension to score-based models, whose marginal distributions can be computed analytically given boundary pairs. This results in a simulation-free framework for nonlinear diffusions, where the I²SB training becomes scalable by adopting practical techniques used in standard diffusion models. We validate I²SB in solving various image restoration tasks, including inpainting, super-resolution, deblurring, and JPEG restoration on ImageNet 256x256 and show that I²SB surpasses standard conditional diffusion models with more interpretable generative processes. Moreover, I²SB matches the performance of inverse methods that additionally require the knowledge of the corruption operators. Our work opens up new algorithmic opportunities for developing efficient nonlinear diffusion models on a large scale. scale. Project page: https://i2sb.github.io
Algorithmic Collective Action in Machine Learning
No full textWe initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm
FRoGGeR: Fast Robust Grasp Generation via the Min-Weight Metric
No full textMany approaches to grasp synthesis optimize analytic quality metrics that measure grasp robustness based on finger placements and local surface geometry. However, generating feasible dexterous grasps by optimizing these metrics is slow, often taking minutes. To address this issue, this paper presents FRoGGeR: a method that quickly generates robust precision grasps using the min-weight metric, a novel, almost-everywhere differentiable approximation of the classical epsilon grasp metric. The min-weight metric is simple and interpretable, provides a reasonable measure of grasp robustness, and admits numerically efficient gradients for smooth optimization. We leverage these properties to rapidly synthesize collision-free robust grasps - typically in less than a second. FRoGGeR can refine the candidate grasps generated by other methods (heuristic, data-driven, etc.) and is compatible with many object representations (SDFs, meshes, etc.). We study FRoGGeR's performance on over 40 objects drawn from the YCB dataset, outperforming a competitive baseline in computation time, feasibility rate of grasp synthesis, and picking success in simulation. We conclude that FRoGGeR is fast: it has a median synthesis time of 0.834s over hundreds of experiments
An Active Learning Based Robot Kinematic Calibration Framework Using Gaussian Processes
No full textFuture NASA lander missions to icy moons will require completely automated, accurate, and data efficient calibration methods for the robot manipulator arms that sample icy terrains in the lander's vicinity. To support this need, this paper presents a Gaussian Process (GP) approach to the classical manipulator kinematic calibration process. Instead of identifying a corrected set of Denavit-Hartenberg kinematic parameters, a set of GPs models the residual kinematic error of the arm over the workspace. More importantly, this modeling framework allows a Gaussian Process Upper Confident Bound (GP-UCB) algorithm to efficiently and adaptively select the calibration's measurement points so as to minimize the number of experiments, and therefore minimize the time needed for recalibration. The method is demonstrated in simulation on a simple 2-DOF arm, a 6 DOF arm whose geometry is a candidate for a future NASA mission, and a 7 DOF Barrett WAM arm
Design of an ultra-low mode volume piezo-optomechanical quantum transducer
No full textCoherent transduction of quantum states from the microwave to the optical domain can play a key role in quantum networking and distributed quantum computing. We present the design of a piezo-optomechanical device formed in a hybrid lithium niobate on silicon platform, that is suitable for microwave-to-optical quantum transduction. Our design is based on acoustic hybridization of an ultra-low mode volume piezoacoustic cavity with an optomechanical crystal cavity. The strong piezoelectric nature of lithium niobate allows us to mediate transduction via an acoustic mode which only minimally interacts with the lithium niobate, and is predominantly silicon-like, with very low electrical and acoustic loss. We estimate that this transducer can realize an intrinsic conversion efficiency of up to 35% with <0.5 added noise quanta when resonantly coupled to a superconducting transmon qubit and operated in pulsed mode at 10 kHz repetition rate. The performance improvement gained in such hybrid lithium niobate-silicon transducers make them suitable for heralded entanglement of qubits between superconducting quantum processors connected by optical fiber links
S-duality in TT̅-deformed CFT
No full textTT̅ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the TT̅ deformed partition sum of a symmetric product CFT. We find that it takes the form of a partition sum of a second quantized string theory with a worldsheet given by the product of the seed CFT and a gaussian sigma model with the two-torus as target space. We show that deformed symmetric product theory admits a natural UV completion that exhibits a strong weak coupling ℤ₂ duality that interchanges the momentum and winding numbers and maps the TT̅-coupling λ to its inverse 1/λ. The ℤ₂ duality is part of a full O(2,2,ℤ)-duality group that includes a PSL(2,ℤ) acting on the complexified TT̅ coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6
A machine-readable specification for genomics assays
No full textUnderstanding the structure of sequenced fragments from genomics libraries is essential for accurate read preprocessing. Currently, different assays and sequencing technologies require custom scripts and programs that do not leverage the common structure of sequence elements present in genomics libraries. We present seqspec, a machine-readable specification for libraries produced by genomics assays that facilitates standardization of preprocessing and enables tracking and comparison of genomics assays. The specification and associated seqspec command line tool is available at https://github.com/IGVF/seqspec
Structure of the Inmazeb cocktail and resistance to Ebola virus escape
No full textMonoclonal antibodies can provide important pre- or post-exposure protection against infectious disease for those not yet vaccinated or in individuals that fail to mount a protective immune response after vaccination. Inmazeb (REGN-EB3), a three-antibody cocktail against Ebola virus, lessened disease and improved survival in a controlled trial. Here, we present the cryo-EM structure at 3.1 Å of the Ebola virus glycoprotein, determined without symmetry averaging, in a simultaneous complex with the antibodies in the Inmazeb cocktail. This structure allows the modeling of previously disordered portions of the glycoprotein glycan cap, maps the non-overlapping epitopes of Inmazeb, and illuminates the basis for complementary activities and residues critical for resistance to escape by these and other clinically relevant antibodies. We further provide direct evidence that Inmazeb protects against the rapid emergence of escape mutants, whereas monotherapies even against conserved epitopes do not, supporting the benefit of a cocktail versus a monotherapy approach