Proposes NUQSGD for efficient parallel training of large models.
problem Efficiently compressing gradients for parallel SGD training.
method Nonuniform quantization scheme for improved theoretical and empirical performance.
result NUQSGD outperforms QSGDinf and other compression methods.
A new gradient quantization scheme improves communication efficiency in distributed training.
problem Efficiently compressing gradients for parallel training of large models.
method Proposes a new gradient quantization scheme with theoretical guarantees and empirical performance.
result The new scheme matches and exceeds the performance of existing methods.
New property identifies arithmetic lattices from nonuniform lattices.
problem Characterizing arithmetic lattices among nonuniform lattices.
method Introduced Bounded Clustering (B-C) property.
result B-C property uniquely identifies arithmetic lattices.
This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to conj…
A new network reduces MIMO detection complexity.
problem Reducing computational complexity in massive MIMO systems.
method Learned conjugate gradient descent network (LcgNet) that learns step-sizes and integrates a quantizer.
result The network achieves promising performance with significantly reduced complexity.
New approach to nonuniform learnability using measure theory.
problem Nonuniform learnability of hypotheses with varying sample sizes.
method Measure theoretic approach to redefine nonuniform learnability, introducing a new algorithm (Generalize Measure Learnability).
result Achieved statistical consistency in learning countable hypothesis classes.
The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.
Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtaine…
New geometric theory explains nonuniform origami responses.
problem Understanding nonuniform responses in origami sheets.
method Purely geometric continuum theory capturing nonuniform, nonlinear response.
result Three modes govern nonuniform response, varying smoothly across the sheet.
For any n>1 we determine the uniform and nonuniform lattices of the smallest covolume in the Lie group Sp(n,1). We explicitly describe them in terms of the ring of Hurwitz integers in the nonuniform case with n even, respectively, of the icosian ring in the uniform case for all n>1.
New method shows Hessian estimator from random samples converges to true Hessian on complex manifolds.
problem Uncertainty in Hessian estimator accuracy on complex manifolds with boundaries and nonuniform sampling.
method Locally fitting quadratic polynomials, rigorous theoretical analysis under mild conditions.
result The Hessian estimator asymptotically converges to the true Hessian, even near boundaries.
Let Γ be a nonuniform lattice acting on real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of Γ in SO(n,1). Furthermore, in dimensions 2 and 3, there is a semialgebraic subset of the repr…
If Gamma is a nonuniform, irreducible lattice in a semisimple Lie group whose real rank is greater than 1, we show Gamma contains a subgroup that is isomorphic to a nonuniform, irreducible lattice in either SL(3,R), SL(3,C), or a direct product SL(2,R)^m x SL(2,C)^n$, with m + n > 1. (In geometric terms, this can be in…
The paper explores the dynamics of composite symplectic Dehn twists with nonuniform hyperbolicity.
problem Understanding the dynamics and properties of composite symplectic Dehn twists.
method Analyzing the form of nonuniform hyperbolicity, growth of Floer cohomology, and classification of symplectic mapping classes.
result Composite symplectic Dehn twists exhibit positive topological entropy and exponential growth in Floer cohomology.
Deep networks adapt to function regularity and data distribution.
problem Understanding deep learning's adaptability to function regularity and data distribution.
method Developed nonparametric approximation and estimation theories for a broad class of functions using deep ReLU networks.
result Deep neural networks are adaptive to different regularity of functions and nonuniform data distributions.
Improves statistical inference using machine learning predictions with imputed data.
problem Invalid statistical inference due to machine learning prediction errors.
method Bootstrap confidence intervals for nonuniform samples and arbitrary imputed features.
result Valid confidence intervals without assumptions on machine learning model quality.
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
LA-VDM accelerates VDM using landmarks to improve data analysis.
problem Efficiently analyzing complex datasets with nonuniform sampling densities.
method Landmark-constrained two-stage normalization to accelerate VDM.
result LA-VDM accurately recovers parallel transport and converges to the connection Laplacian.
We prove noncoherence of certain families of lattices in the isometry group of the hyperbolic n-space for n greater than 3. For instance, every nonuniform arithmetic lattice in SO(n,1) is noncoherent, provided that n is at least 6.
We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.
New lattices in higher dimensions have dense surface subgroups.
problem Finding dense subgroups in higher-dimensional arithmetic lattices.
method Exhibited nonuniform arithmetic lattices in SO(n,1).
result Contain Zariski-dense surface subgroups.
New game model improves financial stylized facts reproduction.
problem Difficulty in reproducing financial stylized facts.
method Agent-based speculation game with unique features.
result Successfully reproduces 10 out of 11 stylized facts.
We determine the number of cusps of minimal Picard modular surfaces. The proof also counts cusps of other Picard modular surfaces of arithmetic interest. Consequently, for each N > 0 there are finitely many commensurability classes of nonuniform arithmetic lattices in SU(2, 1) that contain an N-cusped surface. We also …
ERDMD discovers sparse, nonuniformly timed DMD models from chaotic attractors.
problem Discovering high-fidelity, nonuniformly timed DMD models from chaotic data.
method Entropic regression for nonlinear information flow detection, combined with multi-step DMD.
result ERDMD produces highly efficient and robust models with minimal complexity.
We prove Zimmer's conjecture for C2 actions by finite-index subgroups of SL(m,Z) provided m>3. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in SL(m,R) but new ideas are needed to overcome the lack of compactn…
Framework for designing nonlinearities in neural networks with slope constraints.
problem Designing nonlinearities with specific properties for signal processing.
method Variational framework with regularization for slope constraints and optimization of adaptive splines.
result Adaptive nonuniform linear splines achieve global optimum in constrained optimization.
T-Rex uses EM to fit robust factor models in noisy data.
problem Robustly fitting factor models in high-dimensional data with heavy tails and outliers.
method Expectation-Maximization (EM) algorithm based on Tyler's M-estimator for elliptical distributions.
result Demonstrates robustness in direction-of-arrival estimation and subspace recovery.
This paper optimizes subsampling for large datasets using Poisson distribution.
problem Efficiently subsample large datasets for quasi-likelihood estimation.
method Derives optimal Poisson subsampling probabilities and develops a distributed subsampling framework.
result Consistent and asymptotically normal estimators are obtained.
High-order financial derivative pricing method using Radial Basis Functions.
problem Pricing financial derivatives with high accuracy and efficiency.
method Radial Basis Function generated Finite Differences for non-uniform node layouts.
result Fourth-order convergence in space with non-uniform node layouts.
Study approximates probability measures using structured classes of functions.
problem Approximating probability measures in Wasserstein-p distance. method Structured classes of approximators for functions in Lp(Ω), transferring to measures in Wp(Ω). result Linear rate approximation for measures with densities bounded away from zero.
Improved estimation for imbalanced data using log odds correction and optimal sampling.
problem Parameter estimation with nonuniform negative sampling for imbalanced data.
method Derive asymptotic distribution of IPW estimator, derive optimal sampling probability, propose likelihood-based estimator.
result Improved estimator has the smallest asymptotic variance.
Let Γ be a lattice in a connected semisimple Lie group G with trivial center and no compact factors. We introduce a volume invariant for representations of Γ into G, which generalizes the volume invariant for representations of uniform lattices introduced by Goldman. Then, we show that the maximality of this vo…
We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are given. In particular we show that there are compact complex surfaces which admit Riem…
Survey on quantization methods on Kähler manifolds.
problem None explicitly stated; focuses on methods.
method Deformation quantization, geometric quantization, Berezin-Toeplitz quantization, BV quantization.
result New relationships among quantization methods on Kähler manifolds.
If Γ is any nonuniform lattice in the group PU(2,1), let Γ be the quotient of Γ obtained by filling the cusps of Γ (i.e. killing the center of parabolic subgroups). Assuming that such a lattice Γ has positive first Betti number, we prove that for any sufficiently deep subgroup of finite index…
This paper proposes BAT to balance accuracy and robustness in adversarial training.
problem Balancing accuracy and robustness in adversarial training models.
method Blind adversarial training (BAT) uses a cutoff-scale strategy to adaptively estimate a nonuniform budget for AEs.
result BAT improves the overall robustness of adversarial training models.
The paper classifies quantizable functions and explores symmetry in quantization methods.
problem Classifying quantizable functions and understanding symmetry in quantization methods.
method Deformation quantization and geometric quantization methods are compared and classified.
result Formal quantizable functions are of a specific form and relate to Hamiltonian Killing vector fields.
Hierarchical GANs reduce anomaly detection costs.
problem Balancing anomaly detection accuracy and sampling costs.
method Hierarchical GANs for nonuniform sampling and buffer zones.
result Proposed GAN-based detector outperforms baseline in detection delay and average cost of error.
This paper introduces a differentiable, scalable quantization method for neural networks.
problem Previous quantization methods lacked differentiability and scalability.
method The approach is differentiable and scalable, using bit-shifting and logarithmic quantization.
result The method achieves comparable accuracy to state-of-the-art approaches with less training time and lower inference cost.
StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.
problem Optimal quantization parameters selection for deep neural networks with diverse data distributions.
method Statistical error analysis framework for uniform and floating-point quantization, iterative and analytic quantizers designed for arbitrary and Gaussian-like distributions.
result Improved accuracy and stability in training low-precision neural networks.
Smart Quantization adapts binary and ternary quantization for neural networks.
problem Resource constraints in deploying neural networks on devices with limited resources.
method Adaptive combination of binary and ternary quantization with a regularization function.
result Adapts quantization depth during training to maintain high model accuracy.
This study optimizes quantized neural networks by considering model architecture and quantization types.
problem Optimizing quantized neural networks for low-power, high-throughput applications.
method Holistic approach including training methods and quantization-friendly architecture design.
result Deeper models are more sensitive to activation quantization, while wider models improve resilience to both weight and activation quantization.
RATQ is a new quantizer for optimizing noisy gradients in machine learning.
problem Optimizing noisy gradients in stochastic optimization.
method RATQ uses Hadamard transform and adaptive uniform quantization, and achieves near-optimal performance.
result RATQ nearly achieves information theoretic lower bounds for optimization accuracy.
Extends ONNX for quantized neural networks with new formats and operators.
problem Handling arbitrary-precision quantization in neural networks.
method Introduces new formats and operators in ONNX to represent quantized neural networks.
result Enabled representation of uniform quantization in neural networks.
Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using 'simultaneous shots', or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates d…
New method for quantizing symplectic manifolds with Lagrangian bundles.
problem Quantization of symplectic manifolds with Lagrangian bundles.
method A new construction of strict deformation quantization.
result Established a correspondence between differential operators and principal symbols.
HMQ improves quantization for edge devices with mixed precision.
problem Efficient quantization for edge devices with uniform, power-of-two thresholds.
method Introduces HMQ, a mixed precision quantization block that repurposes Gumbel-Softmax for searching over quantization schemes.
result Achieves competitive and state-of-the-art results on ImageNet despite restrictions.
Introduces sheaf quantization, a topological approach to geometric quantization.
problem Topological realization of WKB-states in geometric quantization.
method Enhancement of constructible sheaves, Betti counterpart of Fukaya--Floer theory.
result Introduction to sheaf quantization as a topological realization of WKB-states.