Griffiths extremal metrics solve complex Finsler equations and quantify Kähler geometry.
problem Interpolation of norms and complex Finsler geometry.
method Introduced Griffiths extremal Finsler metrics and solved their Dirichlet problem.
result Griffiths extremal Finsler metrics quantize solutions to a PDE in Kähler geometry.
Study quantized extremal Kähler metrics for algebro-geometric stability.
problem Stability of extremal Kähler metrics and manifolds.
method Quantized extremal Kähler metrics and equivariant Riemann-Roch theorem.
result Proves weak relative Chow polystability and K-semistability.
We extend quantization-aware training to extreme model compression.
problem Maximizing model accuracy with minimal model size.
method Quantize a random subset of weights during training, allowing unbiased gradients through other weights.
result Established new state-of-the-art compromises between accuracy and model size.
A new quantization strategy reduces Transformer model size and inference time.
problem Heavy computation load and memory overhead in Transformer models for mobile devices.
method Mixed precision quantization with varying bits per word in embedding blocks.
result 11.8x smaller model size and 3.5x speed up for on-device NMT.
Improved EXACT strategy reduces GNN memory consumption and runtime.
problem Efficiently training large-scale GNNs with reduced memory usage.
method Block-wise quantization of intermediate activation maps with improved variance minimization.
result Further reduction in memory consumption (>15%) and runtime speedup (5%) with similar performance trade-offs.
BiTAT improves neural network quantization for edge devices by focusing on weight dependencies and disentangling them.
problem Performance degradation of compact neural networks under extreme quantization.
method Task-dependent Aggregated Transformation (BiTAT) method that orthonormalizes weights and progressively quantizes them.
result BiTAT effectively preserves model performance on ImageNet and CIFAR-100 with compact backbones.
In [5], P. Lecomte conjectured the existence of a natural and conformally invariant quantization. In [7], we gave a proof of this theorem thanks to the theory of Cartan connections. In this paper, we give an explicit formula for the natural and conformally invariant quantization of trace-free symbols thanks to the meth…
Enhances LLM quantization with MDBF, improving perplexity and accuracy.
problem Limited performance of Double Binary Factorization in extreme quantization.
method Introduces Multi-envelope DBF, retaining sign matrices and replacing single envelope with rank-l envelope. result Improves perplexity and zero-shot accuracy over previous binary formats.
Two novel network quantization approaches improve deep neural network compression.
problem Efficiently compress deep neural networks for practical usage.
method Single-level network quantization (SLQ) and Multi-level network quantization (MLQ).
result Both SLQ and MLQ achieve impressive results in compressing state-of-the-art neural networks.
The Simanca metric on a blown-up plane has regular quantization properties.
problem Characterizing the quantization properties of the Simanca metric.
method Using the blow-up structure and Tian-Yau-Zelditch expansion, proving regular quantization and vanishing coefficients.
result All coefficients in the Tian-Yau-Zelditch expansion for the Simanca metric vanish, and a dense subset admits Berezin quantization.
New method trains quantized neural networks to global optimality.
problem Training optimal quantized neural networks is intractable due to combinatorial non-convex optimization.
method Convex optimization strategy using hidden convexity, semidefinite lifting, and Grothendieck's identity.
result Quantized NN problems can be solved to global optimality in polynomial-time.
Efficient hybrid networks improve AI performance at the edge.
problem Achieving AI performance at the edge with minimal energy and memory usage.
method Proposed hybrid networks combining binary and full-precision layers.
result Hybrid networks achieve close to full-precision performance with up to 21.8x memory compression.
Quantizes symplectic fibrations to analyze vector bundles and metrics.
problem Quantizing higher rank vector bundles and understanding their metrics.
method Relates Berezin-Toeplitz quantization to hybrid systems and symplectic fibrations.
result Established refined estimates for computing balanced metrics on Kähler manifolds.
Proposes QEP to mitigate quantization error propagation in layer-wise post-training quantization.
problem Growth of quantization errors across layers degrades performance, especially in low-bit regimes.
method Quantization Error Propagation (QEP) framework that explicitly propagates and compensates for quantization errors.
result QEP-enhanced layer-wise PTQ achieves substantially higher accuracy, especially in low-bit regimes.
This paper quantizes CapsNets for efficient edge deployment.
problem CapsNets require intense computations and are not suitable for resource-constrained edge devices.
method Developed a specialized quantization framework for CapsNets.
result Reduced memory footprint by 6.2x with only 0.15% accuracy loss.
Smooth approximations of Kähler-Ricci solitons found using quantized metrics and Futaki invariants.
problem Finding smooth approximations of Kähler-Ricci solitons on Fano manifolds.
method Using semiclassical estimates and quantized Futaki invariants to extend a strategy from Donaldson and Tian-Zhu.
result Smooth approximations of Kähler-Ricci solitons can be found as quantized metrics.
Quantized neural networks reduce model size and energy consumption.
problem Memory and energy constraints in mobile devices.
method Using integer or binary representations to store weights instead of 32-bit floats.
result Quantization can reduce model size and energy consumption without significantly compromising performance.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
This work improves DNN weight quantization with ADMM, achieving lossless binarization and reduced search space.
problem Improving DNN model compression and accuracy with low bit quantization.
method Extending ADMM framework for DNN weight quantization with progressive multi-step approach.
result Achieved lossless and fully binarized DNNs with reduced accuracy loss.
LSQ+ improves quantization of neural nets with Swish activations, achieving state-of-the-art results.
problem Quantization of neural nets with Swish activations, especially negative activations, leads to significant performance loss.
method Introduces learnable scale and offset parameters for asymmetric quantization, and uses MSE-based initialization for quantization parameters.
result Significantly outperforms LSQ for low-bit quantization of neural nets with Swish activations, achieving up to 5.6% gain with W2A2 quantization of EfficientNet-B0.
Quantizes Kähler metrics using Finsler structures.
problem Approximating Kähler metrics by algebraic metrics.
method Quantization of Finsler structures on Kähler potentials.
result Metric completions of Finsler structures on Kähler potentials are recovered.
New approach to geometric quantization for symplectic manifolds.
problem Quantization of symplectic manifolds with non-singular Lagrangian fibrations.
method Using spectral convergence of metric measure spaces, the authors develop a new geometric quantization approach.
result Spectral and quantum Hilbert space convergence results for Kähler and almost Kähler quantizations.
Study proves convergence of quantized geodesics to Mabuchi geodesics.
problem Convergence of quantized geodesics to Mabuchi geodesics in short time.
method Real-analytic initial data and convergence proof.
result Proves convergence of quantized Bergman geodesics to Mabuchi geodesics.
Paper discusses star products and Kähler metrics, linking deformation quantization and constant curvature metrics.
problem Existence of Kähler metrics with constant scalar curvature.
method Analyzes Fedosov and Berezin-Toeplitz star products, and studies K-stability conditions.
result Formulates a cohomology formula for K-stability conditions on Kähler metrics.
Study quantization of Kähler-Einstein metrics using balanced metrics.
problem Approximating Kähler-Einstein metrics by balanced metrics.
method Use canonical Bergman metrics and introduce algebro-geometric obstructions.
result Existence and weak convergence of balanced metrics for CKE manifolds.
Blowups of Kähler manifolds can inherit extremal metrics.
problem Extending extremal metrics to blowups of Kähler manifolds.
method Analyzing the action of a torus on blowups and weighted extremal metrics.
result Blowups of Kähler manifolds can inherit weighted extremal metrics.
Extremal metrics linked to stability in complex geometry.
problem Existence and uniqueness of extremal metrics in complex geometry.
method Proving asymptotic relative Chow stability implies extremal metrics existence and uniqueness.
result Existence and uniqueness of extremal metrics in any polarization.
New interpretation of metrics on special geometric manifolds.
problem Finding metrics on extremal Kähler manifolds.
method Moment map interpretation of relatively balanced metrics.
result Extremal metrics are limits of specific relatively balanced metrics.
Sharp estimates for Bergman metrics derived from Kähler quantization.
problem Estimating Bergman metrics in Kähler quantization.
method Upper and lower bounds on the Bergman metric expressed in terms of φ. result Optimal C1,1ˉ-convergence for quantization of Kähler currents. In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kahler 2-form. We compare the geometric quantization framework wit…
Extremal metrics found on specific manifold operations.
problem Conditions for extremal metrics on blowups.
method Analyzes blowups of extremal Kähler manifolds.
result Extremal metrics exist on blowups of higher codimension.
New extremal metrics found on Kähler manifolds.
problem Constructing extremal metrics on Kähler manifolds.
method Test configurations for strictly semistable Kähler manifolds.
result Infinitely many new examples of manifolds with extremal Kähler metrics.
Paper explores new Kähler metrics from old, aiming to solve YTD conjecture.
problem Extending classical extremal Kähler metrics to include new objects.
method Surveying recent works on weighted extremal Kähler metrics and the YTD conjecture.
result Survey of recent research on weighted extremal Kähler metrics.
BCGD algorithm improves training of quantized neural networks.
problem Training quantized deep neural networks at low bit-widths.
method Introduces coarse gradient descent and blended correction for training.
result BCGD achieves high accuracy in quantized neural networks.
Extremal metrics exist if uniformly K-stable over models.
problem Existence of extremal metrics on complex projective varieties.
method Uniform K-stability over models of extremal tori. result Extremal metrics exist if uniformly K-stable. The study finds no extremal metrics for eigenvalues on compact manifolds but constructs examples for annuli.
problem Finding extremal metrics for eigenvalues on compact manifolds.
method Construction of conformally extremal metrics in annuli and analysis of non-existence.
result Construction of conformally extremal metrics in annuli and characterization of these metrics.
We determine the matrix of the balanced metric of the Siegel-Jacobi ball and its inverse. We calculate the scalar curvature, the Ricci form and the Laplace-Beltrami operator of this manifold. We discuss several geometric aspects related with Berezin quantization on the Siegel-Jacobi ball.
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in this context. We show that balanced metrics converge at the quantum limit toward…
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
problem Existence of extremal Kähler metrics on Fano manifolds.
method Introducing σ-extremal Kähler metrics and relating them to multiplier Hermitian-Einstein metrics. result Existence of σ-extremal Kähler metrics implies existence of multiplier Hermitian-Einstein metrics on Fano manifolds. The paper classifies rotationally symmetric extremal Kähler metrics on complex manifolds.
problem Classifying extremal Kähler metrics on complex manifolds.
method Analyzing polynomial zeros in Calabi's extremal equation.
result No U(n) invariant complete extremal Kähler metrics on Cn with positive bisectional curvature. Uniqueness of weighted extremal metrics on Kähler manifolds proven.
problem Uniqueness of weighted extremal Kähler metrics on compact Kähler manifolds.
method Proof of uniqueness using modified Mabuchi energy and weighted K-semistability.
result Uniqueness of weighted extremal Kähler metrics up to automorphisms.
The paper improves quantization error estimates on Riemannian manifolds.
problem Improving quantization error estimates on Riemannian manifolds.
method Using covering growth estimates of spheres instead of curvature bounds.
result Provides a more general integral condition for quantization error.
Quantizes contact structures using dynamical methods.
problem Quantizing contact structures in a flat connection.
method Constructs a dynamical quantization using a flat connection on a Hilbert tractor bundle.
result Determines a contact tractor connection whose parallel sections determine a distinguished choice of Reeb dynamics.
The paper improves asymptotic polybalanced kernels for extremal Kaehler metrics.
problem Stability and metrics on algebraic manifolds.
method Asymptotic polybalanced kernels associated to extremal Kaehler metrics.
result Stronger asymptotic relative Chow-polystability for extremal Kaehler polarized algebraic manifolds.
DFRot improves LLMs by reducing outlier and massive activation effects.
problem Reducing outlier and massive activation effects in rotated LLMs.
method Weighted loss function and orthogonal Procrustes transforms for rotation matrix refinement.
result DFRot achieves dual free (Outlier-Free and Massive Activation-Free) with significant improvements in perplexity.
The paper explores clustering methods using Bregman divergences.
problem Developing efficient clustering algorithms for complex data.
method Investigates fixed rate quantization and Voronoi diagrams in Riemannian metric spaces induced by separable Bregman divergences.
result Experimental results show improved performance of clustering algorithms using these metrics.
We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal Kähler manifold, an extremal metric attains the minimum of the modified K-energy. The proof uses an idea of C.Li adapted to the extremal metrics using some weighted balanced metrics.
Paper extends Calabi's extremal metric existence to compact Kähler manifolds.
problem Existence of Calabi's extremal metric on compact Kähler manifolds.
method Adapting recent breakthroughs on constant scalar Kähler metrics to extremal case, proving properness of modified Mabuchi energy.
result Existence of extremal metric with extremal vector V if and only if modified Mabuchi energy is proper.