arXiv research

New approach connects stochastic gradient descent to ODE splitting schemes.

The paper proves conditions for Einstein solitons to split into line and manifold.

Study shows splitting schemes can approximate WFR flows faster than the exact flow.

We discuss some geometric conditions under which a complete noncompact shrinking gradient Ricci soliton will split at infinity.

TSSM splits neural networks for parallel training with minimal accuracy loss.

We develop a progressive training approach for neural networks which adaptively grows the network structure by splitting existing neurons to multiple off-springs. By leveraging a functional steepest descent idea, we derive a simple criterion for deciding the best subset of neurons to split and a splitting gradient for …

New minibatching strategy reduces stochastic gradient bias in optimisation.

Backpropagation-free trunk training improves model performance on various benchmarks.

LoBoost improves local conformal prediction for gradient-boosted trees without extra data splits.

Gradient bounds and Liouville theorems for quasi-linear equations on manifolds with nonnegative Ricci curvature.

The works of Donaldson and Mark make the structure of the Seiberg-Witten invariant of 3-manifolds clear. It corresponds to certain torsion type invariants counting flow lines and closed orbits of a gradient flow of a circle-valued Morse map on a 3-manifold. We study these invariants using the Morse-Novikov theory and H…

Temporal difference learning explained through gradient splitting, improving convergence times.

The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.

We investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger-Gromoll-Lichnerowicz splitting theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can pe…

We show that if a closed hyperbolic 3-manifold has infinitely many finite covers of bounded Heegaard genus, then it is virtually fibered. This generalizes a theorem of Lackenby, removing restrictions needed about the regularity of the covers. Furthermore, we can replace the assumption that the covers have bounded Heega…

We prove a splitting theorem for complete gradient Ricci soliton with nonnegative curvature and establish a rigidity theorem for codimension one complete shrinking gradient Ricci soliton in $\mathbb R^{n+1}$ with nonnegative Ricci curvature.

New theorem splits weighted Lorentz-Finsler manifolds into simpler parts.

Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are governed by differential inclusions. In particular, we present an iterative reg…

The study examines gradient Ricci solitons with nonnegative curvature, proving properties of their blow-downs.

We prove a sharp integral gradient estimate for harmonic functions on noncompact Kähler manifolds. As application, we obtain a sharp estimate for the bottom of spectrum of the p-Laplacian and prove a splitting theorem for manifolds achieving this estimate.

agtboost speeds up gradient tree boosting with automatic complexity adjustment.

New method uses symmetric splitting for efficient HMC inference in large neural networks.

New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can get twisted, warped or direct decompositions. Some applications to Lorentzian man…

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $N$ subproblems, and utilizes an augmented Lagrangian b…

A new transformer model accelerates training with optimization techniques.

New algorithms solve monotone inclusions and convex-concave minimax problems.

The paper investigates conditions for compactness of submanifolds in Kahler manifolds.

In this paper we obtain a splitting theorem for the symmetric diffusion operator $Δ_φ=Δ-\left<\nablaφ,\nabla \right>$ and a non-constant $C^3$ function $f$ in a complete Riemannian manifold $M$, under the assumptions that the Ricci curvature associated with $Δ_φ$ satisfies ${\rm Ric}_φ(\nabla f,\nabla f)\ge 0$, that $|…

We characterize complete nonnegatively curved steady gradient soliton with curvature in L^1. We show that there are isometric to a product (R^2,g_{cigar}) times(R^{n-2}, eucl))/Gamma where Gamma is a Bieberbach group of rank n-2. We prove also a similar local splitting result under weaker curvature assumptions.

Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as spin glasses. Proximal algorithms form a class of methods that are broadly applica…

New algorithms split deep learning tasks into representation and uncertainty estimation.

CSE-FSL reduces communication and storage costs in federated learning.

Combining Bayesian deep learning and split conformal prediction affects out-of-distribution coverage.

Innovative method solves nonconvex optimization on manifolds.

Designing energy-efficient networks is of critical importance for enabling state-of-the-art deep learning in mobile and edge settings where the computation and energy budgets are highly limited. Recently, Liu et al. (2019) framed the search of efficient neural architectures into a continuous splitting process: it itera…

Paper proves properties of minimal hypersurfaces in specific solitons.

A novel gradient-based method optimizes decision trees for complex tasks.

Study minimal graphs on non-negative Ricci curvature manifolds.

We generalize the splitting theorem of Cai-Galloway for complete Riemannian manifolds with $\Ric\geq-(n-1)$ admitting a family of compact hypersurfaces tending to infinity with mean curvatures tending to $n-1$ sufficiently fast to the setting of smooth metric measure spaces. This result complements and provides a new p…

Gradient Boosting Decision Tree (GBDT) are popular machine learning algorithms with implementations such as LightGBM and in popular machine learning toolkits like Scikit-Learn. Many implementations can only produce trees in an offline manner and in a greedy manner. We explore ways to convert existing GBDT implementatio…

SketchBoost accelerates GBDT for multioutput problems up to 40x.

New test improves tree ensemble pruning for better model performance.

The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated b…

The study generalizes curvature bounds for manifolds with boundary.

Method solves optimisation problems on non-Riemannian surfaces with bilateral curvature bounds.

LEARN-SAM improves RL from sub-optimal demonstrations by localizing expert policies and selectively using demonstrations.

This paper explores how train-validation splits help in NAS to prevent overfitting.

The folk questions in Lorentzian Geometry, which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime $(M,g)$ admits a smooth time function $τ$ whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth…