Proposes a new method for generating random parameters in neural networks.
problem Improving randomized learning of feedforward neural networks.
method Randomly selects slope angles, rotates activation functions, and distributes them across the input space.
result The method gives better results than the common approach, especially for complex target functions.
Study shows how steepest descent algorithms' geometric margin increases during training.
problem Understanding implicit bias in steepest descent algorithms for neural networks.
method Analysis of steepest descent algorithms with infinitesimal learning rates in homogeneous neural networks.
result Limit points of training trajectories correspond to KKT points of margin-maximization problems.
A new method for growing neural networks by splitting neurons, improving efficiency.
problem Optimizing neural network structures, especially for lightweight architectures.
method A progressive training approach using steepest descent to adaptively grow and split neurons.
result The method provides a computationally efficient way to optimize neural network structures.
This work studies the implicit bias of mini-batch SGD in classification.
problem Understanding the implicit bias of mini-batch SGD in multi-class classification.
method Characterizes how batch size, momentum, and variance reduction affect convergence and max-margin behavior under different norms.
result Momentum enables small-batch convergence to an approximate max-margin solution, while variance reduction recovers the exact full-batch bias.
Let S be a complete surface of constant curvature K = + 1 or -1, i.e. the sphere S^2 or the Lobachevskij plane L^2, and D a bounded convex subset of S. If S = S^2, assume also diameter (D) < pi/2. It is proved that the length of any steepest descent curve of a quasi-convex function in D is less than or equal to the per…
This letter proposes a sparse diffusion steepest-descent algorithm for one bit compressed sensing in wireless sensor networks. The approach exploits the diffusion strategy from distributed learning in the one bit compressed sensing framework. To estimate a common sparse vector cooperatively from only the sign of measur…
Study shows momentum-based optimizers like Muon and MomentumGD bias towards KKT points in smooth homogeneous models.
problem Understanding the implicit bias of momentum-based optimizers on smooth homogeneous models.
method Analysis of Muon, MomentumGD, Signum, and Adam optimizers under decaying learning rate schedules.
result Momentum-based optimizers approximate steepest descent trajectories and bias towards KKT points of margin maximization problems.
New method escapes local optima in neural architecture optimization.
problem Escaping local optima in neural architecture optimization.
method Signed neural splitting in steepest descent framework.
result Escapes local optima, leading to better performance.
New method accelerates steepest descent for convex optimization.
problem Achieving acceleration for general ℓp smooth functions. method Primal-dual iterate sequences with differing norms, implicitly determined interpolation parameter.
result Improves iteration complexity to O(d1−p2) for ℓp norm smooth problems. Improved greedy 2-coordinate updates for optimization problems with constraints.
problem Minimizing smooth functions subject to constraints.
method Exploiting a connection to steepest descent in the 1-norm, we give faster convergence rates and efficient computation.
result Greedy selection converges faster than random selection and can be computed in O(nlogn) time. A new deep model generates molecules by fragments, improving validity and uniqueness.
problem Generating valid and unique molecules using deep learning.
method Develops a language model for molecular fragments, using frequency-based masking.
result Significantly outperforms other language model-based competitors in molecule generation.
This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D scanning of the available fragments. The obtained representations are properly p…
We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding I:Rn→Ham(M) with respect to the fragmentation norm on the group Ham(M) of Hamiltonian diffeomorphisms of a symplectic manifold (M,ω). As an application, we provide an answer to Brandenbursk…
FluxLayer solves cross-chain liquidity fragmentation for better MEV capture.
problem Cross-chain fragmented liquidity and MEV optimization.
method Three-layer framework integrating settlement, intent, and leverage mechanisms.
result FluxLayer enhances cross-chain MEV by capturing more arbitrage opportunities.
Technological progress is leading to proliferation and diversification of trading venues, thus increasing the relevance of the long-standing question of market fragmentation versus consolidation. To address this issue quantitatively, we analyse systems of adaptive traders that choose where to trade based on their previ…
FIRE method improves model performance in federated learning by penalizing fragmentation-induced covariate shifts.
problem Performance degradation in federated learning due to data fragmentation and covariate shift.
method FIRE method accumulates fragmentation-induced covariate shift divergences via approximate Fisher information and uses it as a per-fragment loss penalty.
result FIRE outperforms importance weighting and federated learning benchmarks by up to 5.3% on shifted validation sets.
We prove that manifolds with complicated enough fundamental group admit measure-preserving homeomorphisms which have positive stable fragmentation norm with respect to balls of bounded measure.
Study proves fluid limits of fragmented limit-order markets.
problem Modeling fragmented limit-order markets with small and frequent orders.
method Proved convergence of discrete system to fluid limit characterized by coupled nonlinear ODEs.
result Fluid system converges to stationary equilibrium state over time.
GANs excel at learning high dimensional distributions, but they can update generator parameters in directions that do not correspond to the steepest descent direction of the objective. Prominent examples of problematic update directions include those used in both Goodfellow's original GAN and the WGAN-GP. To formally d…
SILVR generates new molecules fitting protein binding sites.
problem Generating novel small molecule compounds for drug design.
method Selective Iterative Latent Variable Refinement (SILVR) for diffusion-based molecule generation.
result SILVR can generate new molecules similar in shape to original fragments without protein knowledge.
Method approximates Riemannian barycenter on manifolds.
problem Computing the exact Riemannian barycenter is computationally expensive.
method Uses under- and over-approximations of Riemannian distance to compute an approximate barycenter.
result Approximation method is more efficient than exact methods and steepest descent.
Automated rock fragmentation assessment using deep learning and spatial statistics.
problem Assessing post-blast rock fragmentation in real-time.
method Fine-tuned YOLO12l-seg model for instance segmentation, followed by spatial statistics.
result Framework accurately assesses rock fragmentation patterns in real-time.
The paper shows how Hamiltonian diffeomorphisms and homeomorphisms can be broken down into smaller, manageable pieces.
problem Fragmenting Hamiltonian diffeomorphisms and homeomorphisms on surfaces.
method Develops a C0-fragmentation property for Hamiltonian diffeomorphisms and homeomorphisms on surfaces, proving it with a Lipschitz estimate. result Hamiltonian diffeomorphisms and homeomorphisms can be decomposed into smaller, compactly supported pieces with a Lipschitz estimate on the C0-norm. Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese rest…
Generating music medleys is about finding an optimal permutation of a given set of music clips. Toward this goal, we propose a self-supervised learning task, called the music puzzle game, to train neural network models to learn the sequential patterns in music. In essence, such a game requires machines to correctly sor…
New distribution simplifies covariance matrix inference.
problem Efficient inference for covariance matrices in large models.
method Incorporates Inverse G-Wishart distribution for variational message passing.
result Elegant and succinct expression of variational message passing fragments.
Fragment-based autoencoder improves molecule screening with little data.
problem Limited experimental data for molecular optimization.
method Fragment-based graphical autoencoding to generate structural fingerprints.
result Fragment-based autoencoding reduces prediction error in small data.
Fragmented exchanges arise due to speed advantages in high-activity regions.
problem Fragmentation of distributed securities exchanges due to speed advantages in high-activity regions.
method Economic model and Monte Carlo simulations of a decentralized exchange with two miner clusters.
result Speed advantage increases with infrastructure asymmetry between regions.
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection be…
Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.
problem Understanding the basin of attraction for the free boundary free elastic flow.
method Steepest descent gradient flow for elastic energy, numerical evidence.
result Straight lines have a basin of attraction at least to level 1.9615π.
Model shows how multiple markets can coexist or fragment based on trader behavior.
problem Understanding market competition and coexistence among multiple trading venues.
method Stylized model of traders making repeated decisions at three markets, analyzed numerically and analytically.
result Parameters like memory length and choice intensity determine whether markets coexist or fragment.
New model integrates community and link clustering for network data.
problem Lack of embedded prior information and community evolution description in MMSB.
method Fragmentation coagulation process for community and link clustering, with Gibbs sampling for inference.
result Model infers community structure and evolution, improving MMSB.
High-fee pools attract more liquidity but execute less volume; low-fee pools have more stable LPs.
problem Optimal liquidity supply and execution on decentralized exchanges with fixed gas costs.
method Analysis of Uniswap data to compare high- and low-fee pools.
result Fragmented liquidity leads to more LPs and competition, improving overall market efficiency.
The paper optimizes regret using covariance between costs and decisions.
problem Optimizing expected regret in decision-making problems.
method Developed derivative theory of covariance regret functional, derived Gâteaux derivative, and extended to constrained optimization.
result Gradient of covariance regret is the cost covariance matrix, with implications for portfolio optimization.
Microbial clades modeling is a challenging problem in biology based on microarray genome sequences, especially in new species gene isolates discovery and category. Marker family genome sequences play important roles in describing specific microbial clades within species, a framework of support vector machine (SVM) base…
Study replicates market model, finds replication hindered by missing details.
problem Replicating a market model with missing details and limited quantitative reporting.
method Increased simulation runs, bootstrap confidence intervals, and code analysis.
result Achieved relational equivalence for most metrics but rejected quantitative alignment.
Study identifies stable configurations of intertwined threads with repulsive interactions.
problem Stable configurations of entangled systems with repulsive interactions.
method Analysis of steepest descent flow of an energy functional.
result Existence and uniqueness of stable configuration of two layers drifting apart at t1/3 rate. SONIA optimizes machine learning problems with a novel algorithm.
problem Empirical risk minimization in machine learning.
method Symmetric Blockwise Truncated Optimization (SONIA) algorithm combining second-order and steepest descent steps.
result SONIA converges to stationary points in both convex and nonconvex cases.
In optimization, the negative gradient of a function denotes the direction of steepest descent. Furthermore, traveling in any direction orthogonal to the gradient maintains the value of the function. In this work, we show that these orthogonal directions that are ignored by gradient descent can be critical in equilibri…
Diffeomorphisms of surfaces have many unbounded quasi-morphisms.
problem Understanding the quasi-morphisms on surface diffeomorphism groups.
method Constructing a hyperbolic graph and using it to deduce properties of the groups.
result The group is not uniformly perfect and its fragmentation norm is unbounded.
The paper analyzes security issues in blockchain ecosystems with multiple SSPs and proposes two models for better stake management.
problem Security issues in blockchain ecosystems with multiple SSPs and stake fragmentation.
method Formalized the Multiple SSP Problem and analyzed two architectures: Model M and Model S through convex optimization and game-theoretic lens. result Model S achieves tighter security guarantees through single validator sets and aggregated slashing logic. Improved RL model for fragment-based molecule generation.
problem Generating molecules with high docking scores.
method Thorough reproduction, scrutiny, and improvement of the FREED model.
result The improved model produces molecules with superior docking scores.
Study uses outer metrics for PDE-constrained shape optimization over diffeomorphism group.
problem Optimizing shapes governed by PDEs over the diffeomorphism group.
method Outer metrics on diffeomorphism group, Riemannian steepest descent method.
result Riemannian approach outperforms other metrics in solving PDE-constrained shape optimization problems.
This paper extends quasimorphism results to nonorientable surfaces.
problem Understanding quasimorphisms on nonorientable surface diffeomorphism groups.
method Constructing infinitely many quasimorphisms on the identity component of nonorientable surface diffeomorphism groups.
result The space of nontrivial quasimorphisms on the identity component of the diffeomorphism group of a closed nonorientable surface is infinite-dimensional.
Paper introduces a method to predict molecule properties from diverse data sources.
problem Limited ability to accommodate scarce or fragmented training data.
method Adaptive Invariance using invariant risk minimization to generalize beyond heterogeneous data.
result Predictor outperforms state-of-the-art transfer learning methods by significant margin.
Paper improves RLS for sparse outlier detection in linear models.
problem Outliers contaminate linear regression models infrequently.
method Hierarchical-optimization recursive least squares with sparsity-inducing regularization.
result The method robustly estimates linear filters/systems with outliers.
Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealt…
DADC algorithm improves clustering for data with varying density.
problem Sparse cluster loss and cluster fragmentation in density peak clustering.
method Domain-adaptive density measurement, cluster center self-identification, and cluster self-ensemble.
result DADC achieves more reasonable clustering results on data with varying density.