Gradient descent recovers principal components of overparametrized asymmetric matrices without explicit regularization.
problem Asymmetric matrix factorization under overparametrization with minimal rank assumptions.
method Vanilla gradient descent with small random initialization and proper early stopping.
result Gradient descent produces the best low-rank approximation without explicit regularization.
Paper analyzes asymmetry in LoRA initialization for foundation models.
problem Asymmetry in LoRA initialization affects generalization of foundation models.
method Theoretical analysis of asymmetric LoRA with frozen random factors.
result Upper bound on sample complexity of $ ilde{\mathcal{O}}\left(\frac{\sqrt{r}}{\sqrt{N}}
ight)$ with high probability.
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a learning algorithm for quasi-metrics based on sample compression and nearest neighbor…
Gradient descent solves asymmetric low-rank matrix factorization efficiently.
problem Optimizing asymmetric low-rank matrix factorization with non-convex and non-smoothness issues.
method Randomly initialized gradient descent with new symmetrization and perturbation techniques.
result Gradient descent converges to a global minimum of the asymmetric low-rank factorization problem.
Gradient descent solves asymmetric low-rank matrix sensing without balancing.
problem Recovering asymmetric low-rank matrices from linear measurements.
method Gradient descent with spectral initialization, avoiding balancing term.
result Gradient descent converges linearly without balancing, factors stay balanced.
Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…
The paper analyzes how over-parameterization affects GD convergence in matrix sensing problems.
problem Matrix sensing problem with over-parameterized gradient descent.
method Analyzes symmetric and asymmetric parameterizations, provides lower bounds and convergence rates.
result Over-parameterization slows down GD convergence, but asymmetric parameterization can speed up convergence.
Gradient descent converges globally in deep linear residual networks with ZAS initialization.
problem Optimizing deep linear residual networks for convergence.
method Zero-asymmetric (ZAS) initialization for gradient descent.
result Gradient descent converges to an ε-optimal point in O(L^3 log(1/ε)) iterations.
Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.
problem Reconstructing asymmetric low-rank matrices from linear measurements.
method Factorized gradient descent with coupling and regularization properties.
result Gradient descent from small random initialization converges to globally optimal and generalizing solutions.
The dying ReLU refers to the problem when ReLU neurons become inactive and only output 0 for any input. There are many empirical and heuristic explanations of why ReLU neurons die. However, little is known about its theoretical analysis. In this paper, we rigorously prove that a deep ReLU network will eventually die in…
We consider an American contingent claim on a financial market where the buyer has additional information. Both agents (seller and buyer) observe the same prices, while the information available to them may differ due to some extra exogenous knowledge the buyer has. The buyer's information flow is modeled by an initial…
The aim of this paper is to relate Thurston's metric on Teichmüller space to several ideas initiated by T. Sorvali on isomorphisms between Fuchsian groups. In particular, this will give a new formula for Thurston's asymmetric metric for surfaces with punctures. We also update some results of Sorvali on boundary isomorp…
We study surfaces evolving by mean curvature flow (MCF). For an open set of initial data that are C3-close to round, but without assuming rotational symmetry or positive mean curvature, we show that MCF solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singul…
This paper tackles learning Stackelberg equilibrium in asymmetric games efficiently from noisy samples.
problem Learning Stackelberg equilibrium in asymmetric, general-sum games efficiently from noisy samples.
method The paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium in bandit feedback setting.
result Sharp positive results on sample-efficient learning of Stackelberg equilibrium with value optimal up to a fundamental gap identified.
Study of geometric analysis on asymmetric metric spaces, including heat flow and Sobolev spaces.
problem Analysis of geometric properties on asymmetric metric measure spaces.
method Introduction of upper gradients, q-Laplacian, and q-heat flow in asymmetric settings. result Extension of concepts from symmetric to asymmetric metric measure spaces.
Study dynamic equilibrium with insider and general uninformed agent preferences.
problem Analyzing asymmetric information and general utility functions in a continuous-time economy.
method Introducing a new method to prove existence of a partial communication equilibrium (PCE) for agents with general utility functions.
result Identify the equilibrium price in the small and large risk aversion limits for agents with power utility.
A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.
problem Inadequate handling of asymmetric error distributions in adaptive filtering.
method Proposes asymmetric correntropy using an asymmetric Gaussian kernel and develops a robust adaptive filtering algorithm.
result The proposed algorithm shows better steady-state convergence performance for asymmetric error distributions.
New metrics for Anosov representations defined from Thurston's asymmetric metrics.
problem Defining metrics for Anosov representations.
method Generalizing Thurston's asymmetric metric to Anosov representations.
result Provides a (possibly asymmetric) Finsler distance in some cases.
Generalizes Thurston's asymmetric metric to flat metrics.
problem Defining an asymmetric metric on flat metrics.
method Defined an asymmetric metric on the space of unit-area flat metrics.
result Discussed two different topologies from the asymmetry.
This study examines asymmetric cross-correlations in cryptocurrency markets using fractal analysis.
problem Exploring asymmetric multifractal cross-correlations in cryptocurrency markets.
method Fractal analysis and MF-ADCCA method to investigate asymmetric volatility dynamics.
result Cross-correlations are stronger in downtrend markets than in uptrend markets for maturing BTC and ETH.
Theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
problem Lack of precise theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
method Adapting a finite-time convergence analysis to the asymmetric actor-critic setting with linear function approximators.
result A finite-time bound reveals that the asymmetric critic eliminates aliasing errors in the agent state.
This work presents deep asymmetric networks with a set of node-wise variant activation functions. The nodes' sensitivities are affected by activation function selections such that the nodes with smaller indices become increasingly more sensitive. As a result, features learned by the nodes are sorted by the node indices…
We consider the problem of designing locality sensitive hashes (LSH) for inner product similarity, and of the power of asymmetric hashes in this context. Shrivastava and Li argue that there is no symmetric LSH for the problem and propose an asymmetric LSH based on different mappings for query and database points. Howev…
New asymmetric kernel methods improve feature learning.
problem Improving feature learning with asymmetric kernels.
method Coupled covariance eigenproblem and Nyström method.
result Empirical evaluations show benefits of KSVD.
The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.
problem Understanding quasi-alternating surgeries on asymmetric L-space knots.
method Using the Montesinos trick to confirm known surgeries.
result Confirmation of two quasi-alternating surgeries for each of 9 asymmetric L-space knots.
The paper improves asymmetric causality tests by addressing inefficiencies and statistical significance issues.
problem Inefficiencies and statistical significance issues in asymmetric causality tests.
method Improved asymmetric causality tests via partial cumulative sums for positive and negative components, explicitly testing differences between causal parameters.
result Efficiently tested hypotheses on asymmetric causal interaction between financial markets.
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
We propose Deep Asymmetric Multitask Feature Learning (Deep-AMTFL) which can learn deep representations shared across multiple tasks while effectively preventing negative transfer that may happen in the feature sharing process. Specifically, we introduce an asymmetric autoencoder term that allows reliable predictors fo…
In this paper we show how the study of asymmetric R&D alliances, that are those between young and small firms and large and MNEs firms for knowledge exploration and/or exploitation, requires the adoption of a coopetitive framework which consider both collaboration and competition. We draw upon the literature on asymmet…
Randomly initialized transformers show extreme token preferences.
problem Structural biases in randomly initialized transformers.
method Dissection of transformer architecture at initialization.
result Initialization-induced biases persist throughout training.
Bayesian VI copula models capture asymmetric intraday equity dependence.
problem Modeling asymmetric and extreme tail dependence in financial data.
method Bayesian variational inference for skew-t copula models in high dimensions.
result The copula captures substantial heterogeneity in asymmetric dependence over equity pairs and time.
Gradient descent training of neural networks leads to solutions close to natural cubic splines.
problem Understanding the implicit bias of gradient descent in neural networks.
method Analysis of gradient descent training for wide neural networks, focusing on the curvature penalty and initialization schemes.
result The solutions of gradient descent training are polyharmonic splines for certain initialization schemes.
This work describes compactifications of metric spaces and vector spaces using asymmetric norms.
problem Compactifying metric spaces and vector spaces using asymmetric norms.
method Nonstandard methods, ultrapowers of the spaces at hand.
result Polyhedral compactifications of vector spaces with stratified structure.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.
Extends metric to Margulis spacetimes for convex properties.
problem No specific problem stated; extends metric.
method Extends Thurston's asymmetric metric to Margulis spacetimes and proves convex properties.
result Established convex properties of the extended metric.
In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-1 update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence g…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to create generalized asymmetric versions of the Laplace and normal distributions, whic…
Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically resolved by the rectified linear unit (ReLU) activation. However, here we show th…
Enhances reinforcement learning with partial state information.
problem Improving learning under partial observability with limited privileged signals.
method Introduced informed asymmetric actor-critic framework that uses arbitrary state-dependent privileged signals.
result Unbiased policy gradient estimates with arbitrary privileged signals.
New methods train neural networks without changing weights, achieving similar or higher performance.
problem Training neural networks efficiently with randomly initialized weights.
method Switching connections on and off, flipping weights' signs, minimizing changed connections.
result Achieves similar or higher performance with less computational cost than training all weights.
This paper studies gradient flows in asymmetric metric spaces and proves existence results.
problem Investigating gradient flows in asymmetric metric spaces.
method Discrete approximation and natural convexity assumption on potential function.
result Existence of curves of maximal slope in asymmetric metric spaces.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
Proposes a new OAL algorithm for imbalanced data with limited labels.
problem Handling imbalanced unlabeled datastream with limited query budget.
method Integrates asymmetric losses and queries strategies, uses second-order optimization, and applies sketching technique.
result Demonstrates improved performance and efficiency in class imbalance.
Maps and measures on surfaces link best Lipschitz and least gradient functions.
problem Analyzing maps between surfaces and their geometric properties.
method Duality between best Lipschitz and least gradient maps, geodesic laminations, and transverse measures.
result The infinity harmonic map defines a geodesic lamination and the least gradient map defines a transverse measure.
Study uncovers new phase transitions in asymmetric causal inference scenarios.
problem Understanding typical phase transitions in asymmetric causal inference.
method Combining Causal inference (C-inf) and Low-rank recovery (LRR) with Random duality - Free probability theory (RDT-FPT).
result Discovering a doubling low-rankness phenomenon in asymmetric scenarios.
Modified asymmetric hidden Markov models for time series with autoregressive components.
problem Dynamic relationships between variables in time series data.
method Introducing an asymmetric autoregressive component to recent asymmetric hidden Markov models.
result The model can choose the optimal autoregressive order for better likelihood.
Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related non-contaminated mixture, for each (asymmetric) cluster, our model has one param…
In this paper, we propose a novel asymmetric ε-insensitive pinball loss function for quantile estimation. There exists some pinball loss functions which attempt to incorporate the ε-insensitive zone approach in it but, they fail to extend the ε-insensitive approach for quantile estimation in true sense. The propo…