Although various linear log-distance path loss models have been developed, advanced models are requiring to more accurately and flexibly represent the path loss for complex environments such as the urban area. This letter proposes an artificial neural network (ANN) based multi-dimensional regression framework for path …
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48 results for “Path Loss”
Geodesics connect model modes in neural network loss landscapes.
problem Connecting modes in neural network loss landscapes.
method Reframed mode connectivity in Information Geometry, hypothesized geodesics as mode-connecting paths, proposed algorithm to approximate geodesics.
result Geodesics achieve mode connectivity in neural networks.
In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a condition is satisfied, the optimization path of an iterative algorithm on the un…
Gradient descent implicitly follows regularization for general losses.
problem The implicit bias of gradient descent methods in machine learning.
method Empirical risk minimization over linear predictors with arbitrary convex, strictly decreasing losses.
result Gradient descent and regularization paths converge to the same direction for non-attained risks.
New algorithmic view of ℓ2 regularization using ODEs and path-following methods.
problem Optimizing convex loss functions with ℓ2 regularization.
method Established an equivalence between ℓ2-regularized solution paths and ODEs, proposing path-following algorithms based on homotopy methods and numerical ODE solvers.
result The solution path can be viewed as a hybrid of gradient descent and Newton method, providing novel schemes to choose grid points and reducing computational cost.
We consider the generic regularized optimization problem . Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for the LASSO--that is, if is squared error loss and is the norm of --the opti…
Deep nets trained with MSE loss exhibit Neural Collapse, collapsing features and classifiers to class means.
problem Understanding Neural Collapse in MSE-trained deep nets.
method Developed a new MSE loss decomposition and introduced the central path concept.
result Exact dynamics of Neural Collapse along the central path can be predicted.
A novel k-generation propagation model for cyber risk and its application to cyber insuranceq-fin.RM
This research develops a new model for cyber risk and insurance pricing.
problem Accurate calculation of aggregate losses in cyber insurance pricing.
method A path-based k-generation risk contagion model in a tree-shaped network structure.
result Explicit expressions for mean and variance of local loss on a single path.
Research uses CPS to estimate uncertainty in ML radio metric models.
problem Estimating uncertainty in machine learning models for radio metrics and path loss.
method Conformal Prediction (CP) in Conformal Predictive Systems (CPS) with diverse difficulty estimators.
result CPS models maintain high coverage and reliability across different cities.
Generative model for TPPs using signatures and distributional discrepancies.
problem Limitations of signature methods for TPPs and lack of global sequence-level loss in neural models.
method Introduce interarrival embedding to lift jump paths to continuous paths of bounded variation, enabling signature methods for discrete event sequences. Develop sigTPP, a signature-based generative model trained on path-level loss.
result sigTPP achieves the best average rank across multiple metrics and outperforms or is within a standard error of the strongest baseline in 64% of dataset-metric pairs.
Understanding and measuring model risk is important to financial practitioners. However, there lacks a non-parametric approach to model risk quantification in a dynamic setting and with path-dependent losses. We propose a complete theory generalizing the relative-entropic approach by Glasserman and Xu to the dynamic ca…
Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
problem Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
method Identifying entropic barriers arising from the interplay between curvature variations along low-loss paths and noise in optimization dynamics.
result Curvature-induced entropic forces bias noisy dynamics back toward the endpoints, explaining the confinement and connectivity of solutions.
Full-batch GD achieves generalization close to any stationary point with fewer assumptions.
problem Generalization and excess risk bounds for smooth losses, including non-Lipschitz and nonconvex cases.
method Path-dependent analysis of GD's generalization error, focusing on optimization error and stability.
result Generalization error is tightly bound in terms of optimization error and iteration count, bypassing common assumptions.
A surrogate loss function for optimization of score in binary classification with imbalanced datacs.LG
Study proposes a differentiable surrogate loss function for optimizing score in binary classification with imbalanced data.
problem Non-differentiability of score makes it unsuitable for optimization by gradient-based learning.
method Investigated relationship between score and loss functions, proposed a differentiable surrogate loss function.
result Gradient paths of the proposed surrogate loss function approximate the gradient paths of the score.
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of European options. The continuity properties of rough-paths allow us to generali…
Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima -- at least those discovered by gradient-based optimization -- turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with as few as two segm…
SGD with large learning rates can achieve better test accuracy than expected.
problem SGD with large learning rates often outperforms expected convergence bounds.
method Proved that SGD with small learning rates stays close to gradient flow path on modified loss.
result Explicitly adding an implicit regularizer to the loss improves test accuracy.
Linear time dynamic programming for the exact path of optimal models selected from a finite setcs.LG
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
Revisiting Landscape Analysis in Deep Neural Networks: Eliminating Decreasing Paths to Infinitycs.LG
Traditional landscape analysis of deep neural networks aims to show that no sub-optimal local minima exist in some appropriate sense. From this, one may be tempted to conclude that descent algorithms which escape saddle points will reach a good local minimum. However, basic optimization theory tell us that it is also p…
Study online learning in MDPs with aggregate bandit feedback, achieving low regret in both stochastic and adversarial settings.
problem Online learning in finite-horizon episodic MDPs with aggregate bandit feedback.
method Best-of-both-worlds (BOBW) algorithms using FTRL over occupancy measures, self-bounding techniques, and new loss estimators.
result First BOBW algorithms for episodic tabular MDPs with aggregate bandit feedback achieving regret in stochastic and regret in adversarial settings.
Novel approach embeds loss tunnels in neural networks, revealing insights into their structure.
problem Understanding the structure of neural network loss surfaces, especially low-loss tunnels.
method Directly embedding loss tunnels into the loss landscape of neural networks.
result Improved insights into the length and structure of loss tunnels, and better subspace inference in Bayesian neural networks.
Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…
We identify a class of over-parameterized deep neural networks with standard activation functions and cross-entropy loss which provably have no bad local valley, in the sense that from any point in parameter space there exists a continuous path on which the cross-entropy loss is non-increasing and gets arbitrarily clos…
Proposes using mode connectivity to improve adversarial robustness of neural networks.
problem Improving adversarial robustness of deep neural networks.
method Employing mode connectivity in loss landscapes to study adversarial robustness and propose methods for improvement.
result Path connection learned using limited bonafide data can effectively mitigate adversarial effects while maintaining original accuracy.
Diagonal linear networks converge to lasso regularization path during training.
problem Understanding the regularization behavior of diagonal linear networks.
method Analyzing the training trajectory of diagonal linear networks and comparing it to the lasso regularization path.
result The training trajectory of diagonal linear networks is closely related to the lasso regularization path.
PathBoost boosts graph-level predictions using path-based features.
problem Graph-level classification and regression challenges.
method Gradient tree boosting method for graph-level prediction.
result PathBoost outperforms graph neural networks and graph kernel approaches in many cases.
Proposes neuron alignment to optimize mode connectivity in neural networks.
problem Understanding and optimizing mode connectivity in deep neural networks.
method Introduces neuron alignment to approximate optimal weight permutations and improve mode connectivity.
result Neuron alignment significantly alleviates robust loss barriers and improves model robustness and accuracy.
New method generates realistic financial price paths with drawdowns.
problem Lack of realistic drawdown scenarios in financial simulations.
method Variational autoencoder with drawdown reconstruction loss and path signatures.
result Simulated paths closely match empirical drawdown data.
Extends PD-NJ-ODE to noisy observations and dependent observation times.
problem Predicting continuous-time stochastic processes with irregular and noisy observations.
method Extends PD-NJ-ODE to handle conditional independence and noisy observations.
result Theoretical guarantees and empirical examples for handling noisy observations and dependent observation times.
Predicts next actions in soccer possessions using path signatures.
problem Predicting next actions in soccer possessions with high accuracy.
method Leveraging path signatures to encode spatio-temporal structure of recent possessions, avoiding manual feature engineering.
result Our approach outperforms transformer-based benchmarks across various loss metrics and reduces computational cost.
Unified framework connects different neural network models.
problem Understanding the geometry of neural network loss landscapes.
method Unified framework capturing four symmetry classes.
result First discovery of low- and zero-barrier linear interpolation paths.
SGD generalization bounds derived from information theory.
problem Understanding generalization of SGD for non-convex functions.
method Combining information-theoretic bounds with perturbation analysis.
result Upper bounds on SGD's generalization error based on gradient variance and function smoothness.
New algorithms minimize dynamic regret in non-stationary online learning.
problem Universal dynamic regret minimization under exp-concave and smooth losses.
method Strongly Adaptive algorithms with a path variational based on second order differences of the comparator sequence.
result Achieve a dynamic regret of , optimal modulo dependencies.
New method adapts neural networks without losing prior knowledge.
problem Understanding and enabling flexible adaptation of neural networks.
method Differential geometry framework, functionally invariant paths (FIP).
result Achieves comparable state-of-the-art performance on continual learning and sparsification tasks.
We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei and Luo, 2018) is in fact not improvable for adaptive adversary. Despite this neg…
Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.
problem Minimizing loss and constraint violations in online convex optimization with smooth penalties.
method Projected gradient descent over a set around the current action.
result Both dynamic regret and constraint violation are bounded by the path-length.
A new method for stochastic optimal control improves accuracy over existing techniques.
problem Improving the accuracy of stochastic optimal control for noisy systems.
method Stochastic Optimal Control Matching (SOCM) using Iterative Diffusion Optimization (IDO) with path-wise reparameterization trick.
result SOCM achieves lower error than existing techniques for three out of four control problems, sometimes by an order of magnitude.
Study finds non-IID data causes FL performance issues.
problem Reduced performance in federated learning due to non-IID data.
method Investigated from IID to non-IID settings, categorized methods into two strategies.
result Inconsistencies in client loss landscapes are the primary cause of performance degradation.
A model-free method analyzes trading strategies using excursion paths.
problem Analyzing risk and return for dynamic trading strategies without probabilistic assumptions.
method Pathwise analysis of trading signals using δ-excursions.
result Continuous paths can be uniquely decomposed into δ-excursions.
Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, …
SA algorithms control dynamic regret in non-stationary settings with strong convexity or exp-concavity.
problem Non-stationary Online Convex Optimization with dynamic regret control.
method Strongly Adaptive (SA) algorithms view dynamic regret as path variation of the comparator sequence.
result SA algorithms achieve and dynamic regret for strongly convex and exp-concave losses, respectively.
Paper discovers simplicial complexes connecting trained models for improved ensembling.
problem Improving robustness and accuracy of deep learning ensembles.
method Identifies mode-connecting simplicial complexes on loss surfaces.
result Efficiently builds simplicial complexes for ensembling, outperforming independent ensembles.
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or decided data-adaptively. Traditional computational methods rely on solving a set o…
Framework for training stochastic spiking neural networks with rough signals.
problem Training stochastic spiking neural networks with noisy spike timing and dynamics.
method Rough path theory and signature kernels for gradient computation.
result Pathwise gradients of SSNNs' trajectories and event times exist and satisfy a recursive relation.
Study tackles non-stationary bandit convex optimization with new algorithms.
problem Minimizing regret in non-stationary environments with various measures of non-stationarity.
method Proposed Tilted Exponentially Weighted Average with Sleeping Experts (TEWA-SE) for strongly convex losses and clipped Exploration by Optimization (cExO) for general convex losses.
result Proved minimax-optimality of TEWA-SE for strongly convex losses and introduced cExO for general convex losses.
Sequential and temporal data arise in many fields of research, such as quantitative finance, medicine, or computer vision. A novel approach for sequential learning, called the signature method and rooted in rough path theory, is considered. Its basic principle is to represent multidimensional paths by a graded feature …
A multiobjective continuation method to compute the regularization path of deep neural networkscs.LG
Algorithm approximates regularization path for deep neural networks efficiently.
problem Computing the regularization path for high-dimensional deep neural networks.
method Multiobjective continuation method for non-smooth objectives.
result Approximation of the entire Pareto front for regularization path.
Rough kernel hedgingmath.FA
A new algorithm for high-dimensional hedging problems.
problem High-dimensional, path-dependent hedging problems.
method Signature-based algorithm using operator-valued kernels and geometric rough paths.
result Theoretical guarantees on existence and uniqueness of a global minimum.