AGF explains feature learning in neural networks through alternating steps.
problem Understanding what features neural networks learn and how they learn them.
method AGF is an algorithmic framework that approximates the dynamics of feature learning in two-layer networks.
result AGF provides a unified framework to understand feature learning in neural networks, matching experimental results across various architectures.
Enhances linear regression with Kalman filter for loss minimization.
problem Minimizing loss in linear regression models.
method Integrates Kalman filter and SGD for optimal weight updates.
result Develops optimal linear regression equation with minimum area under curve.
LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.
problem Challenges in estimating epistemic uncertainty in LoRA-based Bayesian inference.
method Introduces LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with free and anchored configurations.
result Empirically shows that connecting independent LoRA optima through continuous low-loss valleys improves mutual information of the predictive distribution.
We analyze impermanent loss in AMMs and show G3Ms are simplest.
problem Understanding impermanent loss in automated market makers.
method Developed a general framework and analyzed Geometric Mean Market Makers (G3Ms).
result G3Ms have the simplest impermanent loss characteristics.
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
problem Recovering multiple high-dimensional signals from correlated modalities.
method Bayesian Approximate Message Passing and Sequential Curriculum Learning.
result Sequential learning strategy optimally recovers weak signals in multi-modal settings.
Calibrating classifiers reduces grouping loss using sufficiency criteria.
problem Grouping loss in probabilistic classifier calibration is often overlooked.
method Revisited Langford & Zadrozny's probing reduction approach and introduced Brier curves.
result The probing reduction approach reduces grouping loss and supports sufficient calibration.
The paper presents a multi-power law for predicting loss curves across different learning rate schedules.
problem Understanding and optimizing the relationship between model performance and hyperparameters, especially learning rates.
method Proposes a multi-power law that combines power laws based on the sum of learning rates and additional laws for loss reduction due to decay.
result The multi-power law accurately predicts loss curves for unseen learning rate schedules and finds a schedule that outperforms cosine learning rate.
Analyzes double descent in binary classification models with different losses.
problem Understanding the double descent phenomenon in binary classification models.
method Analytic study of gradient descent with logistic and square losses on binary linear classification models.
result The double descent phenomenon persists but with differences compared to logistic loss.
Investment horizon approach has been used to analyze indexes of Polish stock market.Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain-loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and fo…
Comparison of decision curve analysis and cost curves for model evaluation.
problem Evaluating classification performance across different operating contexts.
method Comparison of Decision Curve Analysis (DCA) and Cost Curves.
result DCA and Cost Curves are closely related, with Brier curves being more generally applicable.
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 optimization method improves AUC for binary classification and changepoint detection.
problem Non-convex AUC and sub-optimal points in ROC curves.
method AUM (Area Under Min(FP, FN)) surrogate loss function based on sorting and summing ROC curve points.
result AUM minimization learning algorithm improves AUC and speeds up compared to previous methods.
New methods evaluate data representations by complexity of low-loss predictor learning.
problem Evaluating quality of data representations for downstream tasks.
method Surplus Description Length (SDL) and ε Sample Complexity (εSC) methods.
result Methods measure the information needed to approximate optimal predictor up to specified tolerance.
Adaptive market maker curves minimize arbitrage losses in DeFi.
problem Asset trading prices in AMMs trail behind centralized exchanges, causing LP losses.
method Adapts market maker bonding curves to trader behavior using a differential equation derived from the Glosten-Milgrom model.
result Optimal adaptive curves minimize arbitrage losses while remaining competitive.
Burq-Gérard-Tzvetkov and Hu established Lp estimates (2≤p≤∞) for the restriction of eigenfunctions to submanifolds. The estimates are sharp, except for the log loss at the endpoint L2 estimates for submanifolds of codimension 2. It has long been believed that the log loss at the endpoint can be remov…
Symmetric losses improve classifier robustness from corrupted labels.
problem Improving classifier performance from corrupted labels.
method Symmetric losses that satisfy a certain condition.
result Symmetric losses enhance robust classification from corrupted labels.
Benguria and Loss have conjectured that, amongst all smooth closed curves of length 2π in the plane, the lowest possible eigenvalue of the operator L=−Δ+κ2 was one. They observed that this value was achieved on a two-parameter family, O, of geometrically distinct ovals containing the round circle and c…
We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are rela…
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.
This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical p…
Model shows loss curve with two distinct exponents due to sparse activations.
problem Sparse activations impact neural network scaling laws.
method Introduced a model for neural scaling laws under sparse activations, derived asymptotic population loss, and analyzed gradient-descent dynamics.
result Loss curve exhibits double-descent peak near interpolation threshold with two distinct scaling exponents.
In the paper, we use and investigate copulas models to represent multivariate dependence in financial time series. We propose the algorithm of risk measure computation using copula models. Using the optimal mean-CVaR portfolio we compute portfolio's Profit and Loss series and corresponded risk measures curves. Value-…
Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logistic loss that incorporates a metric or cost between classes. Unlike previous attempts to use optimal transport distances for learning, our …
The paper shows how the generalization curve can have multiple peaks, influenced by data and learning algorithm biases.
problem Understanding the generalization behavior of linear regression models under varying parameterizations.
method Analyzes generalization loss in linear regression models with varying parameterizations, both under- and over-parameterized.
result The generalization curve can have an arbitrary number of peaks, and their locations can be controlled.
We propose a max-pooling based loss function for training Long Short-Term Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low CPU, memory, and latency requirements. The max-pooling loss training can be further guided by initializing with a cross-entropy loss trained network. A posterior smoothin…
New methods connect low-loss points on neural network surfaces.
problem Connecting low-loss points on neural network loss surfaces.
method Macroscopic distributional assumptions and global connection models.
result Accuracy correlates with complexity and sensitivity.
In this manuscript we propose two objective terms for neural image compression: a compression objective and a cycle loss. These terms are applied on the encoder output of an autoencoder and are used in combination with reconstruction losses. The compression objective encourages sparsity and low entropy in the activatio…
This paper identifies and analyzes the Epochal Sawtooth Phenomenon in training loss curves.
problem Training loss oscillations in adaptive gradient-based optimizers.
method Empirical analysis of Adam and other optimizers, focusing on β parameters, batch size, data shuffling, and sample replacement. result The Epochal Sawtooth Phenomenon (ESP) is a recurring pattern in training loss curves, arising from adaptive learning rate adjustments and data shuffling.
AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize AUC, while owing to the non-convexity and discontinuousness of AUC, almost all …
We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for …
Efficient algorithm for evaluating hierarchical classification methods at multiple operating points.
problem Evaluating hierarchical classification methods at multiple operating points.
method Efficient algorithm to produce operating characteristic curves for any method that assigns scores to every class in the hierarchy.
result Top-down classifiers are dominated by a naive flat softmax classifier across the entire operating range.
New model predicts neural network performance from early training epochs, incorporating architecture impact.
problem Predicting neural network performance from early training epochs, neglecting architecture impact.
method Architecture-aware graph ordinary differential equation model.
result Model outperforms state-of-the-art methods for MLP and CNN learning curves.
WES improves neural network regression by stretching distribution error.
problem Improving prediction performance in neural-network-based regression.
method Proposed weighted empirical stretching (WES) loss function.
result WES outperforms existing loss functions, especially in extreme domains.
This work reveals how label noise can cause a final ascent in neural network performance curves.
problem The impact of label noise on the performance of neural networks.
method Theoretical analysis and extensive experiments on various neural network architectures.
result Label noise can lead to a final ascent in the test loss curve, improving generalization at intermediate model widths.
Improved Strichartz estimates for Schrödinger equation on negatively curved manifolds.
problem Improving Strichartz estimates for Schrödinger equation on negatively curved compact manifolds.
method Analyzing the Schrödinger equation on negatively curved compact manifolds, obtaining improved Strichartz estimates.
result Improved Strichartz estimates, including no-loss estimates for hyperbolic surfaces.
This work analyzes two methods for combining multiple binary labels in bipartite ranking.
problem Combining multiple binary labels for optimal bipartite ranking.
method Loss aggregation vs. label aggregation approaches.
result Label aggregation is preferable to loss aggregation due to label dictatorship issues.
New method saves computational budget by ranking and transferring learning curves.
problem Expensive automated machine learning methods for hyperparameter and neural architecture optimization.
method Tackles as a ranking and transfer learning problem, optimizing a pairwise ranking loss and leveraging learning curves from other datasets.
result Accelerates neural architecture search by a factor of up to 100 without significant performance degradation.
Modified AUC improves CNN training by considering model confidence.
problem Improving binary classifier performance metrics.
method Proposes a modified AUC metric that incorporates model confidence into BCE loss for CNN training.
result Demonstrates improved performance on three datasets: MNIST, prostate MRI, and brain MRI.
Optimizes bond portfolios to avoid worst-case losses.
problem Finding the worst-case value of a bond portfolio over a range of yield curves and spreads.
method Solves a convex-concave saddle point optimization problem to find the worst-case value and construct a robust portfolio.
result Constructs a bond portfolio that includes the worst-case value, ensuring robustness against market uncertainties.
The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these hig…
Flooding prevents deep networks from achieving zero training loss, improving test performance.
problem Deep networks can achieve zero training error but often have zero training loss, leading to overconfidence and poor test performance.
method Flooding prevents training loss from reaching zero by applying gradient ascent when loss is below a preset flood level.
result Flooding improves test performance and induces a double descent curve of the test loss.
Neural network model improves robustness of mortgage bond yield curve estimation.
problem Overfitting and instability in traditional yield curve estimation methods for small mortgage bond markets.
method Neural network framework with a new loss function for smoothness and stability.
result Empirical results show more robust and stable yield curve estimates compared to existing methods.
Investigates how flatness of loss curve relates to generalization in machine learning models.
problem Understanding why flatness correlates with generalization in machine learning models.
method Relates flatness to interpolation from representative data, derives notions of representativeness and feature robustness.
result Derives a novel relative flatness measure that correlates with generalization and solves reparameterization issues.
The paper predicts loss scaling across different datasets and compute scales.
problem Predicting loss scaling across different datasets and compute scales.
method Derive shifted power law relationships between train and test losses.
result Shifted power law relationships hold for various datasets and tasks, improving prediction accuracy.
CURL uses neural curves to enhance global image properties.
problem Global image enhancement using neural networks.
method CURL is a multi-colour space neural retouching block trained in HSV, CIELab, and RGB color spaces.
result CURL produces state-of-the-art image quality in RGB-to-RGB and RAW-to-RGB transformations.
Adma proposes a flexible loss function for neural networks.
problem Static loss functions limit neural network performance.
method Introduces a flexible loss function that adapts to ANN complexity and data distribution.
result Flexible loss function achieves state-of-the-art performance.
Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the generalization performance of online learning algorithms with pairwise loss functions. We…
The study examines the dynamic behavior of RMSprop and Adam algorithms.
problem Understanding the training loss curve patterns of adaptive gradient algorithms.
method Careful numerical experiments and theoretical explanations using the signGD flow.
result Adam converges smoother and faster when momentum factors are close to each other.