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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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48 results for true loss

Local update methods' performance depends on learning rates, affecting convergence rates and alignment with true loss.

problem The performance of local update methods in federated learning and meta-learning is sensitive to learning rates.
method Proved that local update methods perform SGD on a surrogate loss function, characterized the surrogate loss, and derived convergence rates.
result Proper learning rate tuning is crucial for near-optimal behavior in communication-limited settings.

New method estimates grouping loss in neural networks to improve confidence scores.

problem Improving confidence scores in neural networks to reflect true posterior probabilities.
method Proposed an estimator to approximate the grouping loss.
result Modern neural networks exhibit grouping loss, especially in distribution shifts.

Focal loss improves classification but not class-posterior probability estimation.

problem Improving class-posterior probability estimation from focal loss.
method Proved classification-calibration and derived a transformation to recover true class-posterior probabilities.
result A transformation of the confidence score from focal loss minimization allows recovery of true class-posterior probabilities.

In many applications of classifier learning, training data suffers from label noise. Deep networks are learned using huge training data where the problem of noisy labels is particularly relevant. The current techniques proposed for learning deep networks under label noise focus on modifying the network architecture and…

2017-12-27abs ↗pdf ↗

Generative Adversarial Networks (GANs) were intuitively and attractively explained under the perspective of game theory, wherein two involving parties are a discriminator and a generator. In this game, the task of the discriminator is to discriminate the real and generated (i.e., fake) data, whilst the task of the gene…

2017-11-06abs ↗pdf ↗

UMAP's true loss function differs from what was previously thought, focusing on nearest neighbor graph similarities.

problem Understanding the true effectiveness and mechanism of UMAP for high-dimensional data visualization.
method Deriving UMAP's effective loss function in closed form and analyzing its optimization scheme.
result UMAP aims to reproduce similarities encoded in the nearest neighbor graph, not the full high-dimensional similarities.

The minimization of loss functions is the heart and soul of Machine Learning. In this paper, we propose an off-the-shelf optimization approach that can minimize virtually any non-differentiable and non-decomposable loss function (e.g. Miss-classification Rate, AUC, F1, Jaccard Index, Mathew Correlation Coefficient, etc…

2019-05-24abs ↗pdf ↗

This paper improves risk bounds and calibration for smart predict-then-optimize method.

problem Improving risk bounds and calibration for smart predict-then-optimize method.
method Develops risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss.
result Empirical minimizer of the SPO+ loss achieves low excess true risk with high probability.

New method proves asymptotic normality for matrix sensing problems.

problem Proving asymptotic normality for matrix sensing under general convex losses.
method Riemannian geometry to handle degeneracy of the Hessian due to rotational symmetry.
result Proves n(φ0φ)DN(0,(H)1)\sqrt{n}(φ^0-φ^*)\xrightarrow{D}N(0,(H^*)^{-1}) as non o\infty.

Improved computational complexity in statistical models using second-order information.

problem Polynomial convergence of gradient descent in singular statistical models.
method Normalized Gradient Descent (NormGD) algorithm with second-order information.
result NormGD reaches final statistical radius in logarithmic iterations of nn.

Study connects covariance cleaning theory to information theory for heavy-tailed distributions.

problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.

New method ensures generated data statistics match real data distributions.

problem Ensuring generated data statistics match real data distributions in GANs.
method Added a new loss term to the generator loss function using f-divergences and kernel density estimation.
result Improved performance on synthetic and real-world datasets.

Proposes squentropy loss for improved classification accuracy and model calibration.

problem Theoretical and empirical evidence for cross-entropy loss is lacking.
method Introduces squentropy loss as the sum of cross-entropy and average square loss over incorrect classes.
result Squentropy loss outperforms cross-entropy and rescaled square losses in classification accuracy and model calibration.

The paper analyzes the generalization of deep neural networks for metric and similarity learning.

problem Lack of rigorous understanding of generalization performance in metric and similarity learning.
method Derive explicit form of true metric, construct structured deep ReLU neural network, establish excess risk bounds.
result Explicit excess risk bounds for metric and similarity learning are derived.

Paper proposes a new loss function for PU learning without negative examples.

problem Traditional machine learning struggles with negative examples, leading to biased predictions.
method Developed a collective loss function (cPU) for positive and unlabeled data.
result The cPU consistently outperforms existing methods in PU learning benchmarks and real-world datasets.

Two-layer ReLU networks often converge to simpler solutions, improving generalization.

problem Understanding generalization in overparametrized neural networks, especially for complex tasks.
method Theoretical analysis of two-layer ReLU networks, focusing on the early alignment phase.
result Two-layer ReLU networks often converge to simpler solutions rather than interpolating the training data, leading to better generalization.

The paper analyzes error bounds and KL properties for noisy matrix recovery problems.

problem Noisy low-rank matrix recovery problems.
method Squared F-norm regularization, accelerated alternating minimization method.
result Established error bounds and KL properties for critical points and global minimizers.

Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.

problem Robust low-rank matrix recovery in the presence of corrupted measurements.
method Proposed Sign-RIP, a robust restricted isometry property.
result Sign-RIP guarantees uniform convergence of subdifferentials in robust low-rank matrix recovery.

This paper examines how different decoding algorithms for LLMs align with various goals.

problem Consistency of decoding algorithms with different goals in LLMs.
method Analysis of greedy, lookahead, random sampling, and temperature-scaled random sampling algorithms.
result Random sampling is consistent with the true probability distribution, but other goals require optimal algorithms for specific probability distributions.

We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an accurate approximation for the probability that two inputs fall within a Hamming dista…

2018-10-01abs ↗pdf ↗

Consider a transverse knot which is the binding of an open book for the ambient contact manifold. In this paper, we show that the transverse invariants defined by Lisca, Ozsvath, Stipsicz, and Szabo (LOSS) are nonvanishing for such transverse knots. This is true regardless of whether or not the ambient contact structur…

2008-06-10abs ↗pdf ↗

The paper explores how the depth of neural networks affects their ability to represent data accurately.

problem Understanding the implicit bias and rank of neural networks with large depth.
method Analyzing the convergence of representation cost to a notion of rank as network depth increases, and investigating conditions for recovering the true rank of data.
result There is a range of network depths where the true rank of data is recovered, and this affects the topology of class boundaries.

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.

Proposes a new generalization bound for Bayesian deep nets without strict assumptions.

problem Lack of generalization bounds for Bayesian deep nets without strict assumptions.
method Exploits contractivity of Log-Sobolev inequalities to add a loss-gradient norm term to the generalization bound.
result Introduces a new generalization bound for Bayesian deep nets that avoids strict assumptions.

New method trains generative models without discriminators, improving stability and accuracy.

problem Training implicit generative models with adversarial discriminators leads to instability and mode-dropping.
method Invariant statistical loss function, avoiding discriminators.
result Successfully trains generative models for various complex distributions without mode-dropping.

UREs lead to overfitting in complex models, especially in complementary label learning.

problem Overfitting in weakly supervised learning with complementary labels.
method Proposed a surrogate complementary loss (SCL) framework to reduce gradient variance.
result SCL mitigates overfitting and improves URE-based methods.

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that provide theoretical guarantees on why they are so effective. Lying in the center of…

2016-11-09abs ↗pdf ↗

The paper explains spikes in training loss as catapults, improving feature learning and generalization.

problem Understanding and improving the training process of neural networks.
method Analysis of training loss spikes in SGD, empirical evidence of catapults, and demonstration of AGOP alignment.
result Catapults in training loss promote feature learning and better generalization.

In this paper we refine the process of computing calibration functions for a number of multiclass classification surrogate losses. Calibration functions are a powerful tool for easily converting bounds for the surrogate risk (which can be computed through well-known methods) into bounds for the true risk, the probabili…

2016-09-20abs ↗pdf ↗

New insights into convergence and accuracy trade-offs in federated and meta-learning.

problem Understanding the trade-offs between convergence and accuracy in federated and meta-learning.
method Generalized local update methods, proving equivalence to first-order optimization on a surrogate loss.
result Novel convergence rates and insights into the importance of algorithmic choices in communication-limited settings.

This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We maintain that [13, Proposition 11] is true. ([7] = arXiv:1809.00593, [13] = arXiv:15…

2018-09-06abs ↗pdf ↗

We propose a novel autoencoding model called Pairwise Augmented GANs. We train a generator and an encoder jointly and in an adversarial manner. The generator network learns to sample realistic objects. In turn, the encoder network at the same time is trained to map the true data distribution to the prior in latent spac…

2018-10-11abs ↗pdf ↗

Proposes SOVR loss to improve adversarial robustness by increasing logit margins.

problem Adversarial training's difficulty in robustness against sophisticated attacks.
method Introduces SOVR loss function that switches from cross-entropy to one-vs-the-rest loss for important samples.
result SOVR loss increases logit margins of important samples, improving robustness against Auto-Attack.