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.
We propose NovoGrad, an adaptive stochastic gradient descent method with layer-wise gradient normalization and decoupled weight decay. In our experiments on neural networks for image classification, speech recognition, machine translation, and language modeling, it performs on par or better than well tuned SGD with mom…
Over the past few years, Batch-Normalization has been commonly used in deep networks, allowing faster training and high performance for a wide variety of applications. However, the reasons behind its merits remained unanswered, with several shortcomings that hindered its use for certain tasks. In this work, we present …
We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optim…
SGD and weight decay encourage neural networks to learn low-rank weight matrices.
problem The bias of SGD towards low-rank weight matrices in neural networks.
method The study investigates the effect of SGD and weight decay on the rank of weight matrices in neural networks, both theoretically and empirically.
result Training with SGD and weight decay induces a bias towards rank minimization in weight matrices, which becomes more pronounced with smaller batch sizes and stronger weight decay.
Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of L2 regularization. Literal weight decay has been shown to outperform L2 regularization for…
Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose L-2 penalty on the model parameters resulting in the decay of parameters, called weight-decay, and the …
Under what conditions is an edge present in a social network at time t likely to decay or persist by some future time t + Delta(t)? Previous research addressing this issue suggests that the network range of the people involved in the edge, the extent to which the edge is embedded in a surrounding structure, and the age…
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
problem Understanding the emergence of low-rank bias and neural collapse in L2-regularized networks.
method Unified theoretical framework linking TCV and rank of weight matrices, proving global optimality of DNC1, and establishing a benign landscape property.
result Zero TCV across intermediate layers minimizes representation cost under natural architectural constraints, and DNC1 is globally optimal.
Adaptive weights improve physics-informed neural networks and deep operator networks.
problem Training physics-informed neural networks and deep operator networks can be challenging, leading to unsatisfactory accuracy and efficiency.
method Proposes a pointwise adaptive weighting method that balances the residual decay rate across different training points.
result Our proposed approach of balanced residual decay rates offers advantages including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.
Study reveals dynamics of neural networks with normalization, weight decay, and SGD.
problem Understanding the equilibrium condition in Spherical Motion Dynamics (SMD).
method Investigates SMD by exploring the cause of equilibrium condition, introducing assumptions, proposing angular update, and verifying theoretical results.
result Proves weight norm and angular update can converge at linear rate under given assumptions.
We introduce a new weight-decay scaling rule to maintain sublayer gains across different widths in modern scale-invariant architectures.
problem In modern scale-invariant architectures, training quickly enters a steady state where normalization layers create backward scale sensitivity, degrading learning-rate transfer.
method We introduce a weight-decay scaling rule for AdamW that preserves sublayer gain across widths by equalizing the effective learning rate.
result Our empirical weight-decay scaling rule λ2∝d approximately keeps sublayer gains width invariant, enabling zero-shot transfer of learning rate and weight decay.
Performance-critical machine learning models should be robust to input perturbations not seen during training. Adversarial training is a method for improving a model's robustness to some perturbations by including them in the training process, but this tends to exacerbate other vulnerabilities of the model. The adversa…
Wide neural networks with weight decay exhibit neural collapse.
problem Proving neural collapse in wide neural networks trained with weight decay.
method Generic guarantees on neural collapse for wide networks with weight decay, proving low training error and balancedness, and bounded conditioning.
result First proof of neural collapse in end-to-end training of wide neural networks with weight decay.
In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, r…
DynamicVAE improves disentanglement and reconstruction accuracy without sacrificing one for the other.
problem The inherent trade-off between disentanglement and reconstruction accuracy in VAE models.
method DynamicVAE uses a modified incremental PI controller to dynamically adjust the weight β during training, decoupling disentanglement and reconstruction accuracy.
result DynamicVAE significantly improves reconstruction accuracy while maintaining disentanglement comparable to existing methods.
Regularization is a big issue for training deep neural networks. In this paper, we propose a new information-theory-based regularization scheme named SHADE for SHAnnon DEcay. The originality of the approach is to define a prior based on conditional entropy, which explicitly decouples the learning of invariant represent…
Regularization is a big issue for training deep neural networks. In this paper, we propose a new information-theory-based regularization scheme named SHADE for SHAnnon DEcay. The originality of the approach is to define a prior based on conditional entropy, which explicitly decouples the learning of invariant represent…
The study introduces anytime learning schedules for large language models without fixed horizons.
problem Training large language models without knowing the total training horizon.
method Theoretical analysis and weight averaging to create anytime learning schedules.
result Theoretical and empirical evidence shows that weight averaging with simple step sizes can achieve comparable final loss to well-tuned cosine schedules.