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.
Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g., AdaGrad, AdaDelta, and Adam, eases the job slightly. However, such methods have also …
This paper explains why Adam generalizes worse than SGD by analyzing its components.
problem Understanding why Adam generalizes worse than Stochastic Gradient Descent (SGD).
method Diffusion theoretical framework to disentangle the effects of Adaptive Learning Rate and Momentum.
result Adaptive Learning Rate helps escape saddle points but not select flat minima, while Momentum provides a drift effect to help pass through saddle points.
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.
We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this sett…
Wireless systems perform rate adaptation to transmit at highest possible instantaneous rates. Rate adaptation has been increasingly granular over generations of wireless systems. The base-station uses SINR and packet decode feedback called acknowledgement/no acknowledgement (ACK/NACK) to perform rate adaptation. SINR i…
Most optimizers including stochastic gradient descent (SGD) and its adaptive gradient derivatives face the same problem where an effective learning rate during the training is vastly different. A learning rate scheduling, mostly tuned by hand, is usually employed in practice. In this paper, we propose CProp, a gradient…
Research shows minimal communication limits adaptive function estimation rates.
problem Adaptive estimation of a smooth function under minimal communication constraints.
method Investigates the L∞-risk and L2-risk under different numbers of servers.
result For L∞-risk, optimal rates cannot be achieved under minimal communication. For L2-risk, adaptivity is possible but depends on server number and sample size.
AdaGrad-Norm achieves optimal convergence rates for non-convex objectives without tuning.
problem Optimal convergence rates for non-convex, smooth objectives with adaptive step sizes.
method Adaptive SGD (AdaGrad-Norm) with self-tuning step sizes, analyzing under unbounded gradients and affine variance scaling.
result AdaGrad-Norm achieves order optimal convergence rate of $\mathcal{O}\left(\frac{\mathrm{poly}\log(T)}{\sqrt{T}}
ight)$ under optimal assumptions.
The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its mechanism in details. Pursuing the theory behind warmup, we identify a problem of the ad…
Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which \textit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is straightforward to show that they have the same O(1/N) convergen…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD) with momentum in training deep neural networks. This leaves how to close the gene…
Adaptive learning rate algorithms such as RMSProp are widely used for training deep neural networks. RMSProp offers efficient training since it uses first order gradients to approximate Hessian-based preconditioning. However, since the first order gradients include noise caused by stochastic optimization, the approxima…
From a simplified analysis of adaptive methods, we derive AvaGrad, a new optimizer which outperforms SGD on vision tasks when its adaptability is properly tuned. We observe that the power of our method is partially explained by a decoupling of learning rate and adaptability, greatly simplifying hyperparameter search. I…