This paper introduces Hill-ADAM. Hill-ADAM is an optimizer with its focus towards escaping local minima in prescribed loss landscapes to find the global minimum. Hill-ADAM escapes minima by deterministically exploring the state space. This eliminates uncertainty from random gradient updates in stochastic algorithms while seldom converging at the first minimum that visits. In the paper we first derive an analytical approximation of the ADAM Optimizer step size at a particular model state. From there define the primary condition determining ADAM limitations in escaping local minima. The proposed optimizer algorithm Hill-ADAM alternates between error minimization and maximization. It maximizes to escape the local minimum and minimizes again afterward. This alternation provides an overall exploration throughout the loss space. This allows the deduction of the global minimum's state. Hill-ADAM was tested with 5 loss functions and 12 amber-saturated to cooler-shade image color correction instances.

We thank the reviewers for their time, effort, and helpful feedback. We address individual comments below. The training loss in all of our examples can be written in the form of lines 17-18. We will include these additional references and add a proof to the appendix. Consider equation (6) when the assumptions of Section 2.1 apply, i.e., Our test can be considered as a more general version of testing whether the loss has reached a constant value.

Noisy label learning aims to learn robust networks under the supervision of noisy labels, which plays a critical role in deep learning. Existing work either conducts sample selection or label correction to deal with noisy labels during the model training process. In this paper, we design a simple yet effective sample selection framework, termed Two-Stream Sample Distillation (TSSD), for noisy label learning, which can extract more high-quality samples with clean labels to improve the robustness of network training. Firstly, a novel Parallel Sample Division (PSD) module is designed to generate a certain training set with sufficient reliable positive and negative samples by jointly considering the sample structure in feature space and the human prior in loss space. Secondly, a novel Meta Sample Purification (MSP) module is further designed to mine adequate semi-hard samples from the remaining uncertain training set by learning a strong meta classifier with extra golden data. As a result, more and more high-quality samples will be distilled from the noisy training set to train networks robustly in every iteration. Extensive experiments on four benchmark datasets, including CIFAR-10, CIFAR-100, Tiny-ImageNet, and Clothing-1M, show that our method has achieved state-of-the-art results over its competitors.

In recent years, self-supervised learning has played a pivotal role in advancing machine learning by allowing models to acquire meaningful representations from unlabeled data. An intriguing research avenue involves developing self-supervised models within an information-theoretic framework, but many studies often deviate from the stochasticity assumptions made when deriving their objectives. To gain deeper insights into this issue, we propose to explicitly model the representation with stochastic embeddings and assess their effects on performance, information compression and potential for out-of-distribution detection. From an information-theoretic perspective, we seek to investigate the impact of probabilistic modeling on the information bottleneck, shedding light on a trade-off between compression and preservation of information in both representation and loss space. Emphasizing the importance of distinguishing between these two spaces, we demonstrate how constraining one can affect the other, potentially leading to performance degradation. Moreover, our findings suggest that introducing an additional bottleneck in the loss space can significantly enhance the ability to detect out-of-distribution examples, only leveraging either representation features or the variance of their underlying distribution.

We consider prediction with expert advice when the loss vectors are assumed to lie in a set described by the sum of atomic norm balls. We derive a regret bound for a general version of the online mirror descent (OMD) algorithm that uses a combination of regularizers, each adapted to the constituent atomic norms. The general result recovers standard OMD regret bounds, and yields regret bounds for new structured settings where the loss vectors are (i) noisy versions of vectors from a low-dimensional subspace, (ii) sparse vectors corrupted with noise, and (iii) sparse perturbations of low-rank vectors. For the problem of online learning with structured losses, we also show lower bounds on regret in terms of rank and sparsity of the loss vectors, which implies lower bounds for the above additive loss settings as well.