We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster convergence rate than gradient descent provided the function is strongly smooth - a natural generalization of the standard smoothness assumption on the objective function. When the objective function is convex, we present two frameworks for "accelerating" descent methods, one in the style of Nesterov and the other in the style of Monteiro and Svaiter. Rescaled gradient descent can be accelerated under the same strong smoothness assumption using both frameworks. We provide several examples of strongly smooth loss functions in machine learning and numerical experiments that verify our theoretical findings.

To convert the input into binary code, hashing algorithm has been widely used for approximate nearest neighbor search on large-scale image sets due to its computation and storage efficiency. Deep hashing further improves the retrieval quality by combining the hash coding with deep neural network. However, a major difficulty in deep hashing lies in the discrete constraints imposed on the network output, which generally makes the optimization NP hard. In this work, we adopt the greedy principle to tackle this NP hard problem by iteratively updating the network toward the probable optimal discrete solution in each iteration. A hash coding layer is designed to implement our approach which strictly uses the sign function in forward propagation to maintain the discrete constraints, while in back propagation the gradients are transmitted intactly to the front layer to avoid the vanishing gradients. In addition to the theoretical derivation, we provide a new perspective to visualize and understand the effectiveness and efficiency of our algorithm. Experiments on benchmark datasets show that our scheme outperforms state-of-the-art hashing methods in both supervised and unsupervised tasks.

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster convergence rate than gradient descent provided the function is strongly smooth - a natural generalization of the standard smoothness assumption on the objective function. When the objective function is convex, we present two frameworks for "accelerating" descent methods, one in the style of Nesterov and the other in the style of Monteiro and Svaiter. Rescaled gradient descent can be accelerated under the same strong smoothness assumption using both frameworks. We provide several examples of strongly smooth loss functions in machine learning and numerical experiments that verify our theoretical findings.

I think the first part of the paper has very good original contributions with correct and nicely-written proofs in the appendix. However, I have the following questions regarding the parts of the paper starting at Section 3. Sorry if these are redundant questions with obvious answers that I missed. The RGD framework is mentioned for both convex and non-convex functions (Lemma 4 doesn't require f to be convex). However, the examples provided are all convex functions, and the focus also seems to be quite heavily on convex functions (because none of the papers on nonconvex optimization are compared with). Do the authors have (1) theoretical results and comparisons with existing work and/or (2)experiments, for non-convex functions?

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster convergence rate than gradient descent provided the function is strongly smooth - a natural generalization of the standard smoothness assumption on the objective function. When the objective function is convex, we present two frameworks for "accelerating" descent methods, one in the style of Nesterov and the other in the style of Monteiro and Svaiter. Rescaled gradient descent can be accelerated under the same strong smoothness assumption using both frameworks. We provide several examples of strongly smooth loss functions in machine learning and numerical experiments that verify our theoretical findings.

The paper presents a greedy approach to train a deep neural network to directly produce binary codes that build on the straight through estimator. During forward propagation the model uses the sgn output whereas at the back-propagation stage it passes derivatives as it the output were a simple linear function. There are relevant papers that already proposed such an approach and that are not referred to as earlier work: [1] Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation, Bengio Y. et al. [2] Techniques for learning binary stochastic feedforward neural networks, Tapani R. et al. The experimental setting is not very clear and I would suggest the authors to better explain the supervised setting. Do they produce a binary code of length k and then classify it with a single final output layer?

Classifiers and generators have long been separated. We break down this separation and showcase that conventional neural network classifiers can generate high-quality images of a large number of categories, being comparable to the state-of-the-art generative models (e.g., DDPMs and GANs). We achieve this by computing the partial derivative of the classification loss function with respect to the input to optimize the input to produce an image. Since it is widely known that directly optimizing the inputs is similar to targeted adversarial attacks incapable of generating human-meaningful images, we propose a mask-based stochastic reconstruction module to make the gradients semantic-aware to synthesize plausible images. We further propose a progressive-resolution technique to guarantee fidelity, which produces photorealistic images. Furthermore, we introduce a distance metric loss and a non-trivial distribution loss to ensure classification neural networks can synthesize diverse and high-fidelity images. Using traditional neural network classifiers, we can generate good-quality images of 256$\times$256 resolution on ImageNet. Intriguingly, our method is also applicable to text-to-image generation by regarding image-text foundation models as generalized classifiers. Proving that classifiers have learned the data distribution and are ready for image generation has far-reaching implications, for classifiers are much easier to train than generative models like DDPMs and GANs. We don't even need to train classification models because tons of public ones are available for download. Also, this holds great potential for the interpretability and robustness of classifiers. Project page is at \url{https://classifier-as-generator.github.io/}.

Embedding approaches have become one of the most pervasive techniques for multi-label classification. However, the training process of embedding methods usually involves a complex quadratic or semidefinite programming problem, or the model may even involve an NP-hard problem. Thus, such methods are prohibitive on large-scale applications. More importantly, much of the literature has already shown that the binary relevance (BR) method is usually good enough for some applications. Unfortunately, BR runs slowly due to its linear dependence on the size of the input data. The goal of this paper is to provide a simple method, yet with provable guarantees, which can achieve competitive performance without a complex training process. To achieve our goal, we provide a simple stochastic sketch strategy for multi-label classification and present theoretical results from both algorithmic and statistical learning perspectives. Our comprehensive empirical studies corroborate our theoretical findings and demonstrate the superiority of the proposed methods.

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster convergence rate than gradient descent provided the function is strongly smooth - a natural generalization of the standard smoothness assumption on the objective function. When the objective function is convex, we present two frameworks for "accelerating" descent methods, one in the style of Nesterov and the other in the style of Monteiro and Svaiter. Rescaled gradient descent can be accelerated under the same strong smoothness assumption using both frameworks. We provide several examples of strongly smooth loss functions in machine learning and numerical experiments that verify our theoretical findings.

To convert the input into binary code, hashing algorithm has been widely used for approximate nearest neighbor search on large-scale image sets due to its computation and storage efficiency. Deep hashing further improves the retrieval quality by combining the hash coding with deep neural network. However, a major difficulty in deep hashing lies in the discrete constraints imposed on the network output, which generally makes the optimization NP hard. In this work, we adopt the greedy principle to tackle this NP hard problem by iteratively updating the network toward the probable optimal discrete solution in each iteration. A hash coding layer is designed to implement our approach which strictly uses the sign function in forward propagation to maintain the discrete constraints, while in back propagation the gradients are transmitted intactly to the front layer to avoid the vanishing gradients.