Feature maps for the Laplacian kernel and its generalizations

Abstract: Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being equivalent to that of the neural tangent kernel of deep fully connected networks. However, unlike the Gaussian kernel, the Laplacian kernel is not separable. This poses challenges for techniques to approximate it, especially via the random Fourier features (RFF) methodology and its variants. In this work, we provide random features for the Laplacian kernel and its two generalizations: Mat\'{e}rn kernel and the Exponential power kernel. We provide efficiently implementable schemes to sample weight matrices so that random features approximate these kernels. These weight matrices have a weakly coupled heavy-tailed randomness. Via numerical experiments on real datasets we demonstrate the efficacy of these random feature maps.

Overview of ICML 2025 Formatting Guidelines

The paper "Submission and Formatting Instructions for International Conference on Machine Learning (ICML 2025)" provides comprehensive guidelines for the electronic submission and formatting requirements for work to be submitted to the upcoming ICML conference. While this document primarily serves as a manual for authors aiming to contribute to ICML 2025, its contents are pivotal for establishing a standardized approach to academic paper submissions in the field of Machine Learning.

Submission Process and Guidelines

The paper delineates the electronic submission procedures, with a strong emphasis on the use of the ICML's web-based platform. Authors are instructed to deliver their work in PDF format exclusively, reinforcing consistency in document presentation. Furthermore, the document states strict anonymity protocols for submissions, aligned with the double-blind review process fundamental to ICML, ensuring unbiased evaluations.

Key submission guidelines include:

• A main body page limit of 8 pages, exclusive of references and appendices.
• Mandatory formatting using a 10-point Times font.
• The inclusion of all parts of a paper, such as appendices and references, into a single file to avoid components being overlooked by reviewers.

Formatting Specifications

Detailed specifications for the layout extend to various structural components of a manuscript, ensuring uniformity across submissions:

• Dimensions & Fonts: Text in two-column format, Times typeface, and strict margin guidelines.
• Title & Author Information: Stylistic requirements for titles, including typography and alignment, and timing of author information disclosure depending on paper acceptance status.
• Abstract & Section Headings: Rigorous constraints on abstracts to remain concise and section headings to maintain hierarchical clarity.

Content Structuring

Authors are urged to organize their papers effectively, utilizing sections and subsections to delineate information clearly, alongside suggested formats for figures, algorithms, and tables. The paper underlines crucial considerations for the preparation of graphics and tabular data to aid clarity and comprehension.

Theorems and Citations

The authors of this paper advocate for a standardized approach to presenting mathematical content, including theorems and proofs, recommending consecutive numbering within sections. Citations are formatted according to APA guidelines, with emphasis on the correct presentation of author names and the chronological ordering of references.

Implications and Future Directions

While primarily instructional, this paper implicitly contributes to broader discussions regarding the standardization of research dissemination in Machine Learning. The adoption of such uniform guidelines ensures accessibility and readability, fostering efficient peer review and knowledge exchange.

Future implications potentially extend to increasing the accessibility of Machine Learning literature by providing consistent and predictable document structures, thus aiding both human and machine-driven information extraction. These guidelines may influence extended discussions about digital accessibility, ethical considerations, and the societal impacts of disseminated research.

In summary, the paper is an essential resource for authors preparing submissions for ICML 2025, offering a structured framework and specific formatting instructions crucial for maintaining consistency and quality in academic publishing within the Machine Learning community.