Colloquia and Seminars

In this seminar I will present our paper that was published in NeurIPS 2024. We introduce hierarchical selective classification, which extends selective classification to a hierarchical setting. Our approach leverages the inherent structure of class relationships, enabling models to reduce the specificity of their predictions when faced with uncertainty. We formalize hierarchical risk and coverage, and introduce hierarchical risk-coverage curves. Next, we develop algorithms for hierarchical selective classification (which we refer to as "inference rules"), and propose an efficient algorithm that guarantees a target accuracy constraint with high probability. Lastly, we conduct extensive empirical studies on over a thousand ImageNet classifiers, revealing that training regimes such as CLIP, pretraining on ImageNet21k and knowledge distillation boost hierarchical selective performance.

The process of debugging software can be a time-consuming and tedious task, often requiring developers to guess which lines of code to set breakpoints on in order to gather more information. Time-travel debuggers are tools that record the program's state throughout its run and let the user inspect it afterwards, a.k.a "Post-Mortem". While time travel debuggers have reduced the time required to re-run a program, they still require developers to view the program on a linear timeline, jumping through different time points. To address these challenges, we have developed a new debugging tool called PaLaDiN. PaLaDiN offers several advantages over traditional debugging methods, including a concise, high-level yet expressive query DSL for retrieving trace data, the ability to show summary information for entire program sections, and the ability to focus on a specific slice of the program's run by running high-level predicates. PaLaDiN also allows developers to connect different, possibly unrelated, fragments of the program using join operators, run queries with alternative states, analyze variable lifetimes throughout the program's run, and compare different implementations of the same function. Overall, PaLaDiN provides a comprehensive and flexible approach to debugging that can significantly reduce the time and effort required to identify and fix software bugs.

I will describe several old and new applications of topological and algebraic methods in the derivation of combinatorial results. In all of them the proofs provide no efficient procedures for solving the corresponding algorithmic questions. The problem of finding such procedures (or convincing reasons indicating that they are unlikely to exist) is an intriguing challenge and I will mention some progress in the study of this problem too.

Bio:

Noga Alon is a Professor of Mathematics at Princeton University and a Professor Emeritus of Mathematics and Computer Science at Tel Aviv University.

He works in Discrete Mathematics and its applications in Theoretical Computer Science, Information Theory, Combinatorial Geometry, and Combinatorial Number Theory.

He is a member of the Israel Academy of Sciences and Humanities and of the Academia Europaea, and an honorary member of the Hungarian Academy of Sciences. He received several awards, three recent ones are the 2022 Shaw Prize in Mathematical Sciences, the 2022 Knuth Prize for outstanding contributions to the foundations of computer science and the 2024 Wolf Prize in Mathematics. 

This doctoral research focuses on advancing the autonomy of Unmanned Aerial Vehicles (UAVs) operating in complex, dense urban environments, particularly emphasizing the critical task of identifying safe landing locations. Traditional sensing and decision-making methods often struggle with the intricacies of such settings. This work proposes leveraging semantic segmentation, a machine-learning technique that interprets visual scenes by assigning a class label (e.g., road, building, vegetation) to each pixel in an image, as a sophisticated sensor modality for UAVs.

A primary contribution is a novel multi-resolution strategy for landing site selection. This method involves the UAV collecting visual information at progressively decreasing altitudes, thereby acquiring images with increasing spatial resolution. For each potential terrain patch, a probability distribution representing its suitability for landing is maintained and updated as new data from different altitudes becomes available. A landing site is confirmed once the confidence level for a patch surpasses a predefined threshold. This decision-making process relies on a semantic segmentation algorithm to provide per-pixel likelihoods of different terrain types, which are then integrated with prior knowledge and previous measurements.

To facilitate the development and rigorous evaluation of semantic segmentation algorithms tailored for drone applications, a comprehensive dataset named MESSI (Multi-Elevation Semantic Segmentation Image) was developed. MESSI is distinguished by its inclusion of images captured from a wide range of altitudes and diverse urban locations, reflecting the varied perspectives encountered during a realistic 3D drone flight. This richly annotated dataset serves as a valuable resource for training deep neural networks and benchmarking their performance in understanding urban scenes.

Furthermore, this research addresses a fundamental challenge in applying semantic segmentation to probabilistic search problems: the statistical nature of its outputs differs from assumptions in classical detection theory. A systematic methodology is introduced to bridge this gap, enabling the effective integration of semantic segmentation into established probabilistic search frameworks. This integration provides a more robust foundation for decision-making processes, such as the identification of viable landing sites in partially known environments. The practical feasibility and effectiveness of the proposed approaches are demonstrated through extensive simulations and validation using real-world datasets, highlighting their potential to significantly enhance UAV operational capabilities in challenging urban settings.