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UID:436@math.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20250409T133000

DTEND;TZID=Asia/Jerusalem:20250409T143000

DTSTAMP:20250408T060533Z

URL:https://math.technion.ac.il/events/deep-learning-on-multisets-and-meas
 ures-via-euclidean-embeddings/

SUMMARY:Deep Learning on Multisets and Measures via Euclidean Embeddings
DESCRIPTION:Lecturer:Tal Amir (Technion)\n Location:Amado 619\n \n\n\n\n\nR
 ecent advances in machine learning have focused on non-Euclidean data\, su
 ch as sets\, point clouds\, and graphs. Developing efficient methods to em
 bed these data types into Euclidean space is critical\, as it allows for t
 he direct application of standard machine learning tools such as neural ne
 tworks. In particular\, Euclidean embeddings for more complex structures l
 ike point clouds and graphs typically rely on Euclidean embeddings for mul
 tisets as a fundamental building block.\n\nIn this talk\, I will present t
 wo novel methods for embedding multisets and measures into Euclidean space
 : the first is based on sum-pooled shallow neural networks with carefully 
 chosen activation functions [1]\; the second\, inspired by optimal transpo
 rt\, uses Fourier sampling of projected quantile functions [2]. I will dis
 cuss the theoretical properties of these methods\, including injectivity a
 nd bi-Lipschitzness\, and demonstrate their advantages in practical learni
 ng tasks. Additionally\, I will present two impossibility results: (1) emb
 eddings based on sum-pooling can never be bi-Lipschitz on multisets\, and 
 (2) no embedding can be bi-Lipschitz on distributions.\n\n\nReferences\n\n
 [1] Amir\, T.\, Gortler\, S.\, Avni\, I.\, Ravina\, R.\, &amp\; Dym\, N. (
 2023). Neural injective functions for multisets\, measures and graphs via 
 a finite witness theorem. Advances in Neural Information Processing System
 s\, 36\, 42516-42551.\n\n[2] Amir\, Tal\, and Nadav Dym. Fourier Sliced-Wa
 sserstein Embedding for Multisets and Measures. To appear in the Proceedin
 gs of the International Conference on Learning Representations (ICLR)\, 20
 25.\n\n\n\n\n\n 
CATEGORIES:Pizza Seminar,Seminars
LOCATION:Amado 619

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