Formally Verifying Fenwick Trees

Anthony Wang — Sat, 15 Mar 2025 21:30:06 -0400

Kublai: Hey, it’s you again! That formal verification thing you mentioned last time sucks!

Huh? You mean our proof of the ICan’tBelieveItCanSort algorithm?

Kublai: Yeah! ICan’tBelieveItCanSort? More like ICanBelieveItObviouslyCanSort! After watching that visualization a few times, it intuitively makes so much sense. It’s trivial.

Trivial? I’m banning that word. If you consider something to be trivial, you probably haven’t pondered it deeply enough.

Solving Shortest Paths With Transformers

Anthony Wang — Wed, 11 Dec 2024 11:29:07 -0500

Introduction

Motivation

Neural networks are capable of impressive feats of off-distribution generalization. For instance, we discussed in class a program trained to convert sketches of cats into realistic looking pictures of cats that was able to draw a cat with three eyes given a sketch with three eyes, even though there were no 3-eyed cats in the training data. However, neural networks also often learn non-robust features that cause them to perform poorly off-distribution (e.g., adversarial examples for an image classifier). In this project, we will investigate the question of when transformers generalize off-distribution via a case study on a simple synthetic task. More specifically, the goal of our project is to make progress towards answering the following question:

Insane on Unnamed Website

Formally Verifying Fenwick Trees

Solving Shortest Paths With Transformers

Introduction

Motivation