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We prove the "Most informative boolean function" conjecture of Courtade and Kumar for high noise $\epsilon \ge 1/2 - \delta$, for some absolute constant $\delta > 0$. Namely, if $X$ is uniformly distributed in $\{0,1\}^n$ and $Y$ is…
We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
Any interactive protocol between a pair of parties can be reliably simulated in the presence of noise with a multiplicative overhead on the number of rounds (Schulman 1996). The reciprocal of the best (least) overhead is called the…
For particle filters and ensemble Kalman filters it is of practical importance to understand how and why data assimilation methods can be effective when used with a fixed small number of particles, since for many large-scale applications it…
Quantum error correcting (QEC) codes protect quantum information against environmental noise. Computational errors caused by the environment change the quantum state within the qubit subspace, whereas quantum erasures correspond to the loss…
We consider approximation algorithms for covering integer programs of the form min $\langle c, x \rangle $ over $x \in \mathbb{N}^n $ subject to $A x \geq b $ and $x \leq d$; where $A \in \mathbb{R}_{\geq 0}^{m \times n}$, $b \in…
Processing-using-DRAM (PuD) is an emerging paradigm that leverages the analog operational properties of DRAM circuitry to enable massively parallel in-DRAM computation. PuD has the potential to reduce or eliminate costly data movement…
Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…
Incremental learning requires a model to continually learn new tasks from streaming data. However, traditional fine-tuning of a well-trained deep neural network on a new task will dramatically degrade performance on the old task -- a…
In this paper we revisit the efficacy of knowledge distillation as a function matching and metric learning problem. In doing so we verify three important design decisions, namely the normalisation, soft maximum function, and projection…
Thinking aloud is an effective meta-cognitive strategy human reasoners apply to solve difficult problems. We suggest to improve the reasoning ability of pre-trained neural language models in a similar way, namely by expanding a task's…
Several decision problems that are encountered in various business domains can be modeled as mathematical programs, i.e. optimization problems. The process of conducting such modeling often requires the involvement of experts trained in…
For crosslingual conversation and trade, Neural Machine Translation (NMT) is pivotal yet faces persistent challenges with monotony and repetition in generated content. Traditional solutions that rely on penalizing text redundancy or token…
Contrastive Learning (CL) has been proved to be a powerful self-supervised approach for a wide range of domains, including computer vision and graph representation learning. However, the incremental learning issue of CL has rarely been…
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…
We introduce ZeroSCROLLS, a zero-shot benchmark for natural language understanding over long texts, which contains only test and small validation sets, without training data. We adapt six tasks from the SCROLLS benchmark, and add four new…
Machine unlearning in neural information retrieval (IR) systems requires removing specific data whilst maintaining model performance. Applying existing machine unlearning methods to IR may compromise retrieval effectiveness or inadvertently…
Imitation Learning (IL) is a promising paradigm for teaching robots to perform novel tasks using demonstrations. Most existing approaches for IL utilize neural networks (NN), however, these methods suffer from several well-known…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…