Related papers: On the robustness of double-word addition algorith…
In the Shortest Superstring problem, we are given a set of strings and we are asking for a common superstring, which has the minimum number of characters. The Shortest Superstring problem is NP-hard and several constant-factor approximation…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and…
Online mirror descent (OMD) and dual averaging (DA) -- two fundamental algorithms for online convex optimization -- are known to have very similar (and sometimes identical) performance guarantees when used with a fixed learning rate. Under…
Doubly robust (DR) estimators guard against model misspecification but remain sensitive to weak covariate overlap. We show that trimming propensity scores reduces variance but eliminates double robustness. We introduce DR estimators that…
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
The most widely used algorithm for floating point complex division, known as Smith's method, may fail more often than expected. This document presents two improved complex division algorithms. We present a proof of the robustness of the…
We analyse the forward error in the floating point summation of real numbers, from algorithms that do not require recourse to higher precision or better hardware. We derive informative explicit expressions, and new deterministic and…
We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and…
In online convex optimization (OCO), Lipschitz continuity of the functions is commonly assumed in order to obtain sublinear regret. Moreover, many algorithms have only logarithmic regret when these functions are also strongly convex.…
In this paper we derive sufficient conditions for the convergence of two popular alternating minimisation algorithms for dictionary learning - the Method of Optimal Directions (MOD) and Online Dictionary Learning (ODL), which can also be…
We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…
It is well-known that typical word embedding methods such as Word2Vec and GloVe have the property that the meaning can be composed by adding up the embeddings (additive compositionality). Several theories have been proposed to explain…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…
Large language models used for clinical abstraction are sensitive to prompt wording, yet most work treats prompts as fixed and studies uncertainty in isolation. We argue these should be treated jointly. Across two clinical tasks (MedAlign…
Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using…