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- Aran Nayebi
- 2009

On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen's fast matrix multiplication algorithm with DNA based on an n-moduli set in… (More)

- Aran Nayebi, Matt Vitelli
- 2015

We compare the performance of two different types of recurrent neural networks (RNNs) for the task of algorithmic music generation, with audio waveforms as input. In particular, we focus on RNNs that have a sophisticated gating mechanism , namely, the Long Short-Term Memory (LSTM) network and the recently introduced Gated Recurrent Unit (GRU). Our results… (More)

A central challenge in sensory neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of accurate computational models… (More)

We leverage vector space embeddings of sentences and nearest-neighbor methods to transform a small amount of labelled training data into a significantly larger training set using an unlabelled corpus. The quality of the larger training set is measured by prediction accuracy on a benchmark sentiment analysis task. Our results indicate it is possible to… (More)

- Aran Nayebi, Scott Aaronson, Aleksandrs Belovs, Luca Trevisan
- Quantum Information & Computation
- 2014

Given a random permutation f : [N ] → [N ] as a black box and y ∈ [N ], we want to output x = f −1 (y). Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but not on the input y. Classically, there is a data structure of size˜O(S) and an algorithm that with the… (More)

- Aran Nayebi, Surya Ganguli
- ArXiv
- 2017

Inspired by biophysical principles underlying nonlinear dendritic computation in neural circuits , we develop a scheme to train deep neu-ral networks to make them robust to adversar-ial attacks. Our scheme generates highly nonlin-ear, saturated neural networks that achieve state of the art performance on gradient based adver-sarial examples on MNIST,… (More)

- Aran Nayebi
- ArXiv
- 2012

- Aran Nayebi, Virginia Vassilevska Williams
- ArXiv
- 2014

We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in O(n 3) time, while the trivial algorithm in the quantum setting runs iñ O(n 2.5) time, using Grover search. A major open problem in classical algorithms is to… (More)

- Aran Nayebi
- Minds and Machines
- 2013

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to… (More)

- Aran Nayebi
- ArXiv
- 2009

Let R k (n) be the number of representations of an integer n as the sum of a prime and a k-th power for k ≥ 2. Furthermore, set E k (X) = |{n ≤ X, n ∈ I k , n not a sum of a prime and a k-th power}|. In the present paper we use sieve techniques to obtain a strong upper bound on R k (n) for n ≤ X with no exceptions, and we improve upon the results of A.… (More)