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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)

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)

- 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, 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)

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
- ArXiv
- 2012

- 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)

- Aran Nayebi
- ArXiv
- 2009

- Aran Nayebi
- 2009

Building upon the work of Carl Pomerance and others, the central purpose of this discourse is to discuss the distribution of base-2 pseudoprimes, as well as improve upon Pomerance's conjecture regarding the Carmichael number counting function [8]. All conjectured formulas apply to any base b ≥ 2 for x ≥ x 0 (b). A table of base-2 pseudoprime, 2-strong… (More)