Everybody Compose: Deep Beats To Music

This project presents a deep learning approach to generate monophonic melodies based on input beats, allowing even amateurs to create their own music compositions. Three effective methods - LSTM with Full Attention, LSTM with Local Attention, and Transformer with Relative Position Representation - are proposed for this novel task, providing great variation, harmony, and structure in the generated music. This project allows anyone to compose their own music by tapping their keyboards or ``recoloring'' beat sequences from existing works.Comment: Accepted MMSys '2

Variational quantum solutions to the Shortest Vector Problem

A fundamental computational problem is to find a shortest non-zero vector in Euclidean lattices, a problem known as the Shortest Vector Problem (SVP). This problem is believed to be hard even on quantum computers and thus plays a pivotal role in post-quantum cryptography. In this work we explore how (efficiently) Noisy Intermediate Scale Quantum (NISQ) devices may be used to solve SVP. Specifically, we map the problem to that of finding the ground state of a suitable Hamiltonian. In particular, (i) we establish new bounds for lattice enumeration, this allows us to obtain new bounds (resp.~estimates) for the number of qubits required per dimension for any lattices (resp.~random q-ary lattices) to solve SVP; (ii) we exclude the zero vector from the optimization space by proposing (a) a different classical optimisation loop or alternatively (b) a new mapping to the Hamiltonian. These improvements allow us to solve SVP in dimension up to 28 in a quantum emulation, significantly more than what was previously achieved, even for special cases. Finally, we extrapolate the size of NISQ devices that is required to be able to solve instances of lattices that are hard even for the best classical algorithms and find that with approximately $10^3$ noisy qubits such instances can be tackled

Improved Classical and Quantum Algorithms for Subset-Sum

We present new classical and quantum algorithms for solving random subset-sum instances. First, we improve over the Becker-Coron-Joux algorithm (EUROCRYPT 2011) from $\tilde{\mathcal{O}}(2^{0.291 n})$ downto $\tilde{\mathcal{O}}(2^{0.283 n})$, using more general representations with values in $\{-1,0,1,2\}$. Next, we improve the state of the art of quantum algorithms for this problem in several directions. By combining the Howgrave-Graham-Joux algorithm (EUROCRYPT 2010) and quantum search, we devise an algorithm with asymptotic cost $\tilde{\mathcal{O}}(2^{0.236 n})$, lower than the cost of the quantum walk based on the same classical algorithm proposed by Bernstein, Jeffery, Lange and Meurer (PQCRYPTO 2013). This algorithm has the advantage of using \emph{classical} memory with quantum random access, while the previously known algorithms used the quantum walk framework, and required \emph{quantum} memory with quantum random access. We also propose new quantum walks for subset-sum, performing better than the previous best time complexity of $\tilde{\mathcal{O}}(2^{0.226 n})$ given by Helm and May (TQC 2018). We combine our new techniques to reach a time $\tilde{\mathcal{O}}(2^{0.216 n})$. This time is dependent on a heuristic on quantum walk updates, formalized by Helm and May, that is also required by the previous algorithms. We show how to partially overcome this heuristic, and we obtain an algorithm with quantum time $\tilde{\mathcal{O}}(2^{0.218 n})$ requiring only the standard classical subset-sum heuristics

Improved Classical and Quantum Algorithms for the Shortest Vector Problem via Bounded Distance Decoding

The most important computational problem on lattices is the Shortest Vector Problem (SVP). In this paper, we present new algorithms that improve the state-of-the-art for provable classical/quantum algorithms for SVP. We present the following results. $\bullet$ A new algorithm for SVP that provides a smooth tradeoff between time complexity and memory requirement. For any positive integer $4\leq q\leq \sqrt{n}$, our algorithm takes $q^{13n+o(n)}$ time and requires $poly(n)\cdot q^{16n/q^2}$ memory. This tradeoff which ranges from enumeration ($q=\sqrt{n}$) to sieving ($q$ constant), is a consequence of a new time-memory tradeoff for Discrete Gaussian sampling above the smoothing parameter. $\bullet$ A quantum algorithm for SVP that runs in time $2^{0.953n+o(n)}$ and requires $2^{0.5n+o(n)}$ classical memory and poly(n) qubits. In Quantum Random Access Memory (QRAM) model this algorithm takes only $2^{0.873n+o(n)}$ time and requires a QRAM of size $2^{0.1604n+o(n)}$, poly(n) qubits and $2^{0.5n}$ classical space. This improves over the previously fastest classical (which is also the fastest quantum) algorithm due to [ADRS15] that has a time and space complexity $2^{n+o(n)}$. $\bullet$ A classical algorithm for SVP that runs in time $2^{1.741n+o(n)}$ time and $2^{0.5n+o(n)}$ space. This improves over an algorithm of [CCL18] that has the same space complexity. The time complexity of our classical and quantum algorithms are obtained using a known upper bound on a quantity related to the lattice kissing number which is $2^{0.402n}$. We conjecture that for most lattices this quantity is a $2^{o(n)}$. Assuming that this is the case, our classical algorithm runs in time $2^{1.292n+o(n)}$, our quantum algorithm runs in time $2^{0.750n+o(n)}$ and our quantum algorithm in QRAM model runs in time $2^{0.667n+o(n)}$.Comment: Faster Quantum Algorithm for SVP in QRAM, 43 pages, 4 figure

Investigating the modulation of stimulus types on language switching costs: Do semantic and repetition priming effect matter?

IntroductionIn the present study, I investigated the influence of stimulus types on bilingual control in the language switching process. The commonly employed stimuli in language switching studies – Arabic digits and objects – were compared to further investigate the way in which inhibitory control could be modulated by semantic and repetition priming effects. The digit stimuli have two unique characteristics in the language switching paradigm, for example, they are present repeatedly and are semantically related to each other, compared with pictural stimuli. Thus, these unique characteristics might influence the operation of inhibitory control in bilingual language production, modulating the size and asymmetry of switching costs.MethodsTwo picture control sets were set up to match those characteristics: (1) a semantic control set, in which picture stimuli belong to the same category group, such as, animals, occupations or transportation and specific semantic categories were presented in a blocked condition; and (2) a repeated control set, in which nine different picture stimuli were repeatedly presented like the Arabic digits from 1 to 9.ResultsWhen comparing the digit condition and the standard picture condition, analyses of naming latencies and accuracy rates revealed that switching costs were reliably smaller for digit naming than for picture naming and the L1 elicited more switching costs for picture naming than for digit naming. On the other hand, when comparing the digit condition and the two picture control sets, it was found that the magnitude of switching costs became identical and the asymmetry in switching costs became much smaller between the two languages

Provable Dual Attacks on Learning with Errors

Learning with Errors (LWE) is an important problem for post-quantum cryptography (PQC) that underlines the security of several NIST PQC selected algorithms. Several recent papers have claimed improvements on the complexity of so-called dual attacks on LWE. These improvements make dual attacks comparable to or even better than primal attacks in certain parameter regimes. Unfortunately, those improvements rely on a number of untested and hard-to-test statistical assumptions. Furthermore, a recent paper claims that the whole premise of those improvements might be incorrect. The goal of this paper is to improve the situation by proving the correctness of a dual attack without relying on any statistical assumption. Although our attack is greatly simplified compared to the recent ones, it shares many important technical elements with those attacks and can serve as a basis for the analysis of more advanced attacks. Our main contribution is to clearly identify a set of parameters under which our attack (and presumably other recent dual attacks) can work. Furthermore, our analysis completely departs from the existing statistics-based analysis and is instead rooted in geometry. We also compare the regime in which our algorithm works to the ``contradictory regime\u27\u27 of [Ducas and Pulles,2023]. We observe that those two regimes are essentially complementary. Finally, we give a quantum version of our algorithm to speed up the computation. The algorithm is inspired by [Albrecht, and Shen,2022] but is completely formal and does not rely on any heuristics