Related papers: Simulating Raga Notes with a Markov Chain of Order…
This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction…
Stochastic approximation (SA) is an iterative algorithm for finding the fixed point of an operator using noisy samples and widely used in optimization and Reinforcement Learning (RL). The noise in RL exhibits a Markovian structure, and in…
Resonance based numerical schemes are those in which cancellations in the oscillatory components of the equation are taken advantage of in order to reduce the regularity required of the initial data to achieve a particular order of error…
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing…
Music relies heavily on repetition to build structure and meaning. Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure. The Transformer (Vaswani…
In recent years, neural networks have been used to generate symbolic melodies. However, the long-term structure in the melody has posed great difficulty for designing a good model. In this paper, we present a hierarchical recurrent neural…
Criticality is a behavioral state in dynamical systems that is known to present the highest computation capabilities, i.e., information transmission, storage, and modification. Therefore, such systems are ideal candidates as a substrate for…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the…
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be…
Most of Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) algorithms in existing probabilistic programming systems suboptimally use only model priors as proposal distributions. In this work, we describe an approach for…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
This paper presents a novel method for the automated synthesis of probabilistic programs. The starting point is a program sketch representing a finite family of finite-state Markov chains with related but distinct topologies, and a PCTL…
Existing approaches to the synthesis of reactive systems typically involve the construction of transition systems such as Mealy automata. However, in order to obtain a succinct representation of the desired system, structured programs can…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
Algorithmic music composition is a way of composing musical pieces with minimal to no human intervention. While recurrent neural networks are traditionally applied to many sequence-to-sequence prediction tasks, including successful…
Methods for analyzing representations in neural systems have become a popular tool in both neuroscience and mechanistic interpretability. Having measures to compare how similar activations of neurons are across conditions, architectures,…
Ragas form the foundation for Indian Classical Music. The task of Raga Recognition has gained traction in the Music Information Retrieval community in the recent past, which can be attributed to the nuances of Indian Classical Music that…
Despite -- or perhaps because of -- their simplicity, n-grams, or contiguous sequences of tokens, have been used with great success in computational linguistics since their introduction in the late 20th century. Recast as k-mers, or…
Raga identification is an important problem within the domain of Indian Art music, as Ragas are fundamental to its composition and performance, playing a crucial role in music retrieval, preservation, and education. Few studies that have…