We present a general learning-based approach for phrase-level sentiment analysis that adopts an ordinal sentiment scale and is explicitly compositional in nature. Thus, we can model the compositional effects required for accurate assignment of phrase-level sentiment. For example, combining an adverb (e.g., “very”) with a positive polar adjective (e.g., “good”) produces a phrase (“very good”) wi...

The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory which interpolate between given initial and final string configurations. Each instanton is characterized by a Riemann surface of genus h with n punctures, which...

In order to get the general framework describing a nonlocalizable object beyond the bilocal field theory early proposed by Markov and Yukawa, the quantization of space-time is reconsidered and further developed. Space-time quantities are there not only noncommutative with U -field describing the nonlocalizable object, as in the bilocal field theory, but also become noncommutative among themselv...

We study matrix string scattering amplitudes and matrix string instantons on a marked Riemann surface in the limit of a vanishing string coupling constant. We give an explicit parameterization of the moduli space of such instantons. We also give a description of the set of fermionic supermoduli. The integration over the supermoduli leads to the inclusion of picture changing operators at the int...

A new computational technique is presented by which large structured matrices can be inverted. The specified matrix is viewed as the input-output operator of a time-varying system. Recently developed state space algorithms which apply to such systems are then used to compute a QR factorization first and subsequently the inverse of the matrix, starting from a state realization of the matrix. The...

We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator...

The Schrödinger equation as a quantum superposition describes the atomic orbital as a linear difference functions basis set. Another alternative is that this equation could be written as a m-dimensional state space linear stochastic system with unknown matrix coefficients with smooth movements around the stationary region. Thus, the matrix is estimated in a probability sense considering the dis...

We propose CMSMs, a novel type of generic compositional models for syntactic and semantic aspects of natural language, based on matrix multiplication. We argue for the structural and cognitive plausibility of this model and show that it is able to cover and combine various common compositional NLP approaches ranging from statistical word space models to symbolic grammar formalisms.

Recent advances in tree structured sentence encoding models have shown that explicitly modeling syntax can help handle compositionality. More specifically, recent works by Socher et al. (2012), Socher et al. (2013), and Chen et al. (2013) have shown that using more powerful composition functions with multiplicative interactions within tree-structured models can yield significant improvements in...

In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to optimize ground-state approximations, implement real-time evolution and describe elementary ...