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When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity bound for such methods for convergence to approximate…
Expensive multi-objective optimization is a prevalent and crucial concern in many real-world scenarios, where sample-efficiency is vital due to the limited evaluations to recover the true Pareto front for decision making. Existing works…
In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the $SU(3)_H$-gauge family symmetry. We also develop some…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
I discuss the construction of realistic superstring standard--like models in the four dimensional free fermionic formulation. I discuss the massless spectrum of the superstring standard--like models and the texture of fermion mass matrices.…
We define the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra that is an appropriate noncommutative generalization of the vertex operator superalgebra. We also illustrate an example that can be viewed as a…
The discovery that the number of physically consistent string vacua is on the order of 10^500 has prompted several statistical studies of string phenomenology. Contained here is one such study that focuses on the Weakly Coupled Free…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
Plant breeding programs use data obtained from multi-environment selection experiments to produce improved varieties with the ultimate aim of maintaining high levels of genetic gain. Selection accuracy can be improved with the use of…
We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of…
We study the problem of evaluating a Monadic Second Order (MSO) query over strings under updates in the setting of direct access. We present an algorithm that, given an MSO query with first-order free variables represented by an unambiguous…
We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the…
In the author's paper (Phys.Rev. D80, 041901(R) (2009)), the integrable structure of the symmetry reduced bosonic dynamics in the low energy heterotic string effective theory was presented. In that paper, for a complete system of massless…
In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
We develop a hierarchical matrix construction algorithm using matrix-vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses $\mathcal{O}(\log n)$ applications of the matrix on…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…