A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New statistical model improves protein alignment accuracy.
Defect of knot polynomials remains invariant under certain braid substitutions.
We show that the Lawrence--Krammer representation is unitary. We explicitly present the non-singular matrix representing the sesquilinear pairing invariant under the action. We show that reversing the orientation of a braid is equivalent to the transposition of its Lawrence--Krammer matrix followed by a certain conjuga…
We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by iteration of a 2-dimensional topological substitution. We prove that there is no primitive substitutive tiling of the hyperbolic plane $\mathbb{H…
A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT), effectively substitutes the correlation coefficient matrix used in treelets with a symm…
A method estimates causal parameters using a latent variable recovery.
We elaborate on the recent observation that evolution for twist knots simplifies when described in terms of triangular evolution matrix , not just its eigenvalues , and provide a universal formula for , applicable to arbitrary rectangular representation . This expression is in terms of s…
We introduce Markov substitute processes, a new model at the crossroad of statistics and formal grammars, and prove its main property : Markov substitute processes with a given support form an exponential family.
Study generalizes Lebesgue curves to new space-filling and fractal sets.
The definition of deposit substitutes in Philippine tax law fails to consider the maturity of a debt instrument. This makes it possible for long-term bonds to be considered as deposit substitutes if they meet the 20-lender rule, taxable at 20% final tax. However, long-term debt instruments cannot realistically function…
The topological entropy of a braid is the infimum of the entropies of all homeomorphisms of the disc which have a finite invariant set represented by the braid. When the isotopy class represented by the braid is pseudo-Anosov or is reducible with a pseudo-Anosov component, this entropy is positive. Fried and Kolev prov…
We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the -Weyl algebra of -operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discus…
New method removes contrastive loss by adding a prediction head, revealing learning mechanisms.
Geometric theory explains substitutability in market outcomes based on production constraints.
SAFER method certifies robustness to word substitutions without model structure.
New algorithm for clustering data streams with no substitutions.
The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W representation familiar from character calculus applications to matrix models and Hurwi…
We study the sample-based k-median clustering objective under a sequential setting without substitutions. In this setting, an i.i.d. sequence of examples is observed. An example can be selected as a center only immediately after it is observed, and it cannot be substituted later. The goal is to select a set of centers …
This paper investigates and compares currency substitution between the currencies of Central and Eastern European (CEE) countries and the euro. In addition, we develop a model with microeconomic foundations, which identifies difference between currency substitution and money demand sensitivity to exchange rate variatio…
In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a …
Enhances influence functions for deep models without costly Hessian inversion.
In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression …
PASS protects private attributes by stochastically substituting data.
Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limi…
Deep neural networks (DNNs) are one of the most prominent technologies of our time, as they achieve state-of-the-art performance in many machine learning tasks, including but not limited to image classification, text mining, and speech processing. However, recent research on DNNs has indicated ever-increasing concern o…
Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically analyze this method and its properties, and show how it can be viewed as a type of 2…
A novel algorithm converges for solving a specific matrix decomposition problem.
Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict…
This paper explores how the generalization of substitute classifiers affects the success of black-box adversarial attacks.
Network models assume unrealistic idiosyncratic risk, which can be mitigated by allowing for correlated shocks.
The paper investigates polynomial alternatives to softmax in transformer models.
The paper introduces a method to improve adversarial robustness in neural networks using randomized perturbations.
Develops methods to improve demand counterfactuals from imperfect proxies.
Flexible Kernels for Protein Property Prediction
We analyze the practical consequences of the bilateral counterparty risk adjustment. We point out that past literature assumes that, at the moment of the first default, a risk-free closeout amount will be used. We argue that the legal (ISDA) documentation suggests in many points that a substitution closeout should be u…
We continue to develop the tensor-algebra approach to knot polynomials with the goal to present the story in elementary and comprehensible form. The previously reviewed description of Khovanov cohomologies for the gauge group of rank N-1=1 was based on the cut-and-join calculus of the planar cycles, which are involved …
Integrated Assessment Models (IAMs) are mainstay tools for assessing the long-term interactions between climate and the economy and for deriving optimal policy responses in the form of carbon prices. IAMs have been criticized for controversial discount rate assumptions, arbitrary climate damage functions, and the inade…
The "color" in the colored Jones polynomial is an integer parameter. In this paper, a periodic pattern of the values of the colored Jones polynomial at the second and the third roots of unity is found. If we substitute -1 to the colored Jones polynomial, the value is alternately 1 or the determinant of the given link. …
New proof shows how to fill a square with Fibonacci curve.
The goal of homomorphic encryption is to encrypt data such that another party can operate on it without being explicitly exposed to the content of the original data. We introduce an idea for a privacy-preserving transformation on natural language data, inspired by homomorphic encryption. Our primary tool is {\em obfusc…
We present Distributed Equivalent Substitution (DES) training, a novel distributed training framework for large-scale recommender systems with dynamic sparse features. DES introduces fully synchronous training to large-scale recommendation system for the first time by reducing communication, thus making the training of…
Generative model learns from simpler distributions on Lie groups.
Deep neural network (DNN) as a popular machine learning model is found to be vulnerable to adversarial attack. This attack constructs adversarial examples by adding small perturbations to the raw input, while appearing unmodified to human eyes but will be misclassified by a well-trained classifier. In this paper, we fo…
We propose a procedure for assigning a relevance measure to each explanatory variable in a complex predictive model. We assume that we have a training set to fit the model and a test set to check the out of sample performance. First, the individual relevance of each variable is computed by comparing the predictions in …
We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimat…
The paper studies symplectic operations on Stein fillings of Brieskorn singularities.
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual and . These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conv…
Is the elasticity of intertemporal substitution (EIS) more or less than one? This question can be answered by confronting theoretical results of asset pricing models with investor behaviour during episodes of stock market panic. If we consider these episodes as periods of high risk aversion, then lower asset prices are…