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.
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
We prove the ADO invariants are a q-holonomic family and establish recursion relations.
We formulate a probabilistic Markov property in discrete time under a dynamic risk framework with minimal assumptions. This is useful for recursive solutions to risk-sensitive versions of dynamic optimisation problems such as optimal prediction, where at each stage the recursion depends on the whole future. The propert…
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…
LASER compresses recursive model activations by exploiting their low-dimensional structure.
This paper simplifies complex game dynamics by using a recursive representation.
Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that summarize the past and future around an instance, we propose a novel architecture …
The Darboux-Egoroff system of PDEs with any number of independent variables plays an essential role in the problems of describing -dimensional flat diagonal metrics of Egoroff type and Frobenius manifolds. We construct a recursion operator and its inverse for symmetries of the Darboux-Egoroff system and des…
We introduce Recurrent Predictive State Policy (RPSP) networks, a recurrent architecture that brings insights from predictive state representations to reinforcement learning in partially observable environments. Predictive state policy networks consist of a recursive filter, which keeps track of a belief about the stat…
Study optimal hedging for claims with random weights in discrete time.
This paper develops efficient algorithms for multibody dynamics using screw and Lie group theory.
New spin on Hurwitz theory connects to Gromov-Witten theory and topological recursion.
Deep learning solves dynamic programming with recursive utility.
New approach solves utility maximization problems using Delta family.
New invariant simplifies computing geometric invariants of recursive group orbits.
Solves optimal stopping problem with Poisson constraints using jumps.
RISE framework unifies and improves time series learning with missing data.
New method for estimating treatment effects without complex propensity models.
Neural machine translation is a relatively new approach to statistical machine translation based purely on neural networks. The neural machine translation models often consist of an encoder and a decoder. The encoder extracts a fixed-length representation from a variable-length input sentence, and the decoder generates…
Pulling back the weight system associated with the spinor representation of the Lie algebra so(7) by the universal Vassiliev-Kontsevich invariant yields a numerical link invariant with values in formal power series. Computing some skein relations satisfied by this invariant, I derive a recursive algorithm for its evalu…
Modern machine learning techniques, such as convolutional, recurrent and recursive neural networks, have shown promise for jet substructure at the Large Hadron Collider. For example, they have demonstrated effectiveness at boosted top or W boson identification or for quark/gluon discrimination. We explore these methods…
Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet fail to efficiently represent and execute such neural networks, due to lack of s…
Training deep neural networks on large-scale datasets requires significant hardware resources whose costs (even on cloud platforms) put them out of reach of smaller organizations, groups, and individuals. Backpropagation, the workhorse for training these networks, is an inherently sequential process that is difficult t…
We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we obtain the existence of an (a,q) super-polynomial of all knots in 3-space. Our result has implications on the quantizatio…
Paper defines Farey Recursive Functions and explores their properties.
We study an optimal investment/consumption problem in a model capturing market and credit risk dependencies. Stochastic factors drive both the default intensity and the volatility of the stocks in the portfolio. We use the martingale approach and analyze the recursive system of nonlinear Hamilton-Jacobi-Bellman equatio…
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
Worldsheet skein D-module for Hopf link conormal uniquely determines partition functions.
While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
A new recursive mixture estimation algorithm improves VAE inference efficiency and accuracy.
We use categorical skew Howe duality to find recursion rules that compute categorified sl(N) invariants of rational tangles colored by exterior powers of the standard representation. Further, we offer a geometric interpretation of these rules which suggests a connection to Floer theory. Along the way we make progress t…
Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and distance approaches to recurrent, recursive, and convolutional neural networks. Re…
Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and implement dynamic market risk measures based on recursion and state economy representat…
Tab-TRM uses recursive model for insurance pricing on tabular data.
New recursion formula for non-orientable surfaces resolves divergences.
Harer and Zagier proved a recursion to enumerate gluings of a -gon that result in an orientable genus surface, in their work on Euler characteristics of moduli spaces of curves. Analogous results have been discovered for other enumerative problems, so it is natural to pose the following question: how large is t…
This paper studies recursive ensembles driven by Fibonacci updates, improving learning dynamics.
XR-Transformer accelerates XMC by recursively fine-tuning on multi-resolution objectives.
Solves a recursion for Gromov-Witten invariants of the unknot.
Dynamic risk measures follow law invariance principles over time.
New recursion found for hyperbolic sphere volumes.
A new probability distribution on full rooted trees helps in model selection.
Filter banks are a popular tool for the analysis of piecewise smooth signals such as natural images. Motivated by the empirically observed properties of scale and detail coefficients of images in the wavelet domain, we propose a hierarchical deep generative model of piecewise smooth signals that is a recursion across s…
Improved disentanglement of data factors using recursive training.
This work generalizes a formula linking Seiberg-Witten prepotential and topological recursion.
We describe a method for recursively calculating Gromov-Witten invariants of all blowups of the projective plane. This recursive formula is different from the recursive formulas due to Göttsche and Pandharipande in the zero genus case, and Caporaso and Harris in the case of no blowups. We use tropical curves and a recu…
Topological recursion recovers a specific partition function for colored knots.
Combines neural networks with splitting-up method for filtering equations.