arXiv research

Tensor models decode human perception and memory using SPO triples.

Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predict…

This study explains and mitigates inflated returns and turnover in SPO-based portfolio optimization.

This paper improves risk bounds and calibration for smart predict-then-optimize method.

SPO optimizes LLMs by eliminating group-based baselines and variance issues.

Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently…

Develops active learning method for linear optimization with margin-based criterion.

New loss function handles uncertain constraints in CSLO problems.

We consider the space of differential operators $\mathcal{D}_{λμ}$ acting between $λ$- and $μ$-densities defined on $S^{1|2}$ endowed with its standard contact structure. This contact structure allows one to define a filtration on $\mathcal{D}_{λμ}$ which is finer than the classical one, obtained by writting a differen…

A new autoregressive SPO method improves decision-making for dependent data.

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted…

Proposes BU-SPO method to improve text classification robustness.

Paper proposes SPO paradigm for better portfolio optimization in real markets.

The paper optimizes portfolios by selecting financial ratios via PCA for better value investment.

In this paper, we show that the Lie superalgebra $\mathfrak{spo}(2l+2|n)$ is into the intersection of Lie superalgebra of contact vector fields $\mathcal{K}(2l+1|n)$ and the Lie superalgebra of projective vector fields $\mathfrak{pgl}(2l+2|n)$. We use mainly the embedding used by P. Mathonet and F. Radoux in "\textit{ …

dboost optimizes prediction models for convex cone problems.

Decision trees improve decision-making by optimizing predictions of unknown parameters.

In this paper, we generalize the known results on the super circles $S^{1|1}$ and $S^{1|2}$. We construct the fine equivariant quantization on the super circle $S^{1|n}$ for $n\geqslant 3$. The equivariant Lie superalgebra is $\spo(2|n)$ which is constituted of the contact projective vector fields on $S^{1|n}$. In orde…

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under certain conditions, SVGD experiences a theoretical pitfall, {\it i.e.}, particles te…

New method identifies latent treatment effects from proxy models.

The paper integrates Lie-Leibniz triples into Lie group-rack triples.

Improves drug properties using a novel LLM and reinforcement learning.

Introduces new spectral triples for parabolic geometry.

Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each triple point, is a triple-crossing diagram of the link. We give a set of diagrammatic moves on triple-crossing diagrams analogous to the Re…

Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise disjoint. We conjecture that it can be algorithmically checked if an (ordered or unorde…

Triple linking numbers were defined for 3-component oriented surface-links in 4-space using signed triple points on projections in 3-space. In this paper we give an algebraic formulation using intersections of homology classes (or cup products on cohomology groups). We prove that spherical links have trivial triple lin…

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point $p$ of the cylinder is called {\em coherent} if all three branches intersect at $p$ pairwise with the same index. A {\em triple unknotting} of a classical knot $K$ is a homotopy which connects $K$ with the trivial knot and which has as singu…

Extends Einstein-Hilbert action to higher-order spectral triples.

Computing Chern-Simons action for perturbed Dirac triples

In this paper we present a systematic method to generate prime knot and prime link minimal triple-point projections, and then classify all classical prime knots and prime links with triple-crossing number at most four. We also extend the table of known knots and links with triple-crossing number equal to five. By intro…

In the 1950's Milnor defined a family of higher order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received and fruitful study since its inception. In the case that $L$ has vanishing pairwise linking numbers, this triple linking number gives an integ…

We give the classification of solvable and splitting Lie triple system and it turn that, up to isomorphism there exist 7 non isomorphic canonical Lie triple systems and 6 non isomorphic splitting canonical Lie triple systems and find the solvable Lie algebras associated.

Study describes moduli of quaternionic hyperbolic triples of points.

The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. We consider a certain $m$-component $T^2$-link ($m \geq 3$) determined from two commutative pure $m$-braids $a$ and $b$. We present the triple linking number of such a $T^2$-link, by usin…

Extends Manin triples to Lie bialgebroids over Lie groupoids.

Invariant detects triple points in sphere immersions.

This paper shows how to create surface-links with many triple points.

Paper explores relationships between triple chords and a specific homotopy relation in knot theory.

Homotopy on nanophrases is an equivalence relation defined using some data called a homotopy data triple. We define a product on homotopy data triples. We show that any homotopy data triple can be factorized into a product of prime homotopy data triples and this factorization is unique up to isomorphism and order. If a…

Symmetric spaces' connections form Lie admissible triple algebras.

Constructs perturbations of a minimal surface with triple junctions.

Characterizes critical points in convex double and triple bubbles.

A smart method predicts and optimizes decisions online with resource constraints.

LA-Courant algebroids link double Lie bialgebroids via Manin triples.

Construct spectral triples on C*-algebras with group actions.

This paper compiles and calculates triple point numbers for surface-links in Yoshikawa's table.

Triple-crossing number bound for knots and links, especially torus knots.