We use SMC with twist functions to improve probabilistic inference in LLMs.
problem Improving probabilistic inference in large language models.
method We use Sequential Monte Carlo with learned twist functions to estimate expected future values and focus inference on promising sequences.
result Twisted SMC improves the accuracy of language model inference and evaluation.
Twisted Neumann--Zagier matrices for quantum invariants.
problem Constructing quantum invariants from ideal triangulations.
method Define and compute twisted Neumann--Zagier matrices from combinatorics.
result Twisted 1-loop invariant equals adjoint twisted Alexander polynomial.
TDS provides exact samples for conditional distributions in diffusion models.
problem Lack of exact sampling methods for diffusion models.
method Sequential Monte Carlo (SMC) algorithm with twisting technique.
result TDS offers more accurate approximations with fewer particles compared to heuristics.
Paper proposes a new method for sampling from complex distributions.
problem Sampling from unnormalised density functions in complex distributions.
method Combines amortised and particle-based methods with reinforcement learning.
result Improves sampling from complex distributions compared to existing methods.
The paper explores non-trivial welded knots and ribbon torus-knots, proving their existence.
problem Proving the non-triviality of welded knots and ribbon torus-knots.
method By generating examples and determining the fundamental group of the concerned welded knot.
result Non-triviality of welded knots and ribbon torus-knots is demonstrated.
Improves inference-time alignment for diffusion models without updating weights.
problem Aligning diffusion models without updating weights for high-reward outputs.
method Trust-Region Iterative Twisted Sequential Monte Carlo (TRI-TSMC) for variance reduction and efficiency.
result Improves primary alignment objectives on text generation tasks.
Time-resolved angiography with interleaved stochastic trajectories (TWIST) has been widely used for dynamic contrast enhanced MRI (DCE-MRI). To achieve highly accelerated acquisitions, TWIST combines the periphery of the k-space data from several adjacent frames to reconstruct one temporal frame. However, this view-sha…
We introduce the concept of twisted contact groupoids, as an extension either of contact groupoids or of twisted symplectic ones, and we discuss the integration of twisted Jacobi manifolds by twisted contact groupoids. We also investigate the very close relationships which link homogeneous twisted Poisson manifolds wit…
New infinite families of twisted torus knots found.
problem Identifying new types of twisted torus knots.
method Finding new infinite families of twisted torus knots with a single negative twist.
result Eight new infinite families of twisted torus knots are discovered.
The study finds hyperbolic twisted torus links for certain twists.
problem Identifying hyperbolic twisted torus links.
method Analyzing (p,q)-torus links with r strands twisted s times. result All hyperbolic twisted torus links are identified for ∣s∣>3. The paper introduces a method to deform submanifolds in Euclidean space using Drinfel'd twists.
problem Constructing noncommutative deformations of submanifolds in Euclidean space.
method Using Drinfel'd twist deformation of differential geometry, the paper proposes a general procedure to construct noncommutative deformations of an embedded submanifold.
result The method allows for consistent projection of connections and can be applied to various submanifolds like cylinders and hyperboloids.
Paper constructs Chern character for higher twists and shows isomorphism between K-theory and cohomology.
problem Mapping higher twisted K-theory to higher twisted cohomology.
method Constructing Chern character for higher twists and showing isomorphism.
result Chern character gives isomorphism between higher twisted K-theory and higher twisted cohomology.
The paper studies the twisted Calabi flow on Kähler manifolds.
problem Analyzing the behavior of the twisted Calabi flow on compact Kähler manifolds.
method Establishing convexity, proving short-time existence, and demonstrating stability of the flow.
result The stability of the twisted Calabi flow near twisted constant scalar curvature Kähler metrics.
Construct noncommutative deformations of algebraic submanifolds in R^n.
problem Deforming algebraic submanifolds in noncommutative geometry.
method Using twisted differential geometry and Drinfel'd twists, constructing noncommutative deformations of algebraic submanifolds.
result Explicitly worked out deformations of quadrics in R^3.
In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem in twisted K-theory and find some applications in the study of twisted K-theory o…
Study on singular twisted links and virtual braids, extending knot theory concepts.
problem Extending knot theory concepts to singular twisted links and virtual braids.
method Definition and analysis of singular twisted virtual braids and their monoid structure.
result Presentation of monoid and reduced monoid for singular twisted virtual braids.
Paper proves any twisted link can be described as a unique twisted braid.
problem Understanding twisted links and braids.
method Proved using Alexander and Markov Theorems for classical braids and links.
result Any twisted link can be described as the closure of a unique twisted braid.
The paper extends knot theory to twisted virtual braids and links.
problem Generalizing knot theory to include twists.
method Introduced twisted virtual braids and proved theorems for twisted links.
result The Alexander and Markov theorems were extended to twisted links.
Solves infinite family of cubic polynomial problems.
problem Infinite family of twisted polynomial problems.
method Using Dehn twists and 9-adic expansions.
result Result of twisting depends on 9-adic expansion.
The paper introduces colorings and invariants for twisted links and shows how double coverings can be equivalent.
problem Understanding and distinguishing twisted links.
method Twisted intersection colorings and double coverings.
result There exist infinitely many pairs of twisted links with equivalent double coverings.
This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion class. By differential twists we will mean smooth U(1)-gerbes with connection, and w…
We study twisted Jacobi manifolds, a concept that we had introduced in a previous Note. Twisted Jacobi manifolds can be characterized using twisted Dirac-Jacobi, which are sub-bundles of Courant-Jacobi algebroids. We show that each twisted Jacobi manifold has an associated Lie algebroid with a 1-cocycle. We introduce t…
A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidem…
We generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form Σ×[0,1] for Σ a compact closed 2-manifold up to stable equivalence. We introduce a related algebraic structure known as twisted virtual bikeigebras whose axiom…
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
New families of twisted torus knots found with essential surfaces.
problem Whether all twisted torus knots have essential tori.
method Analyzing sequences of twists on torus knots.
result Found two new families of toroidal twisted torus knots.
Formula for Alexander polynomial of twisted torus knots derived.
problem Calculating Alexander polynomial for a specific class of knots.
method Knot group presentation combined with Fox's calculus.
result Explicit formula for Alexander polynomial of twisted torus knots.
Study lattice paths from twist knots and double twist knots.
problem Understanding combinatorics of twist knots and double twist knots.
method Analyzing quiver generating series of HOMFLY-PT polynomial limits.
result Lattice path models for twist knots and double twist knots.
The paper classifies twisted torus links that are unlinks.
problem Identifying conditions for twisted torus links to be unlinks.
method Characterization of parameter families (p,q,r,s) for unlinking twisted torus links. result Complete characterization of parameter families for unlinking twisted torus links.
Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.
problem Modeling and understanding twisted Spin^c-bordism and its dual.
method Geometric construction using bundle gerbes, gerbe modules, and eta-invariants.
result Definition of a twisted anomaly map from differential twisted K-theory to differential Anderson dual of twisted Spin^c-bordism.
Paper shows how to twist knots to make them trivial or non-trivial.
problem Understanding the behavior of knots under twist-spinning operations.
method Analyzes the effect of m1- and m2-twist-spinning on classical knots. result Shows conditions for a knot to be trivial or non-trivial after certain twist-spinning operations.
The paper uses Floer homology to study twist coefficients and their behavior after capping off.
problem Behavior of twist coefficients after capping off a boundary component.
method Heegaard Floer homology to constrain twist coefficients.
result Results about fractional Dehn twists and Floer homology of cyclic branched covers.
We study the characteristic foliation of a twisted Jacobi manifold. We show that a twisted Jacobi manifold is foliated into leaves that are, according to the parity of the dimension, endowed with a twisted contact or a twisted locally conformal symplectic structure.
A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in F, the genus 2 Heegaard surface for S3. Primitive/primitive and primitive/Seifert knots lie in F in a particular way. Dean gives sufficient conditions for the parameters of the tw…
The union of singular orbits of an effective locally smooth circle action on the 4-sphere consists of two 2-knots, K and K′, intersecting at two points transversely. Each of K and K′ is called a branched twist spin. A twist spun knot is an example of a branched twist spin. The Gluck twists along…
The article examines twisted cohomologies on algebraic and analytic varieties.
problem Understanding and comparing twisted cohomologies on algebraic and analytic varieties.
method Comparison and definition of twisting parameters in both categories, algebraic and analytic.
result Reviewed isomorphisms of twisted cohomologies for cohomologous twisting parameters.
The paper classifies hyperbolic and satellite T-links formed by twisting.
problem Classifying hyperbolic and satellite T-links formed by twisting.
method Classification through Dehn filling and analysis of parent links.
result Classification of hyperbolic and satellite T-links formed by twisting.
Lee's work on twisted torus knots with Fibonacci parameters is extended to Horadam parameters.
problem Classifying twisted torus knots with Horadam parameters.
method Using recursive Horadam parameters to generalize Lee's work on Fibonacci parameters.
result Families of twisted torus knots with Horadam parameters are provided.
In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S1-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure Kαi⊗Kβj→Kα+βi+j are derived. Our approach provides a uniform framework …
Satellite links with many twists have simpler companions.
problem Relationship between satellite and companion links' complexity.
method Constructing satellite links with multiple full twists and analyzing their companion links.
result Satellite links with many twists have simpler companion links.
We prove an existence result for twisted Kähler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.
Gluck twisting certain knots results in standard 4-spheres.
problem Understanding when Gluck twists yield standard 4-spheres.
method Analyzing smooth homotopy 4-spheres and diffeomorphisms.
result Infinite collection of twisted doubles of corks are standard.
We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hiros…
The paper calculates knot invariants using Blanchfield forms and obstructs sliceness.
problem Computing and obstructing the sliceness of knots.
method Algorithmic computation of twisted signature invariants using twisted Blanchfield forms and satellite formulas.
result Illustrated algorithm for (2,q)-torus knots and obstruction of sliceness for certain knots. The paper studies twisted Alexander polynomials for knot groups in various extensions.
problem Understanding twisted Alexander polynomials in knot groups for different extensions.
method Developed mod p formula for twisted Alexander polynomials and studied central extensions.
result Established formulas for twisted Alexander polynomials in knot groups for various extensions.
Paper studies convergence of Yang-Mills-Higgs flow on Kähler manifolds.
problem Analyzing convergence of Yang-Mills-Higgs flow for twisted Higgs pairs.
method Proves convergence to a reflexive twisted Higgs sheaf outside a closed subset.
result Limiting twisted Higgs sheaf is isomorphic to the double dual of graded twisted Higgs sheaves.
Solves generalized twisted rabbit problems for higher degree polynomials.
problem When a quadratic polynomial is twisted by a cyclic subgroup, what polynomial is equivalent?
method Uses d2-adic expansion instead of 4-adic for higher degree polynomials. result Provides a solution that depends on the d2-adic expansion of the power of the mapping class element. It follows from earlier work of Silver-Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopf link. We now show that twisted Alexander polynomials also detect the trefoil and the figure-8 knot, that twisted Alexander polynomials detect whether a link is split and that twisted Alexand…