New estimator for SDEs is shown to be an adjoint state method.
problem Estimating gradients for overparameterized SDEs efficiently.
method Demonstrates generator gradient estimator as an adjoint state method.
result Generator gradient estimator is an adjoint state method for SDEs.
Proposes DAM for optimizing discrete generative models.
problem Challenges in optimizing discrete generative models.
method Discrete Adjoint Matching (DAM) for discrete state spaces.
result Demonstrates effectiveness on synthetic and mathematical reasoning tasks.
Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.
problem Challenges in learning discrete neural samplers due to gradients and combinatorial complexity.
method Introduces discrete ASBS, a unified framework that extends adjoint Schrödinger bridge sampler to discrete spaces.
result Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.
Investigates the relationship between ResNets and Neural ODEs, quantifying their closeness and providing training methods.
problem Quantifying the distance between ResNet dynamics and Neural ODE solutions.
method Bounding the distance between hidden state trajectories and Neural ODE solutions, using gradient descent and Heun's method.
result Gradient descent and Heun's method can implicitly regularize ResNets towards Neural ODEs, especially for smooth residual functions.
This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This is due to the mixed Lagrangian-Eulerian formulation of large-displacement FSI in…
Adjoint SA speeds up bioprocess parameter learning.
problem Challenges in digital twin development for biomanufacturing.
method Adjoint sensitivity analysis on multi-scale enzymatic reaction networks.
result Resilient sensitivities reveal bioprocess regulatory mechanisms.
NDDV estimates data point value from a single stochastic trajectory.
problem Estimating marginal contributions of data points over stochastic training paths.
method Introduces Neural Dynamic Data Valuation (NDDV) using stochastic state and adjoint equations.
result NDDV provides a one-run, trajectory-conditioned estimator of data point value.
The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.
problem Does the coadjoint orbits of Lie groups support a Kähler structure?
method Examined three Lie groups: Weyl-Heisenberg, SU(2), and SU(1,1). Used coherent and squeezed states to explore Kähler structures.
result Coherent states provide Kähler embeddings, while squeezed states only symplectic embeddings.
Efficiently differentiate functions of large matrices using new adjoint systems.
problem Differentiating functions of large matrices in scientific and probabilistic machine learning models.
method Deriving and implementing new adjoint systems for Lanczos and Arnoldi iterations in JAX.
result Efficient differentiation of PDEs, Gaussian process models, and Bayesian neural networks.
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formalism in which self-adjoint (Schroedinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we …
SNAPO optimizes policies for complex sequential decisions using differentiable simulation.
problem Optimizing policies for high-dimensional, sequential decisions under uncertainty.
method Embeds neural policy in a differentiable simulator, computes gradients efficiently.
result Produces sensitivities at a cost proportional to one reverse pass, regardless of sensitivity count.
Deep learning models for inverse problems are evaluated over time.
problem Solving inverse problems for natural systems from measurements.
method Comparing deep learning approaches on benchmark tasks and proposing neural-adjoint method.
result Neural-adjoint method achieves best performance in many scenarios.
Framework calculates positional influence in causal residual Transformers.
problem Understanding positional influence in causal residual Transformers.
method Adjoint-sensitivity framework for positional influence in causal residual Transformers.
result Exact evolution of adjoint-energy influence density and decomposition into residual transmission, nonlocal Volterra, and local channels.
Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow us to determine exactly which sums of adjoint orbits in su(m) and pro…
Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.
problem Limited theory and algorithms for sampling infinite-dimensional function spaces.
method Adjoint Sampler for infinite-dimensional function spaces based on stochastic maximum principle.
result FAS achieves superior performance in synthetic and real systems.
Paper proves index theorem for self-adjoint elliptic boundary problems.
problem Proving index theorem for self-adjoint elliptic boundary problems.
method Topological and pseudo-differential methods, generalized Atiyah-Singer approach.
result Removed technical assumption to prove index theorem.
We use AD to compute gradients for complex functionals in stochastic model calibration.
problem Computing gradients for functions involving expectations in stochastic models.
method Automatic Adjoint Differentiation and parallelization.
result Faster and easier to implement approaches for gradient computation.
We establish a lower bound for the real eigenvalues of a Laplace-Beltrami operator with an L∞-drift term. We make no assumptions that the operator is self-adjoint or that the drift has any additional regularity. In the case where the operator is self-adjoint, this establishes a lower bound on the spectrum witho…
It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the n-wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on …
Derives adjoint polynomials of torus knots in explicit form.
problem Understanding adjoint invariants of torus knots.
method Closed-form double sum expression derivation.
result Explicit double sum form of adjoint polynomials.
Unified framework for convergence of discrete diffusion models without state space size dependence.
problem Fundamental limitations in existing convergence theory for discrete diffusion models, especially under singular priors and large vocabularies.
method Unified adjoint-equation-based framework that establishes dimension-free convergence guarantees in any integral probability metric (IPM).
result First dimension-free convergence bounds applicable to both masked and uniform priors, free of state space size S. Graph neural networks learn PDEs from sparse, irregular data.
problem Learning PDEs from irregularly spaced data.
method Continuous-time differential model with graph neural networks for arbitrary discretizations.
result Efficient inference with continuous-time adjoint method.
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.
AdjointDEIS simplifies diffusion model optimization.
problem Optimizing diffusion models with respect to a differentiable metric.
method Novel bespoke ODE solvers for continuous adjoint equations.
result Continuous adjoint equations simplify to a simple ODE, improving efficiency.
This paper explores hyperkähler structures on specific orbits using different methods.
problem Investigate hyperkähler structures on adjoint orbits.
method Infinite dimensional hyperkähler reduction and symplectic geometry.
result Differences and connections between two methods are thoroughly investigated.
Proves formal self-adjointness of certain differential operators.
problem Verifying conjectures about differential operators.
method Proving formal self-adjointness through mathematical proof.
result Proves two conjectures about differential operators.
Study of adjoint orbits in simplest non-trivial Lie algebra case.
problem Geometric properties of adjoint orbits in sl(2,R). method Analysis of adjoint orbits, showing three possibilities: hyperboloids or cones.
result Just three possibilities for adjoint orbits: hyperboloids or cones.
Abstracts a construction of boundary triplets for self-adjoint elliptic problems.
problem Computing the index of families of self-adjoint elliptic boundary problems.
method Abstract axiomatic version of boundary triplets and their applications.
result Analytic proof of index theorem and computation of index differences.
Derives variance kernel for reaction boundary in financial models.
problem Separating components in financial volatility models.
method Operational-time variance kernel, damped Abel response kernel, closed asymptotic form.
result Operational variance has a closed asymptotic form involving various parameters.
Derives operational-time variance kernel for reaction boundaries in financial markets.
problem Separating components in volatility models to better understand market dynamics.
method Derives a variance kernel for a latent-order-book reaction boundary, separating structural boundary cumulant, clock projection, and pricing-measure choice.
result Operational variance has a closed asymptotic form for long-memory forcing, with effective signed-forcing intensity and resilience.
Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians.
problem Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians. method Consider the sum of the adjoint Reidemeister torsions and prove integrality for twist knots and meridians.
result Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians. Quantizes Stäckel integrable systems into self-adjoint operators.
problem Quantizing Stäckel integrable systems into self-adjoint operators.
method Constructs commutative self-adjoint operators from quadratic Hamiltonians in involution.
result Proves multiplicative separation of variables for Stäckel integrable systems.
We give explicit descriptions of the adjoint group of the Coxeter quandle QW associated with an arbitrary Coxeter group W. The adjoint group of QW turns out to be an intermediate group between W and the corresponding Artin group AW, and fits into a central extension of W by a finitely generated free abel…
Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…
Paper analyzes double twist knots using adjoint hyperbolic torsion polynomial.
problem Determining the genus and fibering of double twist knots.
method Uses adjoint hyperbolic torsion polynomial to analyze double twist knots.
result The adjoint hyperbolic torsion polynomial determines the genus and fibering of double twist knots.
Derives adjoint formulas for matrix operations and applies them to specific cases.
problem Computing adjoints for matrix operations and specific matrix types.
method Derives adjoint formulas for matrix operations and applies them to specific cases.
result Closed-form expressions for adjoints in specific matrix types.
DA-PredGAN uses GANs for accurate COVID-19 spread predictions and data assimilation.
problem Predicting and understanding the spread of COVID-19.
method Generative adversarial network (GAN) for predictions and data assimilation.
result DA-PredGAN accurately predicts and assimilates COVID-19 spread data.
ACA method improves gradient estimation for neural ODEs, reducing error and training time.
problem Inaccurate gradient estimation methods hinder the performance of neural ODEs on benchmark tasks.
method Adaptive Checkpoint Adjoint (ACA) method that applies trajectory checkpointing, deletes redundant components, and supports adaptive solvers.
result ACA reduces error rate by half and training time by half compared to adjoint and naive methods on image classification tasks.
We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e. partial flag varieties associated to maximal parabolic subgroups in a simple algebraic group. We explain how the decomposition is concentrated in global sections for so-called (co)minuscule and (co)…
Explicit formula for Reidemeister torsion of two-bridge knots.
problem Calculating Reidemeister torsion for two-bridge knots.
method Provided an explicit formula and proved vanishing identities.
result Adjoint Reidemeister torsion satisfies vanishing identities.
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in p…
The paper explores self-adjointness of Laplace-Beltrami operator on special geometric manifolds.
problem Characterizing self-adjoint extensions of the Laplace-Beltrami operator on α-Grushin manifolds. method Introducing an exotic calculus of pseudodifferential operators adapted to the geometry of the singularity.
result Criterion for essential self-adjointness and determination of several self-adjoint extensions.
Study extends Vogel's universality to torus knots in adjoint representation.
problem Applying Vogel's universality to knot invariants in adjoint representation theory.
method Extending Vogel's parameters to include torus knots T[m,n] and focusing on T[4,n] with odd n. result Unified description of adjoint invariants for torus knots T[4,n] with odd n. QAM uses adjoint matching to optimize continuous-action RL policies efficiently.
problem Efficient optimization of expressive diffusion or flow-matching policies with respect to a Q-function.
method QAM leverages adjoint matching to bypass the numerical instability of backpropagation through multi-step denoising processes.
result QAM consistently outperforms prior approaches on hard, sparse reward tasks in offline and offline-to-online RL.
Extends adjoint representation concept to higher Lie groupoids.
problem Defining adjoint representation for higher Lie groupoids.
method Generalizes standard construction to higher Lie groupoids using simplicial vector bundles.
result Adjoint representation up to homotopy is well-defined and unique.
New knot theory module shows torsion-ness in number theory.
problem Torsion-ness of Selmer modules in Galois representations.
method Introducing adjoint homological Selmer module for SL2-representations of knot groups. result Finitely generated torsion-ness of the new Selmer module.
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential eq…