Abstract: Defines differential equations in tangent categories, providing conditions for completeness and new perspectives.
problem Defining and working with differential equations in abstract tangent categories.
method Introduces curve objects and dynamical systems, providing conditions for completeness and exploring exponential maps.
result Provides abstract conditions for dynamical systems to be complete and introduces differential exponential rig.
Develops scalable differentiable physics for complex object interactions.
problem Limited scalability of existing differentiable physics solvers.
method Adopting meshes for arbitrary geometry, localized collision handling, and accelerated implicit differentiation.
result Significantly reduces memory and computation requirements compared to particle-based methods.
Study differential invariants of objects and their images under surjective maps.
problem Reconstruction of objects from multiple-view images.
method Analysis of differential invariants under surjective maps, considering projectable and non-projectable cases.
result Constructible isomorphism between object and image invariants in the projectable case.
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
problem Applying the h-principle to partial differential relations.
method Interprets flexible sheaves as fibrant objects in a model structure.
result Flexible sheaves can be understood as fibrant objects.
Paper compares semi-supervised training for differentiable particle filters.
problem Lack of labelled data in real-world applications.
method Compares two semi-supervised training objectives.
result Improved performance in environments with scarce labelled data.
New algebraic formalism for differential calculus in Diolic algebras.
problem Studying differential calculus in vector bundles.
method Introducing functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this to Diolic algebras.
result Recovery of well-known objects and notions from ordinary differential, symplectic, and Poisson geometry, with unique aspects.
This paper explores differential and sector forms in tangent categories, finding rich structures and connections.
problem Understanding differential and sector forms in tangent categories.
method Investigates differential and sector forms in tangent categories, developing new equational presentations and structures.
result Sector forms in tangent categories form a symmetric cosimplicial object, with a subcomplex isomorphic to the de Rham complex of differential forms.
The study finds infinitely many divisors in a specific space of geometric objects.
problem Understanding the effective cone of moduli spaces of abelian differentials.
method Exhibiting extremal effective divisors from abelian differential strata.
result Infinitely many extremal effective divisors discovered in Mg,n. We optimize rank-based metrics using blackbox differentiation.
problem Challenges in directly optimizing rank-based metrics due to their non-differentiable and non-decomposable nature.
method Efficient, theoretically sound, and general method for differentiating rank-based metrics with mini-batch gradient descent.
result Competitive performance on standard image retrieval datasets and improved performance on object detectors.
The paper introduces relative objects and proves a transversality theorem.
problem Lack of general notions for relative objects in differential topology.
method Introduces the notion of arrangements of manifolds and constructs jet bundles.
result Proves a relative version of the Transversality Theorem.
Study improves sampling efficiency of diffusion models using RL and PDEs.
problem Training neural stochastic differential equations without access to target samples.
method Proves equivalences between RL methods and PDEs, uses coarse time discretization.
result Improves sample efficiency and reduces computational cost.
Algorithm improves vanilla option pricing accuracy during and before COVID-19.
problem Improving vanilla option pricing accuracy during and before the pandemic.
method Combinational Mutation Strategy of Differential Evolution (CmDE) algorithm for bi-objective optimization.
result Algorithm approximates real market vanilla option prices more accurately than Black-Scholes.
This paper develops differential bundles and fibrations in tangent categories.
problem Abstract setting for differential geometry in categories.
method Develops differential bundles and fibrations in tangent categories, considering their relation to differential objects.
result Strikingly, in display differential bundles, fibres are Cartesian differential categories.
This paper analyzes privacy-preserving methods for sparse model optimization.
problem Privacy-preserving sparse model optimization with non-differentiable norms.
method Differential privacy techniques applied to Frank-Wolfe and objective perturbation algorithms.
result Excess risk bounds for Frank-Wolfe and objective perturbation algorithms are derived.
A new parallel BO method with exact gradients for multi-objective optimization.
problem Efficiently optimizing multiple objectives in a sample-efficient manner.
method Derive q-Expected Hypervolume Improvement (qEHVI) for parallel, constrained evaluation.
result qEHVI is computationally tractable and outperforms state-of-the-art methods.
BoTier optimizes experiments by balancing multiple objectives hierarchically.
problem Balancing multiple competing objectives in scientific experiments.
method Composite objective that flexibly represents a hierarchy of preferences over outcomes and parameters.
result Demonstrates robust applicability across various use cases and seamless integration.
Advances M-polyfolds for complex geometry applications.
problem Complex geometry challenges in differential geometry.
method Introduces and proves geometric structures within M-polyfolds.
result Establishes M-polyfolds as useful differential geometric objects.
The paper connects Riemann surface deformations with integrable Whitham hierarchies.
problem Understanding deformations of complex structures on Riemann surfaces.
method Variational formulas for holomorphic objects on Riemann surfaces, using canonical objects on the moduli space.
result The universal Whitham hierarchy is integrable by hydrodynamic reductions.
Variational approach to basic manifold structures.
problem Understanding basic differential geometric structures.
method Variational description of geometric structures.
result Variational formulation of manifold structures.
Differentiable CEM enables end-to-end learning of non-convex optimization problems.
problem Non-convex optimization of continuous, parameterized objective functions.
method Introducing a differentiable variant of the cross-entropy method (CEM).
result Differentiation of CEM output with respect to parameters enables end-to-end learning.
Develops geometric integration for rough differential forms.
problem Integrating rough differential forms with low regularity.
method Uses rough path theory to construct geometric integration.
result Constructs geometric integration for rough differential forms.
Abstract Lie algebroids generalize Lie algebroids to abstract categories.
problem Generalizing Lie algebroids to abstract categories.
method Generalized differentiation procedure to groupoid objects in categories with tangent structures.
result Abstract Lie algebroids are defined and examples include various groupoids.
New method tackles rugged optimization landscapes in contact-rich scenarios.
problem Optimization challenges in dynamic environments with deformable objects.
method Combines Bayesian optimization with semi-local 'leaps' for global search.
result Outperforms gradient-based and gradient-free baselines in simulation and real robot experiments.
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of…
New framework for differential privacy in vertically partitioned multiparty learning.
problem Challenges in preserving differential privacy under multiparty, especially vertically partitioned, settings.
method Functional mechanism with noise addition and secure aggregation.
result Released model achieves the same utility as centralized setting with one round of noise addition and secure aggregation.
In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned with differential-geometric developments within the above axiomatic scheme, this…
New tools understand and control dynamics in n-player differentiable games.
problem Understanding and controlling the behavior of gradient-based methods in games.
method Developed new tools to understand and control the dynamics in n-player differentiable games, decomposing the game Jacobian into symmetric and antisymmetric components.
result Motivated Symplectic Gradient Adjustment (SGA) algorithm for finding stable fixed points in differentiable games.
Develops a new higher-order calculus using cubic algebra.
problem Foundational issues in differential calculus.
method Generalizes local linear algebra to higher order local linear algebra using cubic combinatorial objects.
result New conceptual cubic calculus theories provide insights into foundational issues.
The Lagrangian formalism on a arbitrary non-fibrating manifold is considered. The kinematical description of this generic situation is based on the concept of (higher-order) Grassmann manifolds which is the factorization of the regular velocity manifold to the action of the differential group. Here we introduce in this…
Paper develops a differentiable approach for 3D imaging models using Fourier slice theorem.
problem Uncertainty in 3D structure modeling and pose estimation in scientific imaging.
method Differentiable probabilistic models in Fourier space with backpropagation through projection.
result Validates approach on 3D protein reconstruction and extends to probabilistic models.
The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have emancipated microlinearity from within well-adapted models…
A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the categ…
New algorithm for variational inference on non-differentiable models.
problem Challenges in stochastic variational inference for non-differentiable models.
method Generalizes reparameterization trick for non-differentiable models, splitting latent variables into differentiable and non-differentiable regions.
result Our algorithm reduces variance and remains unbiased for non-differentiable models.
3D object detection improved using energy-based models.
problem Accurate 3D object detection in cluttered environments from sparse LiDAR data.
method Designing a differentiable pooling operator for 3D bounding boxes integrated into a state-of-the-art 3D object detector.
result Our approach consistently outperforms the SA-SSD baseline across all 3DOD metrics on the KITTI dataset.
The caloron correspondence is a tool that gives an equivalence between principal G-bundles based over the manifold M×S1 and principal LG-bundles on M, where LG is the Fréchet Lie group of smooth loops in the Lie group G. This thesis uses the caloron correspondence to construct certain differential f…
Study of monopoles and q-difference modules correspondence.
problem Finding a correspondence between algebraic and differential geometric objects.
method Analogue of non-abelian Hodge theory for q-difference modules. result Doubly periodic monopoles and parabolic q-difference modules correspond. This work analyzes the convergence rate of unrolling for optimizing quadratic objectives.
problem The challenge of accurately computing Jacobians through optimization.
method Non-asymptotic convergence-rate analysis of unrolled differentiation for gradient descent and Chebyshev method.
result There is a trade-off between fast asymptotic convergence and immediate but slower convergence due to the learning rate.
New method improves training stochastic neural networks with tighter guarantees.
problem Training stochastic neural networks with provable guarantees.
method Developed partially-aggregated estimators and reformulated PAC-Bayesian bounds.
result Derives a differentiable objective leading to tighter generalisation guarantees.
Defines continuous versions of combinatorial objects from lattice paths.
problem Lattice path enumeration and combinatorial identities.
method Continuous analog of lattice paths and binomials.
result Defines continuous versions of combinatorial objects.
A new variational method for SSMs improves inference efficiency.
problem Hard variational inference for state space models.
method Proposes variational marginal particle filter (VMPF) based on Rao-Blackwellization.
result VMPF provides tighter variational bounds and sometimes benefits from unbiased reparameterization.
Study periodic monopoles via algebraic difference modules.
problem Classify periodic monopoles of GCK type.
method Relate geometric monopoles to algebraic difference modules.
result Established a Kobayashi-Hitchin correspondence for periodic monopoles.
The thesis explores stability conditions and metrics in differential geometry.
problem Understanding extremal objects in differential geometry.
method Introduces and analyzes Z-critical metrics and optimal symplectic connections. result Proves a correspondence between existence of metrics and stability conditions.
Study of curves and surfaces from single-direction projections.
problem Obtaining complete shape information from a single view.
method Theoretical study of differential geometric information from multiple orthogonal projections.
result Formulae for recovering certain information on curves or surfaces from their projections.
The paper analyzes and proposes methods for privately sharing individual privacy losses using per-instance differential privacy.
problem The standard differential privacy framework provides a worst-case bound that may not accurately reflect individual privacy losses.
method The paper analyzes per-instance differential privacy and proposes methods to privately and accurately publish per-instance privacy losses.
result The methods privately and accurately publish per-instance differential privacy losses with minimal additional privacy cost.
Improved set prediction model using multiset-equivariant operations and approximate implicit differentiation.
problem Existing set prediction models struggle with multisets and cannot represent certain functions.
method Introduced multiset-equivariance, improved DSPN with approximate implicit differentiation, and applied to CLEVR object property prediction.
result Significantly improved object property prediction on CLEVR dataset.
Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some significant examples from mechanics and economics are presented.
Integrates differential privacy and demographic parity in multi-class classification.
problem Ensuring fairness and privacy in sensitive applications.
method Designs DP2DP algorithm that enforces both demographic parity and differential privacy.
result DP2DP converges towards demographic parity at nearly the same rate as non-private methods, achieving state-of-the-art trade-offs.
New method stabilizes private LASSO for high-dimensional data with diverse covariate scales.
problem Privacy constraints and heterogeneity in covariate scales degrade LASSO stability and accuracy.
method Gram-based anisotropic objective perturbation to counteract covariate structure.
result Significantly improves convergence and statistical efficiency of private LASSO estimators.