We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra a…
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48 results for “algebraic transfer”
Simple construction of Rumin algebra for contact manifolds.
problem Computing the de Rham cohomology algebra of contact manifolds.
method Using Markl's Homotopy Transfer Theorem for a simple explicit construction.
result Recovery of the Rumin algebra as a contact invariant -algebra.
Randomized Geometric Algebra for Convex Neural Networks Optimizes Transfer Learning.
problem Training neural networks to global optimality via convex optimization.
method Randomized algorithms in Clifford's Geometric Algebra for hypercomplex vector spaces.
result Convex optimization and geometric algebra improve LLMs' robustness and reliability in transfer learning.
This paper provides a rational model for fiberwise THH transfer using A-infinity algebras.
problem Rational models for fiberwise THH transfer of fibrations over a base space.
method Explicit description of Hochschild homology transfer in terms of A-infinity algebras.
result Rational models for Becker-Gottlieb transfer and fiberwise THH-simple structures.
This paper confirms Singer's conjecture for rank 4 in specific generic degrees.
problem Determining the injectivity of the algebraic transfer for rank 4.
method Using the Singer algebraic transfer and novel algorithms.
result Established Singer's conjecture for rank four in specific generic degrees.
Paper improves AIRL by enhancing policy imitation and addressing reward recovery issues.
problem Inadequate policy imitation and limited transferable reward recovery in AIRL.
method Substituted built-in algorithm with SAC for policy updating and proposed PPO-AIRL + SAC hybrid framework.
result SAC improves policy imitation but hinders reward recovery; PPO-AIRL + SAC achieves satisfactory transfer effect.
We propose a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a recent work on transferring curved -structures we show that, under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Sp…
We record various properties of twisted Becker-Gottlieb transfer maps and study their multiplicative properties analogous to Becker-Gottlieb transfer. We show these twisted transfer maps factorise through Becker-Schultz-Mann-Miller-Miller transfer; some of these might be well known. We apply this to show that $BSO(2n+1…
We prove the Farrell-Jones Conjecture for algebraic K-theory of spaces for virtually poly-Z-groups. For this, we transfer the 'Farrell-Hsiang method' from the linear case to categories of equivariant, controlled retractive spaces.
The paper proves a category of dg manifolds with finite positive amplitude.
problem Understanding the structure of dg manifolds with finite positive amplitude.
method Using path spaces and homotopy transfer theorem for curved -algebras.
result Proves that dg manifolds of finite positive amplitude form a category of fibrant objects.
The paper proves a generalized inverse function theorem for curved spaces.
problem Proving a generalized inverse function theorem for curved spaces.
method Obstruction theory for homomorphisms and homotopy transfer theorem for curved algebras.
result A morphism of curved spaces which is a quasi-isomorphism at a point has a local homotopy inverse.
We describe two constructions giving rise to curved -algebras. The first consists of deforming -algebras, while the second involves transferring curved dg structures that are deformations of (ordinary) dg structures along chain contractions. As an application of the second construction, given a …
On the computation of for math.AT
Computes cohomology of Steenrod algebra for k ≤ 5.
problem Determining a basis of cohomology for Steenrod algebra.
method Algorithm based on generators and Adams relations.
result Verification of hand-computed results for k = 4.
This paper reinterprets Khovanov-Sano symmetries using BV formalism.
problem Understanding symmetries in equivariant Khovanov homology.
method Identifying Shumakovitch operator as a BV Laplacian and proving -algebra structure.
result Construction of an intrinsic -algebra on the Khovanov-Sano complex.
We have previously shown that the truncated Weil algebra of any Lie algebra is a Hopf-cyclic type complex with nontrivial coefficients. In this paper we apply this result to transfer the characteristic classes of transversely orientable foliations into the cyclic cohomology of the groupoid action algebra. Our result in…
We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show th…
A formula for the Riemannian metric tensor of differentiable manifolds of linear dynamical systems of same McMillan degree is presented in terms of their transfer function matrices. The necessary calculations for its application to ARMA and state space overlapping parametrizations are drafted. The importance of this ap…
New method encodes manifold homotopy types into algebra structures, extending previous bounds.
problem Encoding the real homotopy type of compact manifolds into algebraic structures.
method Homotopy transfer of unital DGCA structure from de Rham algebra to cohomology.
result Multiplication vanishes for all k ≥ ℓ-1 in minimal unital C∞-algebra for certain dimensions.
We develop an algebraic framework for the description and analysis of financial behaviours, that is, behaviours that consist of transferring certain amounts of money at planned times. To a large extent, analysis of financial products amounts to analysis of such behaviours. We formalize the cumulative interest compliant…
STS clarifies chaos and stochastic dynamics, linking algebraic topology and physics.
problem Chaos and stochastic dynamics in arbitrary form SDEs.
method Supersymmetric theory of stochastic dynamics (STS) using generalized transfer operator (GTO) and topological field theories (TFT).
result Positive 'pressure' in GTOs corresponds to spontaneous breakdown of topological supersymmetry, explaining 1/f noise.
We study the shifted analogue of the "Lie--Poisson" construction for algebroids and we prove that any algebroid naturally gives rise to shifted derived Poisson manifolds. We also investigate derived Poisson structures from a purely algebraic perspective and, in particular, we establish a homotopy …
New concept of coisotropic structures for differentiable stacks defined.
problem Defining coisotropic structures for differentiable stacks.
method Using twisted Dirac structures and Morita equivalences.
result 1-shifted coisotropic structures transfer through Morita equivalences.
We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the im…
Kapranov algebrasmath.DG
New algebraic structure derived from Kähler manifolds.
problem Understanding algebraic structures on differential forms.
method Introducing -algebras and proving linearization theorems.
result Induced -algebra structures on are linearizable under certain conditions.
Proves finiteness and holonomicity of skein modules for 3-manifolds.
problem Finiteness and holonomicity of skein modules for 3-manifolds.
method Defining skein transfer bimodules and using q-analogues of D-module theory.
result Internal skein modules are holonomic modules over the internal skein algebra of the boundary.
Transfer learning improves portfolio optimization by identifying transfer risk.
problem Financial portfolio optimization problem.
method Introduces transfer risk concept within transfer learning framework.
result Transfer risk is a significant indicator of transferability and enhances portfolio management efficiency.
Paper analyzes transfer risk in transfer learning for finance.
problem Evaluate transferability of transfer learning in finance.
method Proposes transfer risk concept and applies to stock return prediction and portfolio optimization.
result Transfer risk correlates with transfer learning performance and identifies appropriate source tasks.
This paper explores the connection between adversarial and knowledge transferability.
problem Understanding the factors affecting knowledge transferability.
method Theoretical analysis and practical metrics for adversarial transferability.
result Adversarial transferability and knowledge transferability are closely related.
Mathematical framework for transfer learning feasibility and transfer risk.
problem Theoretical analysis of transfer learning.
method Reformulated transfer learning as an optimization problem, introduced transfer risk concept.
result Demonstrated the potential and benefits of incorporating transfer risk in transfer learning evaluation.
Learning to Transfercs.AI
Transfer learning borrows knowledge from a source domain to facilitate learning in a target domain. Two primary issues to be addressed in transfer learning are what and how to transfer. For a pair of domains, adopting different transfer learning algorithms results in different knowledge transferred between them. To dis…
Develops derived differential geometry theory.
problem Homotopy and intersection in smooth manifolds.
method Using -algebras and homotopy transfer.
result Derived manifolds form a category of fibrant objects.
Using technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so called quantum master equation satisfying certain boundary conditions are proven to be in 1-1 correspondence with representations of …
New Max-Plus neural network exploits subgradient sparsity for efficient training.
problem Training Max-Plus neural networks is challenging due to dense subgradients.
method Proposes a sparse subgradient algorithm tailored to Max-Plus models.
result Achieves more efficient updates while retaining theoretical guarantees.
Study measures impact of data and neural net similarity on transferability in restaurant sales data.
problem Identify indicators for successful transferability of neural nets across different data sets.
method Empirical study on sales data from six restaurants, calculating indicators based on data and neural net similarities.
result Negative correlations between transferability and indicators, allowing better model performance and fewer transfers.
The paper analyzes phase transitions in transfer learning for perceptrons.
problem Understanding when transfer learning from a source task to a target task is beneficial.
method Theoretical analysis of a pair of related perceptron learning tasks.
result Reveals a phase transition from negative to positive transfer as task similarity changes.
Adaptive source selection for positive transfer in linear models improves target dataset performance.
problem Limited task-specific labeled data in business settings.
method Greedily decides from which sources and how many samples to incorporate into the target dataset using an accept/reject rule based on a data-dependent estimate of the transfer gain.
result Consistent gains over classical and recent strong baselines while avoiding negative transfer.
Limits of Transfer Learningstat.ML
New research on limits of transfer learning, proving key selection and dependence requirements.
problem Insufficient theoretical foundation for transfer learning.
method Proved novel results on transfer learning, emphasizing selection of information and dependence between domains.
result Upper bound on improvement possible with transfer learning, highlighting the need for careful selection.
Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prosp…
Proposes a transfer learning method for high-dimensional quantile regression.
problem Inadequate handling of heterogeneity and heavy tails in transfer learning.
method High-dimensional quantile regression framework with double transfer learning estimator.
result Established error bounds and valid confidence intervals for high-dimensional quantile regression coefficients.
Localized transfer learning improves nonparametric regression performance.
problem Improving nonparametric regression performance on target tasks.
method Localized transfer learning framework that models heterogeneity and partition covariate space into cells.
result Sharp minimax rates show local transfer mitigates the curse of dimensionality.
Transfer learning aims at building robust prediction models by transferring knowledge gained from one problem to another. In the semantic Web, learning tasks are enhanced with semantic representations. We exploit their semantics to augment transfer learning by dealing with when to transfer with semantic measurements an…
Investigates transfer learning in spatial statistics.
problem Applying transfer learning to spatial statistics.
method Simple MLP models for spatial data.
result Potential of transfer learning in spatial statistics.
This work transfers causal knowledge between tasks for Individual Treatment Effect estimation.
problem Estimating Individual Treatment Effects (ITE) requires a large amount of data, making it challenging.
method The authors introduce a practical framework for efficient transfer of causal knowledge between tasks, using a Causal Inference Task Affinity (CITA) measure.
result ITE knowledge transfer can significantly reduce the amount of data needed for ITE estimation.
With the help of transfer entropy, we analyze information flows between communities of complex networks. We show that the transfer entropy provides a coherent description of interactions between communities, including non-linear interactions. To put some flesh on the bare bones, we analyze transfer entropies between co…
Simple methods improve regression transferability estimation.
problem Estimating how well regression models transfer between tasks.
method Two simple, computationally efficient approaches based on negative regularized mean squared error.
result Significantly outperform existing methods in accuracy and efficiency.
This paper defines and quantifies transferability in domain generalization.
problem Understanding and quantifying transferability between domains.
method Formal definition and estimation of transferability, upper bound for target error.
result Many algorithms do not learn transferable features, proposing a new algorithm.
Training a source model optimally for its own task is suboptimal for downstream transfer.
problem The optimality of a source model for its own task hinders downstream transfer performance.
method Analyzes L2-SP ridge regression, characterizes transfer-optimal source penalty, and identifies alignment-dependent effects.
result Transfer benefits from stronger source regularization when aligned imperfectly, and from weaker regularization when aligned perfectly.
AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regressionstat.ML
AdaTrans adapts to feature and sample transfer in high-dimensional regression.
problem High-dimensional linear regression with more features than samples.
method F-AdaTrans and S-AdaTrans methods using fused-penalties and adaptive weights.
result AdaTrans achieves convergence rates close to oracle estimators and near-minimax optimal rates.