DM improves self-supervised transfer learning by matching target distributions.
problem Improving self-supervised transfer learning performance.
method Distribution Matching (DM) method that drives representation distribution towards a predefined reference distribution.
result DM outperforms existing methods on target classification tasks.
Proves Riemannian positive mass theorem with singularities.
problem Proves Riemannian positive mass theorem for specific types of singular manifolds.
method Uses initial data sets with a second fundamental form to transfer convexity between different singularity components.
result Proves the theorem for manifolds with some mean-concave components and others mean-convex.
The paper proves a generalized inverse function theorem for curved L∞ spaces.
problem Proving a generalized inverse function theorem for curved L∞ spaces. method Obstruction theory for L∞ homomorphisms and homotopy transfer theorem for curved L∞ algebras. result A morphism of curved L∞ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. 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 C∞-algebra. Paper formalizes analogy between data sets and models using Hoare logic.
problem Lack of formal criteria for transferring machine learning models between data domains.
method Formalization of analogy using first-order logic and Hoare logic, rigorous theorem proving.
result Rigorous formalization of analogy in knowledge transfer between machine learning models.
Paper tackles robust transfer learning with unreliable source data.
problem Challenges in robust transfer learning stemming from ambiguity in Bayes classifiers and weak transferable signals.
method Introduces ambiguity level, proposes Transfer Around Boundary (TAB) model, establishes general theorem.
result Demonstrates efficiency and robustness of TAB model improving classification while avoiding negative transfer.
This work extends GNNs to handle multiple graphs with non-commuting operators, proving transferability.
problem Handling multiple graphs with non-commuting operators in graph neural networks.
method Developed a mathematical theory for graph-tuple neural networks (GtNNs) with non-commuting non-expansive operators.
result Proved universal transferability of GtNNs, ensuring no non-transferable energy under convergence.
We explain how the Transference Principles from Diophantine approximation can be interpreted in terms of geometry of the locally symmetric spaces Tn=SO(n)\SL(n,R)/SL(n,Z) with n>1, and how, via this dictionary, they become transparent geometric remarks and can be easily proved. Indeed, a finite family …
Transfer learning has recently attracted significant research attention, as it simultaneously learns from different source domains, which have plenty of labeled data, and transfers the relevant knowledge to the target domain with limited labeled data to improve the prediction performance. We propose a Bayesian transfer…
New method automates asymmetric choice for better skill transfer in reinforcement learning.
problem Improving sample efficiency and transferability of reinforcement learning agents.
method Attentive Priors for Expressive and Transferable Skills (APES) using hierarchical KL-regularization.
result APES automates asymmetric choice, leading to better skill transfer across sequential tasks.
Domain adaptation leverages the knowledge in one domain - the source domain - to improve learning efficiency in another domain - the target domain. Existing heterogeneous domain adaptation research is relatively well-progressed, but only in situations where the target domain contains at least a few labeled instances. I…
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 L∞[1]-algebras. result Proves that dg manifolds of finite positive amplitude form a category of fibrant objects.
Paper tackles skill transfer in RL for morphologically different agents.
problem Transfer skills between morphologically different reinforcement learning agents.
method Proposes a paired variational encoder-decoder model (PVED) for subspace learning.
result Demonstrates improved skill transfer efficiency compared to state-of-the-art methods.
The paper extends Menelaus' and Ceva's theorems to translation triangles in various Thurston geometries.
problem Extending classical theorems to non-Euclidean geometries.
method Using projective models of Thurston geometries and defining a ``surface of a translation-like triangle".
result Generalization of Menelaus' and Ceva's theorems to non-constant curvature Thurston geometries.
Researchers prove an L-theoretic signature transfer in codimension 2.
problem Proving an L-theoretic signature invariance in codimension 2. method Constructing a transfer map between symmetric L-groups. result Signature transfer up to a torsion of order at most 4.
A new machine learning framework reduces IoT data transfer by two orders of magnitude.
problem Reducing data transfer in IoT devices over wireless channels.
method Developed a machine learning framework for distributed functional compression over GMAC and AWGN channels.
result The framework reduces communication by two orders of magnitude compared to cloud-based methods.
A transfer learning technique speeds up GAN training.
problem Training GANs on high-quality images is resource-intensive.
method Freezing low-level layers and using an autoencoder constraint.
result Significant reduction in training time, up to two orders of magnitude.
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present…
Formalizes integral curves on Banach manifolds in Lean.
problem Existence and uniqueness of integral curves on Banach manifolds.
method Formalized differential equations on Banach spaces, then generalized to Banach manifolds.
result Established theorems for integral curves on Banach manifolds.
New proof improves differential privacy guarantees for adaptive data analysis.
problem Ensuring accuracy of statistical queries in adaptive data analysis.
method Elementary proof of transfer theorem using posterior distributions and resampling.
result Better concrete bounds on accuracy out-of-sample for differential privacy mechanisms.
Effective drilling and filling bounds for hyperbolic 3-manifolds.
problem Understanding changes in metrics and geodesics during Dehn fillings of hyperbolic 3-manifolds.
method Combining tools from Kleinian group theory to transfer results from finite-volume to infinite-volume manifolds.
result Effective bilipschitz and complex length bounds quantifying filling theorems.
New metrics solve machine learning limitations.
problem Previous success metrics restrict application to specific forms of machine learning.
method Define decomposable metrics as linear operations on probability distributions.
result Demonstrated theorems bounding success in various ways, generalizing existing results.
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nas…
Proves a synthetic Lorentzian Cartan-Hadamard theorem.
problem Formulates and proves a theorem for Lorentzian geometry.
method Uses an appropriate notion of local concavity for Lorentzian (pre-)length spaces.
result Establishes existence and uniqueness of timelike geodesics.
We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …
The paper counts primes in complex orthospectra and polynomial orbits.
problem Counting primes in complex orthospectra and polynomial orbits.
method Analytic number theory and Thermodynamic Formalism.
result Equidistribution of holonomy in dynamical systems.
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.
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…
In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentu…
Survey connects and systematizes transfer learning research.
problem Reduce dependence on target domain data for target learners.
method Systematic review of 40+ transfer learning approaches.
result Importance of choosing appropriate transfer learning models.
Revisits the connection between neural networks and the Kolmogorov-Arnold theorem.
problem Explains the limitations of using the Kolmogorov-Arnold theorem to explain neural networks with multiple hidden layers.
method Derives modifications of the Kolmogorov-Arnold representation that transfer smoothness properties to the outer function and can be well approximated by ReLU networks.
result Shows that a deep neural network with most layers approximating the interior function is a more natural interpretation of the Kolmogorov-Arnold representation.
Enhances transfer learning with semantic reasoning for robust predictions.
problem Improving robustness of transfer learning models.
method Integrates semantic representations for better knowledge transfer.
result Demonstrated robustness in bus delay and air quality forecasting.
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.
Paper defines and mitigates negative transfer in transfer learning.
problem Negative transfer occurs when transferring knowledge from a less related source task inversely harms target performance.
method Formal definition, analysis of three aspects, adversarial networks-based technique.
result The proposed method consistently improves target performance and largely avoids negative transfer.
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.
Upper bounds for Steklov eigenvalues in subgraphs of polynomial growth Cayley graphs.
problem Finding upper bounds for Steklov eigenvalues in subgraphs of polynomial growth Cayley graphs.
method Discretizing a bounded domain and using comparison theorems.
result The $k^{\mbox{th}}$ eigenvalue tends to 0 proportionally to 1/∣B∣d−11. 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.
Random groups prove length constraints on product of conjugates.
problem Quantify products of conjugates in random groups.
method Sharp van Kampen diagram argument and boundary block-counting.
result Prove a sharp inequality for products of conjugates in random groups.
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.
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.
Our work extends Coase's theorem to settings with uncertainty, showing how to maximize social welfare through property rights and learning.
problem Theoretical models of externality often assume perfect knowledge, limiting practical solutions.
method We extend Coase's theorem to a two-player bandit setting with uncertainty, designing a learning policy to maximize social welfare.
result We show that property rights and learning can recover Coase's theorem in settings with uncertainty.
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.
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.
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…