Model learns product vectors from baskets and browsing sessions for better complementary product recommendations.
problem Inferring complementary products from basket and browsing data.
method Proposes BB2vec model that learns product vectors from both baskets and browsing sessions.
result The BB2vec model improves complementary product recommendations and alleviates the cold start problem.
Proposes dual product embedding for complementary product representation learning.
problem Detecting complementary relationships from noisy and sparse customer purchase activities.
method Knowledge-aware dual product embedding with multi-task learning and user bias terms.
result Complementary relationships are captured more accurately than simple similarity.
Framework learns item representations from text data for complementary and similar items.
problem Generating accurate complementary item recommendations from textual data.
method Quadruplet network learning framework for latent space representation of items.
result Items are placed closer together in latent space for similar and complementary items compared to non-complementary items.
We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting…
Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of…
The paper proves integral formulas for manifolds with multiple orthogonal distributions.
problem Understanding geometric properties of manifolds with multiple orthogonal distributions.
method Develops integral formulas for Riemannian manifolds with k>2 orthogonal complementary distributions. result Generalizes known formulas for k=2 and applies to manifold splitting and immersions. The paper studies Einstein-Hilbert action on complex manifolds.
problem Deriving equations for the Einstein-Hilbert action on almost k-product manifolds. method Adapted variations of metric, deriving Euler-Lagrange equations.
result Presented a nice form of Einstein equation.
The paper explores formulas and applications for mixed scalar curvature in multi-product manifolds.
problem Integral and variation formulas for mixed scalar curvature in multi-product manifolds.
method Generalizes results from pseudo-Riemannian almost product manifolds to multi-product structures.
result Generalizes formulas for mixed scalar curvature in multi-product manifolds.
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies conformally along one of the distributions. Then w…
Three RFF-based methods for nonlinear causal discovery in mixed data.
problem Nonlinear causal discovery in mixed data with computational constraints.
method FFML, TRFF, and FFCI methods for score-based, constraint-based, and hybrid causal discovery.
result FFML and TRFF methods provide complementary performance in causal discovery.
Average intersection estimate for diffeomorphisms on manifolds.
problem Estimating geometric intersection numbers for diffeomorphisms on manifolds.
method Analyzing families of C1 diffeomorphisms and using volume products as an approximation. result The average geometric intersection number is approximately the product of volumes.
We show that if a closed atoroidal 3-manifold M contains a genuine lamination, then it is group negatively curved in the sense of Gromov. Specifically, we exploit the structure of the non-product complementary regions of the genuine lamination and then apply the first author's Ubiquity Theorem to show that M satisfies …
We develop SHOPPER, a sequential probabilistic model of shopping data. SHOPPER uses interpretable components to model the forces that drive how a customer chooses products; in particular, we designed SHOPPER to capture how items interact with other items. We develop an efficient posterior inference algorithm to estimat…
Are large scale research programs that include many projects more productive than smaller ones with fewer projects? This problem of economy of scale is particularly relevant for understanding recent mergers in particular in the pharmaceutical industry. We present a quantitative theory based on the characterization of d…
We consider the possible Euler characteristics and fundamental groups of the complementary components X and Y of an embedding of a connected closed 3-manifold M in S4. We use a 2-knot satellite construction to change the fundamental groups, and Massey products to limit the values of χ(X) and χ(Y) when M …
The study finds cash productivity predicts stock performance in a specific subset of firms.
problem Predicting future stock performance using cash productivity.
method Using financial and market data, calculated cash returns as a proxy for operational efficiency, and tested a long-only strategy on Nasdaq-listed non-financial firms.
result Cash productivity has significant predictive power in a handpicked portfolio but limited across the broader Nasdaq universe.
Study relationships between intrinsic and extrinsic invariants of Riemannian almost k-product manifolds.
problem Find a relationship between intrinsic and extrinsic invariants of Riemannian almost k-product manifolds isometrically immersed in another Riemannian manifold.
method Establish an optimal inequality involving mixed scalar curvature and square of mean curvature.
result Optimal inequality that includes mixed scalar curvature and square of mean curvature.
Study irrational rotations and construct 2-filling rays on infinite type surfaces.
problem Understanding dense orbits in skew product transformations.
method Skew product transformation with continued fraction analysis.
result Existence of infinite cliques of 2-filling rays on infinite type surfaces.
In this paper we study a Ricci-Hessian type manifold (M,g,φ,f,λ) which is closely related to the construction of almost Ricci soliton realized as a warped product. We classify certain classes of the Ricci-Hessian type manifolds and derive some implications for almost Ricci solitons and generalized m--qu…
We show that each classical pseudoriemann symmetric space G/H can be realized as space of pairs of complementary subspaces in a linear space. For each classical symmetric space we construct an open embedding to a grassmannian or to a product of two grassmanianns. We also show that the representation of the group G in L…
In this work, we find an equation that relates the Ricci curvature of a riemannian manifold M and the second fundamental forms of two orthogonal foliations of complementary dimensions, F and F⊥, defined on M. Using this equation, we show a sufficient condition for the manifold M to be …
Paper proposes a method to adapt classifiers using complementary labels instead of true labels.
problem Training classifiers with true labels from the source domain is costly and sometimes impossible.
method Proposes a novel setting with complementary labels and a complementary label adversarial network (CLARINET).
result CLARINET significantly outperforms baselines on handwritten digits and object recognition tasks.
We show that any self-complementary graph with n vertices contains a K⌊2n+1⌋ minor. We derive topological properties of self-complementary graphs.
NSBI approach detects Higgs trilinear coupling with high luminosity upgrade constraints.
problem Determining the Higgs trilinear self-coupling via off-shell Higgs production.
method Hybrid neural simulation-based inference (NSBI) incorporating SMEFT and quantum interference effects.
result NSBI achieves sensitivity close to theoretical optimum for Higgs trilinear self-coupling.
Proposes a new framework for learning from labeled and unlabeled data.
problem Learning from unlabeled and multi-label samples with arbitrary loss functions.
method Multi-complementary and unlabeled learning framework.
result Effective estimation of classification risk with optimal convergence rate.
In 1972, Marcel Berger defined a metric invariant that captures the `size' of k-dimensional homology of a Riemannian manifold. This invariant came to be called the k-dimensional SYSTOLE. He asked if the systoles can be constrained by the volume, in the spirit of the 1949 theorem of C. Loewner. We construct metrics, ins…
In this paper, we study the classification problem in which we have access to easily obtainable surrogate for true labels, namely complementary labels, which specify classes that observations do \textbf{not} belong to. Let Y and Yˉ be the true and complementary labels, respectively. We first model the annotati…
Paper bridges ordinary-label and complementary-label learning frameworks.
problem Combining complementary-label learning with ordinary-label learning.
method Integrates loss functions for one-versus-all and pairwise classification.
result Derives classification risk and error bound for additivity and duality loss functions.
Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.
problem Multi-view clustering where views have both consistent and complementary information.
method Consistent and complementary graph-regularized multi-view subspace clustering (GRMSC).
result The proposed method outperforms state-of-the-art methods on benchmark datasets.
Generative-discriminative method improves label prediction and instance generation.
problem Difficulty in obtaining high-quality labeled instances.
method Generative-discriminative complementary learning method using CC-GAN.
result Improves accuracy in predicting ordinary labels and generating high-quality instances.
In this note we study the Seifert rational homology spheres with two complementary legs, i.e. with a pair of invariants whose fractions add up to one. We give a complete classification of the Seifert manifolds with 3 exceptional fibers and two complementary legs which bound rational homology balls. The result translate…
Collecting labeled data is costly and thus a critical bottleneck in real-world classification tasks. To mitigate this problem, we propose a novel setting, namely learning from complementary labels for multi-class classification. A complementary label specifies a class that a pattern does not belong to. Collecting compl…
Clarinet uses complementary labels to train classifiers with less source data.
problem Training classifiers with true-label data from source domain is costly.
method Proposes CLARINET to train classifiers with complementary-label source data and unlabeled target data.
result CLARINET significantly outperforms baselines in unsupervised domain adaptation.
Study on quaternionic contact structures with integrable complementary distribution.
problem Characterize quaternionic contact structures with integrable complementary distributions.
method Analyze positive definite quaternionic contact (4n+3)-manifolds, focusing on the integrable complementary distribution and its relationship with Sasaki and 3-Sasaki structures. result Identify a new class of quaternionic contact structures with integrable complementary distributions that are not isomorphic to su(2). Hydra boosts efficiency for long-context reasoning in resource-constrained settings.
problem Quadratic complexity of transformers limits long-context reasoning in resource-constrained systems.
method Hydra uses a modular architecture with adaptive routing between sparse global attention, mixture-of-experts, and dual memories.
result Hydra achieves significant throughput and accuracy improvements for long-context reasoning.
This paper introduces a new learning method for classification without true labels.
problem Learning with only complementary labels, not true class labels.
method Derives a novel framework for arbitrary losses and models, using unbiased risk estimation.
result Demonstrates improved risk estimator through non-negative correction and gradient ascent.
We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.
Feature selection has attracted significant attention in data mining and machine learning in the past decades. Many existing feature selection methods eliminate redundancy by measuring pairwise inter-correlation of features, whereas the complementariness of features and higher inter-correlation among more than two feat…
UREs lead to overfitting in complex models, especially in complementary label learning.
problem Overfitting in weakly supervised learning with complementary labels.
method Proposed a surrogate complementary loss (SCL) framework to reduce gradient variance.
result SCL mitigates overfitting and improves URE-based methods.
A method for identifying joint and individual subspaces from multi-view data.
problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.
Study curvature of orthogonal distributions on manifolds.
problem Understanding curvature of orthogonal distributions on manifolds.
method Derived Euler-Lagrange equations for a functional of Riemannian metrics.
result Examples of critical metrics for specific distributions.
The relation between time series irreversibility and entropy production has been recently investigated in thermodynamic systems operating away from equilibrium. In this work we explore this concept in the context of financial time series. We make use of visibility algorithms to quantify in graph-theoretical terms time …
This paper analyzes SHAP values using Fourier expansions for model interpretability.
problem Understanding and interpreting SHAP values in complex models.
method Developed a spectral framework using Fourier expansions for SHAP values in various model regimes.
result SHAP values are Lipschitz continuous in the deterministic regime and converge to Gaussian process values in the probabilistic regime.
Framework transfers complementary operating conditions to train anomaly detectors.
problem Training anomaly detectors on changing operating conditions requires comprehensive data, which is hard to obtain.
method Proposes unsupervised transfer learning to align and combine data from different units.
result Demonstrates improved anomaly detection in changing operating conditions.
Amortizes MIPS by training neural networks to predict optimal keys.
problem Efficiently solving Maximum Inner Product Search for repeated queries.
method Regression-based SupportNet and KeyNet models trained on support functions.
result Significant improvement in IVF match rates for document embeddings.
Adaptive regularization improves neural network performance on small datasets.
problem Improving neural network performance on limited data.
method Adaptive regularization using a matrix-variate normal prior with a Kronecker product structure.
result The method leads to networks with smaller stable ranks and spectral norms, suggesting better generalization.
GenAI adoption paradoxically lowers ROE for U.S. banks, with spillovers but systemic risk concerns.
problem Productivity paradox and implementation costs in U.S. banking sector with AI adoption.
method Dynamic Spatial Durbin Models (DSDM) and Synthetic Difference-in-Differences (SDID) for causal inference.
result AI adoption leads to a 428-basis-point decline in ROE for banks, with spillovers but systemic risk implications.
This paper studies an environment of simultaneous, separate, first-price auctions for complementary goods. Agents observe private values of each good before making bids, and the complementarity between goods is explicitly incorporated in their utility. For simplicity, a model is presented with two first-price auctions …