Modified cosine distance improves similarity performance in data with variance and correlation.
problem Limitations of traditional cosine similarity in random variable spaces with variance and correlation.
method Proposed a variance-adjusted cosine distance metric to overcome limitations of traditional cosine similarity.
result Modified cosine distance shows 100% test accuracy in KNN model on the Wisconsin Breast Cancer Dataset.
The study compares Euclidean and cosine distances in medical drug prescription prediction.
problem Comparing Euclidean and cosine distances in medical drug prescription prediction.
method Established geometric properties and compared distances in real-world medical data.
result Different distances lead to different optimizing nonlinear kernel embedding frameworks.
Person recognition aims at recognizing the same identity across time and space with complicated scenes and similar appearance. In this paper, we propose a novel method to address this task by training a network to obtain robust and representative features. The intuition is that we directly compare and optimize the cosi…
This study investigates self-supervised learning with Wasserstein distance on tree structures.
problem Improving self-supervised learning methods using Wasserstein distance.
method Utilized Tree-Wasserstein distance (TWD) and Jeffrey divergence regularization for training.
result A simple combination of softmax function and Tree-Wasserstein distance outperforms cosine similarity-based methods.
Paper uses Sinkhorn distances to improve imitation learning effectiveness.
problem Improving imitation learning algorithms by comparing occupancy measures.
method Formulates imitation learning as Sinkhorn distance minimization, combining optimal transport and cosine distances.
result Proposes a new critic network and transport plan that guide imitation learning.
Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final an…
The main purpose of incremental learning is to learn new knowledge while not forgetting the knowledge which have been learned before. At present, the main challenge in this area is the catastrophe forgetting, namely the network will lose their performance in the old tasks after training for new tasks. In this paper, we…
A new topology design improves zero-shot classification performance in contrastive learning.
problem Improving zero-shot classification performance in contrastive visual-textual alignment.
method Proposed an alternative topology design using multiple class tokens and an oblique manifold with negative inner product.
result Improves zero-shot classification performance by an average of 6.1%.
New LSH methods for tensor data improve efficiency and space usage.
problem Efficiency and space usage issues in LSH for tensor data.
method Proposes new LSH methods using CP and TT decompositions for Euclidean and cosine similarity.
result Space-efficient and scalable LSH for tensor data.
A new geometric metric identifies true data changes from parametrization artifacts in high-dimensional representations.
problem Quantifying representation drift in high-dimensional data using Euclidean or cosine distances can misattribute changes due to arbitrary parametrizations.
method Introducing the Fubini Study metric to identify representations that differ only by gauge transformations.
result The Fubini Study metric isolates intrinsic evolution by remaining invariant under gauge-induced fluctuations, providing a diagnostic for meaningful structural changes.
SHAP Distance assesses semantic fidelity of synthetic tabular data.
problem Semantic fidelity of synthetic tabular data is not well evaluated.
method SHAP Distance, defined as cosine distance between global SHAP attribution vectors.
result SHAP Distance detects semantic discrepancies overlooked by standard measures.
A novel criterion selects optimal distance metrics for cell profile analysis.
problem Determining the most accurate distance metric for high-dimensional cell profiles.
method Generalized proposition and corollaries to evaluate and select distance metrics.
result Wasserstein and cosine similarity metrics are optimal for general cases.
The paper finds inequalities in Grassmannian geometry.
problem Understanding geometric properties of Grassmannians.
method Analyzes inequalities for elements in Grassmannians.
result Law of Cosines and geodesic triangle inequalities.
New insights show embedding lengths correlate with semantic properties.
problem Contrastive embedding norms ignore embedding magnitudes but correlate with semantic properties.
method Formal theoretical framework and analysis of optimization dynamics.
result Embedding lengths encode semantic information as a byproduct of training.
Improved MoE performance through perturbing cosine router.
problem Representation collapse and parameter redundancy in MoE models.
method Least square estimation of cosine router in MoE, followed by noise addition to improve convergence rates.
result Perturbed cosine router leads to polynomial convergence rates for MoE models.
We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are obtained in the genera…
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change o…
Researchers establish bounds and continuity of decomposed Möbius energies using cosine formula.
problem Estimating the bounds and continuity of decomposed Möbius energies.
method Using the cosine formula to evaluate upper and lower bounds and modulus of continuity of decomposed energies.
result Affirmative answer to the question of estimating decomposed energies using the cosine formula.
Cosine schedule is optimal for discrete diffusion models.
problem Choosing the best discretization schedule for diffusion models.
method Optimized using Fisher-Rao geometry.
result Cosine schedule is Fisher-Rao optimal.
Derives hyperbolic laws of cosines and sines with fermionic corrections.
problem Deriving hyperbolic laws of cosines and sines with new mathematical corrections.
method Using Minkowski supergeometry, the laws of cosines and sines are derived in the super hyperbolic plane.
result Identical formulae to classical cases with fermionic corrections for cosines and sines.
We propose weighted inner product similarity (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative values. Despite its simplicity, WIPS can approximate arbitrary general similarities in…
Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the classification task is particularly challenging, such as when the document-term ma…
This paper proposes a new method for embedding sequences using Wasserstein distances.
problem Embedding sequences in a metric space for better pattern recognition.
method Develops a deep learning model that embeds sequences as distributions and uses Wasserstein distances for comparison.
result Distributional embeddings using Wasserstein distances outperform traditional vector embeddings.
Unified understanding of neural representation similarity measures.
problem Fragmented research landscape of neural network similarity measures.
method Observation and exploration of connections between shape distances and normalized Bures similarity.
result Cosine of the Riemannian shape distance equals normalized Bures similarity.
Cosine similarity can force points to grow in magnitude, causing convergence issues.
problem Cosine similarity loss can lead to convergence issues in deep learning.
method Analyzing under-explored settings and proposing cut-initialization.
result Cosine similarity optimization forces points to grow in magnitude, leading to convergence issues.
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels us…
The NL score optimizes speaker recognition tasks.
problem Improving speaker recognition accuracy.
method Established the theory of optimal scores based on normalized likelihood.
result NL score is equivalent to PLDA likelihood ratio under certain conditions.
End-to-end approach learns pseudo-distance for verifying example sets.
problem Verifying example sets from same or different classes.
method Jointly trains parametric pseudo-distance with encoder.
result End-to-end approach outperforms simple scorers and classifiers.
We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fe…
New method for European option pricing faster and more robust.
problem Pricing European options efficiently and accurately.
method Fourier cosine series expansions for models with known characteristic functions.
result More robust and faster than the original COS method.
We propose a new class of metrics on sets, vectors, and functions that can be used in various stages of data mining, including exploratory data analysis, learning, and result interpretation. These new distance functions unify and generalize some of the popular metrics, such as the Jaccard and bag distances on sets, Man…
We propose shifted inner-product similarity (SIPS), which is a novel yet very simple extension of the ordinary inner-product similarity (IPS) for neural-network based graph embedding (GE). In contrast to IPS, that is limited to approximating positive-definite (PD) similarities, SIPS goes beyond the limitation by introd…
Feedback alignment methods need to be evaluated for accuracy and gradient cosine similarity.
problem Evaluating feedback alignment methods
method Proposed diagnostic evaluation protocol
result Identified silent failures in standard reporting pair
Study laws of cosines and sines for hyperbolic shapes with ideal vertices.
problem Formulating trigonometric laws for shapes with ideal vertices in hyperbolic geometry.
method Using hyperboloid model and Lorentzian geometry, establishing laws for quadrilaterals, pentagons, and partially truncated tetrahedra.
result Transversal lengths of partially truncated tetrahedra depend only on internal edge lengths at ideal vertices.
The paper proposes a new method to evaluate LLM agent responses using ECDF clustering.
problem The standard evaluation of LLM agent responses via majority voting obscures response quality and distribution.
method The paper introduces a novel evaluation framework based on ECDF of cosine similarities and clustering of ECDFs using distances and k-medoids algorithm. result ECDF clustering reveals interpretable group structures in LLM responses, offering insights into agent settings.
Energy functional for Legendrian knots in Heisenberg group, invariant under PU(2,1).
problem Energy functional for Legendrian knots in Heisenberg group.
method Regularization of divergent integral with Korányi distance, invariant under PU(2,1).
result Characterization of minimizers and Heisenberg analog of Doyle-Schramm cosine formula.
This paper tackles noise in raw datasets to improve representation learning efficiency.
problem Noise in real-world datasets degrades representation learning quality.
method Proposes denoising Cosine-Similarity (dCS) loss to learn robust representations.
result Empirical results show the dCS loss outperforms baseline objective functions.
Two binary Sine Cosine Algorithms improve feature selection in medical datasets.
problem Optimizing feature selection from medical datasets to enhance model accuracy.
method Proposed SBSCA and VBSCA algorithms using S-shaped and V-shaped transfer functions.
result SBSCA and VBSCA outperform four other binary optimization algorithms in medical datasets.
CWGD measures gradient diversity weighted by curvature, improving SGD convergence.
problem Gradient noise in high-curvature directions is underestimated by standard methods.
method CWGD weights gradient diversity by the inverse square root of the Hessian.
result CWGD-Cosine reduces optimization error by up to 20% compared to standard cosine annealing.
T-PSDA improves speaker recognition accuracy on toroidal submanifolds.
problem Improving speaker recognition accuracy on hypersphere embeddings.
method Extends PSDA to model within and between-speaker variabilities in toroidal submanifolds of the hypersphere.
result T-PSDA achieves accuracy on par with cosine scoring on VoxCeleb and large accuracy gains on NIST SRE'21.
We do further investigation in a certain cosine function defined for smooth Minkowski spaces. We prove that such function is symmetric if and only if the referred space is Euclidean, and also that it can be given in terms of the Gateaux derivative of the norm. As an application we use it to study the ratio between the …
We introduce SARR for symmetric object pose estimation, improving CNN performance.
problem Ambiguities in symmetric object orientations hinder deep learning pose estimation.
method Numeric rotation representation using symmetry-derived trigonometric identities.
result SARR enables standard CNNs to achieve state-of-the-art performance.
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies in convex geometry.
Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of vectors or use unsupervised learning to find a lower-dimensional representation. Th…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information geometry), dually flat spaces play a key role. In a dually flat space, there exist dual a…
We explore the potential of a popular distributional semantics vector space model, word2vec, for capturing meaningful relationships in ecological (complex polyphonic) music. More precisely, the skip-gram version of word2vec is used to model slices of music from a large corpus spanning eight musical genres. In this newl…
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
problem Extending Fourier cosine method to discrete probability distributions.
method Spectral filters and convergence rates analysis.
result Spectral filters achieve one order faster convergence rates than previously recognized.
In this short article, we extend the cosine formula for the Möbius energy to generalized O'Hara energies. The newly derived formula gives us a condition for which the right circle minimizes the energy under the length-constraint. Furthermore, it shows us how far the energy is from the Möbius invariant property.