Study on cosine function in smooth normed spaces, proving symmetry and characterizing planes.
problem Understanding cosine function properties in smooth normed spaces.
method Proved symmetry and derived cosine function in terms of norm's Gateaux derivative.
result Cosine function is symmetric if and only if space is Euclidean.
Cosine normalization uses cosine similarity to reduce neuron variance in neural networks.
problem Large variance in neuron outputs leads to poor generalization and internal covariate shift.
method Replace dot product with cosine similarity or centered cosine similarity in neural networks.
result Cosine normalization improves model performance on various datasets.
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.
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 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…
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.
Cosine loss improves CNN performance on small datasets.
problem Training CNNs from scratch on small datasets without pre-training.
method Used cosine loss instead of cross-entropy loss.
result Accuracy on CUB-200-2011 dataset is 30% higher with cosine loss.
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.
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.
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
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.
Wolpert's cosine formula on Teichmüller space gives the Weil-Petersson Poisson bracket {lα,lβ} for geodesic length functions lα,lβ of closed curves α,β as the sum of the cosines of the angle of intersection of the associated geodesics. This was recently generalized to Hitchin representations by Labourie. I…
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.
Improved text classification performance through conformal transformations of kernels.
problem Text document categorization in high-dimensional spaces.
method Introduced new Gaussian Cosine kernel and two conformal transformations.
result Conformal transformations significantly improve kernel performance, especially for sub-optimal kernels.
Unified method for calculating financial option prices from characteristic functions.
problem Calculating financial option prices from characteristic functions in high dimensions.
method Damped Fourier-cosine expansion (COS) method.
result The method converges exponentially if the characteristic function decays exponentially.
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.
Paper introduces a new method for efficient portfolio risk quantification.
problem Efficiently quantify risk in large portfolios with many trades and few dominant risk factors.
method Combines Fourier-cosine series with tensor decomposition techniques for dimension reduction.
result Achieves relative errors below 0.1% with significant runtime improvement.
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.
Develops an efficient method for compound option valuation.
problem Valuation of compound options with numerical quadrature.
method Analytic Fourier cosine (COS) method for closed-form expressions.
result Improved computational efficiency with high accuracy.
The note evaluates different methods for option pricing using Shannon Wavelets.
problem Efficient computation of Shannon Wavelet coefficients for option pricing.
method Evaluation of cosine expansion, direct algorithms, and Filon quadrature.
result Filon quadrature is more efficient for computing Shannon Wavelet coefficients.
This paper decomposes generalized O'Hara's energies into components.
problem Decomposing generalized O'Hara's energies to understand their components.
method Using an analogue of Doyle-Schramm's cosine formula, the paper derives a decomposition for generalized O'Hara energies.
result Derives a decomposition for generalized O'Hara energies into three components.
The Lp-cosine transform of an even, continuous function $f\in C_e(\Sn)$ is defined by: $$H(x)=\int_{\Sn}|\ip{x}ξ|^pf(ξ) dξ,\quad x\in {\R}^n.$$ It is shown that if p is not an even integer then all partial derivatives of even order of H(x) up to order p+1 (including p+1 if p is an odd integer) exist and ar…
Improved stable pricing for European options using Fourier-Cosine series.
problem Lack of robustness in the COS method for various cases.
method Stable pricing of call options based on Fourier cosine series expansion.
result Stability demonstrated through error analysis and numerical examples.
This work shows cosine similarity is equivalent to Pearson correlation for word vectors, but not all vectors are suitable for cosine.
problem The use of cosine similarity for semantic textual similarity is often taken for granted, despite its limitations.
method Characterized cases where Pearson correlation is unfit and introduced rank correlation as an alternative.
result Pearson correlation is equivalent to cosine similarity for many word vectors but not all, and rank correlation can improve performance.
A new method for person recognition using cosine loss.
problem Recognizing the same identity across time and space with complicated scenes and similar appearance.
method Proposes a congenerous cosine loss to train a network for robust and representative features.
result The proposed method achieves better classification accuracy than previous state-of-the-arts.
The paper analyzes and validates two step size schedules for SGD: exponential and cosine, proving their adaptivity and performance.
problem The variability of SGD performance due to step size choice.
method Analysis and empirical evaluation of exponential and cosine step sizes.
result Exponential and cosine step sizes are adaptive to noise and achieve optimal performance without tuning hyperparameters.
We calculate the higher derivatives of length functions on Teichmuller space along earthquake deformations. This generalizes the cosine formula for the first derivative by Kerckhoff and Wolpert and the sine formula for second derivative by Wolpert.
Improved barrier option pricing in Heston model using COS-BEM method.
problem Efficient barrier option pricing in the Heston model.
method Combining Fourier-cosine series (COS) method with Boundary Element Method (BEM).
result Significant computational efficiency improvement and BEM attractiveness for practitioners.
Model compares news articles and videos using neural networks and machine-learned activation functions.
problem Comparing heterogeneous entities like news articles and videos.
method Artificial neural networks with trainable weighted structural components and machine-learned activation functions.
result Achieved up to 59.2% accuracy in matching videos to news articles.
Extended Möbius energy formula for generalized O'Hara's energies.
problem Maintaining Möbius invariance in O'Hara's energies.
method Extended cosine formula for generalized O'Hara's energies.
result Condition for right circle minimization under length-constraint.
We study rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature like quantities for polyhedral surfaces are introduced. Many of them are shown to determine the polyhedral metric up to isometry. The action functionals in the variational approaches are derived …
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.
Study shows DNNs often extract redundant features, influenced by network size and activation function.
problem Redundancy in deep neural network features.
method Hierarchical clustering of features based on cosine distances, varying network sizes and activation functions.
result Network size and activation function are key factors in DNN redundancy.
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.
New initialization techniques improve the performance and speed of EMI sensor-based object discrimination.
problem Improving the performance and speed of EMI sensor-based object discrimination.
method Proposed and evaluated new initialization techniques for MI-ACE.
result Comparison of initialization approaches shows improved performance and speed.
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 tackles catastrophic forgetting in incremental learning with improved cosine distance and PEDCC-Loss.
problem Tackles catastrophic forgetting in incremental learning.
method Ensemble method based on cosine distance and PEDCC-Loss.
result Outperforms recent methods in preserving old knowledge while learning new classes.
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%.
Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.
problem Identifying and visualizing coherence among multiple time series.
method Fast spectral similarity based on cosine similarity metrics of Fourier-transformed signals and sparse time-frequency wavelet coherence.
result Scalable real-time system for low-latency inference and monitoring of inter-signal relationships.
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.
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.
Optimization rates improved for manifolds with bounded geometry.
problem Optimizing functions on manifolds with bounded geometry.
method Riemannian gradient descent and dynamic trivialization algorithm.
result Curvature-dependent convergence rates computed explicitly for common manifolds.
Knots in Euclidean space which may be parameterized by a single cosine function in each coordinate are called Lissajous knots. We show that twist knots are Lissajous knots if and only if their Arf invariants are zero. We further prove that all 2-bridge knots and all (3,q)-torus knots have Lissajous projections.
Proposes an adversarial process using cosine similarity to improve robustness of models.
problem Improving robustness of models by eliminating subsidiary information.
method Adversarial process using cosine similarity to degrade subsidiary model performance.
result Cosine similarity-based adversarial process efficiently degrades subsidiary model performance.
Layer rotation predicts model generalization, improving test accuracy by up to 30%.
problem Predicting model generalization in deep networks.
method Monitoring the cosine distance between layer weights and their initial values during training.
result Training procedures that maximize layer rotation consistently lead to better generalization performance.
Proves properties of periodic billiard orbits in ellipses.
problem Understanding periodic orbits in ellipses.
method Geometric and complex analytic methods.
result Sum of cosines of angles remains constant in one-parameter family of polygons.