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.
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.
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…
A large body of research into semantic textual similarity has focused on constructing state-of-the-art embeddings using sophisticated modelling, careful choice of learning signals and many clever tricks. By contrast, little attention has been devoted to similarity measures between these embeddings, with cosine similari…
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.
Beta-SOD detects and corrects noisy object re-identification using cosine similarity and Beta mixtures.
problem Noisy object re-identification in image datasets.
method Reframed Re-ID as a similarity task, using Siamese networks and Beta mixture models.
result Superior performance in noisy conditions compared to state-of-the-art methods.
Paper explains contrastive learning using cosine similarity and proposes mitigations for batch size effects.
problem Understanding and improving contrastive learning through batch size effects.
method Unified framework of cosine similarity, theoretical insights, and auxiliary loss.
result Performance improvement in small-batch settings through proposed auxiliary loss.
The paper examines how well node similarities are preserved by random projections in graph embeddings.
problem The preservation of node similarities under random projections in graph embeddings.
method Investigation of dot product and cosine similarity preservation by random projections over graph matrix rows.
result Random projections produce unreliable embeddings for dot product, especially for high-degree nodes.
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…
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
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.
Study evaluates relevance metrics for similarity-based model explanations.
problem Providing understandable explanations for complex model predictions.
method Evaluated three relevance metrics using three tests.
result Cosine similarity of gradients performs best for explanations.
SPEQ improves quantized neural networks by stochastic precision sharing and cosine similarity loss.
problem Improving quantized deep neural networks for edge devices.
method SPEQ combines stochastic precision sharing and cosine similarity loss for knowledge distillation.
result SPEQ outperforms existing methods in various tasks.
CLS measures dataset similarity through decision rule performance.
problem Measuring dataset similarity in machine learning, especially for transfer learning and domain adaptation.
method Cross-Learning Score (CLS) measures similarity through bidirectional generalization performance of decision rules, linking to cosine similarity under canonical linear models.
result CLS effectively measures dataset similarity and transferability, validated on synthetic and real-world datasets.
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%.
We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the averag…
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.
Study evaluates thresholds for removing noise from DNN weights using random matrix theory.
problem Removing noise from deep neural network weights for better approximation.
method Model weights as signal + noise, use random matrix theory to estimate thresholds, evaluate using cosine similarity.
result Proposed threshold estimation method improves approximation quality.
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.
An adversarial process between two deep neural networks is a promising approach to train a robust model. In this paper, we propose an adversarial process using cosine similarity, whereas conventional adversarial processes are based on inverted categorical cross entropy (CCE). When used for training an identification mo…
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.
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 …
O'Hara introduced several functionals as knot energies. One of them is the Möbius energy. We know its Möbius invariance from Doyle-Schramm's cosine formula. It is also known that the Möbius energy was decomposed into three components keeping the Möbius invariance. The first component of decomposition represents the ext…
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…
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.
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.
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…
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.
A new weighted FDA method improves face recognition accuracy.
problem Equal treatment of all class pairs in FDA leads to suboptimal performance.
method Cosine-weighted and automatically weighted FDA methods are proposed.
result Improved face recognition accuracy through weighted FDA.
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.
Twitmo analyzes geo-tagged Twitter data for topic modeling and visualization.
problem Analyzing public discourse on Twitter for various topics, parties, or individuals.
method Collects and preprocesses geo-tagged Tweets, applies LDA, CTM, STM, and visualizes results.
result Automatic pooling of Tweets into pseudo-documents improves topic coherence.
Training-free source selection for LLM families with shared vocabularies
problem Source selection for LLM families with shared vocabularies
method Fisher alignment at vocabulary scale
result Fisher alignment is a cosine between kernel mean embeddings in the joint activation-error space
SBSS uses similarity to split data for better classifier training.
problem Training better classifiers with realistic performance estimation.
method SBSS uses both input and output space information to split data using similarity functions.
result SBSS outperformed ordinary stratified 10-fold cross-validation in 75% of scenarios.
Despite the prevalence of collaborative filtering in recommendation systems, there has been little theoretical development on why and how well it works, especially in the "online" setting, where items are recommended to users over time. We address this theoretical gap by introducing a model for online recommendation sy…
This work analyzes when contrastive models are close to PCA or kernel methods.
problem Understanding when contrastive models are equivalent to kernel methods or PCA.
method Analyzing the training dynamics of two-layer contrastive models with non-linear activation.
result Wide contrastive models with cosine similarity based losses are close to PCA.
The paper explores linear representations in language models using counterfactuals.
problem Understanding linear representations and geometric concepts in large language models.
method Formalized linear representation in output and input spaces, identified causal inner product.
result Unified understanding of linear representations and their connection to interpretation and control.
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.
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.
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.
GrokAlign aligns Jacobians to accelerate grokking in deep networks.
problem Accelerating the training dynamics of deep networks to avoid delayed generalisation and robustness.
method Aligning the Jacobians of a deep network with the training data to ensure grokking under a low-rank assumption.
result GrokAlign regularizes Jacobians to induce grokking sooner than conventional methods.
The study analyzes neural network predictions of knot invariants and finds that braid representations work best.
problem Understanding and predicting knot invariants using neural networks.
method Investigated different knot representations and invariants, proposed a cosine similarity score.
result Braid representations are best for predicting knot invariants, and some invariants are easier to learn than others.
One approach to deal with the statistical inefficiency of neural networks is to rely on auxiliary losses that help to build useful representations. However, it is not always trivial to know if an auxiliary task will be helpful for the main task and when it could start hurting. We propose to use the cosine similarity be…
Measuring sentence similarity is a classic topic in natural language processing. Light-weighted similarities are still of particular practical significance even when deep learning models have succeeded in many other tasks. Some light-weighted similarities with more theoretical insights have been demonstrated to be even…
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 …