Daily Papers

The Perturbation Discrimination Score (PDS) is increasingly used to evaluate whether predicted perturbation effects remain distinguishable, including in Systema and the Virtual Cell Challenge. However, its behavior in high-dimensional gene-expression settings has not been examined in detail. We show that PDS is highly sensitive to the choice of similarity or distance measure and to the scale of predicted effects. Analysis of observed perturbation responses reveals that ell_1 and ell_2-based PDS behave very differently from cosine-based measures, even after norm matching. We provide geometric insight and discuss implications for future discrimination-based evaluation metrics.

Identifying parallel passages in biblical Hebrew (BH) is central to biblical scholarship for understanding intertextual relationships. Traditional methods rely on manual comparison, a labor-intensive process prone to human error. This study evaluates the potential of pre-trained transformer-based language models, including E5, AlephBERT, MPNet, and LaBSE, for detecting textual parallels in the Hebrew Bible. Focusing on known parallels between Samuel/Kings and Chronicles, I assessed each model's capability to generate word embeddings distinguishing parallel from non-parallel passages. Using cosine similarity and Wasserstein Distance measures, I found that E5 and AlephBERT show promise; E5 excels in parallel detection, while AlephBERT demonstrates stronger non-parallel differentiation. These findings indicate that pre-trained models can enhance the efficiency and accuracy of detecting intertextual parallels in ancient texts, suggesting broader applications for ancient language studies.

The use of CLIP embeddings to assess the alignment of samples produced by text-to-image generative models has been extensively explored in the literature. While the widely adopted CLIPScore, derived from the cosine similarity of text and image embeddings, effectively measures the relevance of a generated image, it does not quantify the diversity of images generated by a text-to-image model. In this work, we extend the application of CLIP embeddings to quantify and interpret the intrinsic diversity of text-to-image models, which is responsible for generating diverse images from similar text prompts. To achieve this, we propose a decomposition of the CLIP-based kernel covariance matrix of image data into text-based and non-text-based components. Using the Schur complement of the joint image-text kernel covariance matrix, we perform this decomposition and define the matrix-based entropy of the decomposed component as the Schur Complement Entropy (SCE) score, a measure of the intrinsic diversity of a text-to-image model based on data collected with varying text prompts. Additionally, we demonstrate the use of the Schur complement-based decomposition to nullify the influence of a given prompt in the CLIP embedding of an image, enabling focus or defocus of embeddings on specific objects or properties for downstream tasks. We present several numerical results that apply our Schur complement-based approach to evaluate text-to-image models and modify CLIP image embeddings. The codebase is available at https://github.com/aziksh-ospanov/CLIP-DISSECTION

Linear probes are widely used in interpretability research and often compared by cosine similarity. The Mahalanobis cosine similarity (MCS) between two directions, which reweights the inner product by test data covariance, is a natural task-aware refinement. Ying et al. (2026) report that a probe's MCS to a reference probe trained on the out-of-distribution (OOD) data near-perfectly linearly predicts the probe's OOD AUROC (R^2 = 0.98). Here, we extend this empirical finding across models, layers, and concept domains, and prove this general phenomenon in closed form: For balanced classes whose projections are Gaussian, OOD AUROC and MCS to the reference probe are linear because both are sigmoid-shaped functions of the probe's signal-to-noise ratio (SNR) on the test data. The theory also predicts when this linearity fails, which we verify empirically. MCS offers a theoretically grounded and empirically effective alternative to Euclidean cosine similarity for comparing linear probes.

The alignment of vision-language representations endows current Vision-Language Models (VLMs) with strong multi-modal reasoning capabilities. However, the interpretability of the alignment component remains uninvestigated due to the difficulty in mapping the semantics of multi-modal representations into a unified concept set. To address this problem, we propose VL-SAE, a sparse autoencoder that encodes vision-language representations into its hidden activations. Each neuron in its hidden layer correlates to a concept represented by semantically similar images and texts, thereby interpreting these representations with a unified concept set. To establish the neuron-concept correlation, we encourage semantically similar representations to exhibit consistent neuron activations during self-supervised training. First, to measure the semantic similarity of multi-modal representations, we perform their alignment in an explicit form based on cosine similarity. Second, we construct the VL-SAE with a distance-based encoder and two modality-specific decoders to ensure the activation consistency of semantically similar representations. Experiments across multiple VLMs (e.g., CLIP, LLaVA) demonstrate the superior capability of VL-SAE in interpreting and enhancing the vision-language alignment. For interpretation, the alignment between vision and language representations can be understood by comparing their semantics with concepts. For enhancement, the alignment can be strengthened by aligning vision-language representations at the concept level, contributing to performance improvements in downstream tasks, including zero-shot image classification and hallucination elimination. Codes are available at https://github.com/ssfgunner/VL-SAE.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Detection and tracking are the basic tasks of radar systems. Current joint detection tracking methods, which focus on dynamically adjusting detection thresholds from tracking results, still present challenges in fully utilizing the potential of radar signals. These are mainly reflected in the limited capacity of the constant false-alarm rate model to accurately represent information, the insufficient depiction of complex scenes, and the limited information acquired by the tracker. We introduce the Integrated Detection and Tracking based on radar feature (InDT) method, which comprises a network architecture for radar signal detection and a tracker that leverages detection assistance. The InDT detector extracts feature information from each Range-Doppler (RD) matrix and then returns the target position through the feature enhancement module and the detection head. The InDT tracker adaptively updates the measurement noise covariance of the Kalman filter based on detection confidence. The similarity of target RD features is measured by cosine distance, which enhances the data association process by combining location and feature information. Finally, the efficacy of the proposed method was validated through testing on both simulated data and publicly available datasets.

Machine translation is highly sensitive to the size and quality of the training data, which has led to an increasing interest in collecting and filtering large parallel corpora. In this paper, we propose a new method for this task based on multilingual sentence embeddings. In contrast to previous approaches, which rely on nearest neighbor retrieval with a hard threshold over cosine similarity, our proposed method accounts for the scale inconsistencies of this measure, considering the margin between a given sentence pair and its closest candidates instead. Our experiments show large improvements over existing methods. We outperform the best published results on the BUCC mining task and the UN reconstruction task by more than 10 F1 and 30 precision points, respectively. Filtering the English-German ParaCrawl corpus with our approach, we obtain 31.2 BLEU points on newstest2014, an improvement of more than one point over the best official filtered version.

Among closely related North Germanic languages, the quantification of language distance has traditionally relied on qualitative methods, lacking a unified multi-dimensional computational framework. Multilingual pretrained models based on the Transformer architecture can map texts from different languages into a shared vector space, enabling quantitative measurement of language distance. This paper focuses on the three North Germanic languages---Danish, Norwegian (Bokmål), and Swedish---and proposes a three-metric quantitative framework based on pretrained language models: (1)~sentence-level semantic distance, computed as cosine similarity between LaBSE and mBERT encodings of parallel sentences; (2)~orthographic fragmentation rate, measuring subword tokenization efficiency when cross-applying monolingual BERT vocabularies to parallel texts; (3)~MLM predictability, comparing prediction confidence and entropy in masked language modeling using mBERT across languages. Using 150 trilingual parallel sentence triplets from the Tatoeba corpus as controlled samples, we obtain consistent distance rankings on two independent models: LaBSE: da--no 0.012 < no--sv 0.016 < da--sv 0.020; mBERT: da--no 0.016 < no--sv 0.045 approx da--sv 0.046. This ranking is consistent with the historical linguistic conclusion that ``400 years of Danish rule over Norway (1380--1814) led to highly cognate written languages.'' The three metrics---semantic, orthographic, and predictability---converge on the same conclusion, providing a reproducible computational framework for the quantitative study of distance among closely related languages, extensible in principle to more branches of the Indo-European language family, pending validation on additional language groups.

Federated Learning (FL) is a widespread and well-adopted paradigm of decentralised learning that allows training one model from multiple sources without the need to transfer data between participating clients directly. Since its inception in 2015, it has been divided into numerous subfields that deal with application-specific issues, such as data heterogeneity or resource allocation. One such sub-field, Clustered Federated Learning (CFL), deals with the problem of clustering the population of clients into separate cohorts to deliver personalised models. Although a few remarkable works have been published in this domain, the problem remains largely unexplored, as its basic assumptions and settings differ slightly from those of standard FL. In this work, we present One-Shot Clustered Federated Learning (OCFL), a clustering-agnostic algorithm that can automatically detect the earliest suitable moment for clustering. Our algorithm is based on computing the cosine distance between the gradients of the clients and a temperature measure that detects when the federated model starts to converge. We empirically evaluate our methodology by testing various one-shot clustering algorithms for over forty different tasks on five benchmark datasets. Our experiments showcase the good performance of our approach when used to perform CFL in an automated manner without the need to adjust hyperparameters. We also revisit the practical feasibility of CFL algorithms based on the gradients of the clients, providing firm evidence of the high efficiency of density-based clustering methods when used to differentiate between the loss surfaces of neural networks trained on different distributions. Moreover, by inspecting the feasibility of local explanations generated with the help of GradCAM, we can provide more insights into the relationship between personalisation and the explainability of local predictions.

Given the success of Large Language Models (LLMs), there has been considerable interest in studying the properties of model activations. The literature overwhelmingly agrees that LLM representations are dominated by a few ``outlier dimensions'' with exceedingly high variance and magnitude. Several studies in Natural Language Processing (NLP) have sought to mitigate the impact of such outlier dimensions and force LLMs to be isotropic (i.e., have uniform variance across all dimensions in embedding space). Isotropy is thought to be a desirable property for LLMs that improves model performance and more closely aligns textual representations with human intuition. However, many of the claims regarding isotropy in NLP have been based on the average cosine similarity of embeddings, which has recently been shown to be a flawed measure of isotropy. In this paper, we propose I-STAR: IsoScore*-based STable Anisotropic Regularization, a novel regularization method that can be used to increase or decrease levels of isotropy in embedding space during training. I-STAR uses IsoScore*, the first accurate measure of isotropy that is both differentiable and stable on mini-batch computations. In contrast to several previous works, we find that decreasing isotropy in contextualized embeddings improves performance on the majority of tasks and models considered in this paper.

In embedding-based retrieval, Approximate Nearest Neighbor (ANN) search enables efficient retrieval of similar items from large-scale datasets. While maximizing recall of relevant items is usually the goal of retrieval systems, a low precision may lead to a poor search experience. Unlike lexical retrieval, which inherently limits the size of the retrieved set through keyword matching, dense retrieval via ANN search has no natural cutoff. Moreover, the cosine similarity scores of embedding vectors are often optimized via contrastive or ranking losses, which make them difficult to interpret. Consequently, relying on top-K or cosine-similarity cutoff is often insufficient to filter out irrelevant results effectively. This issue is prominent in product search, where the number of relevant products is often small. This paper introduces a novel relevance filtering component (called "Cosine Adapter") for embedding-based retrieval to address this challenge. Our approach maps raw cosine similarity scores to interpretable scores using a query-dependent mapping function. We then apply a global threshold on the mapped scores to filter out irrelevant results. We are able to significantly increase the precision of the retrieved set, at the expense of a small loss of recall. The effectiveness of our approach is demonstrated through experiments on both public MS MARCO dataset and internal Walmart product search data. Furthermore, online A/B testing on the Walmart site validates the practical value of our approach in real-world e-commerce settings.

Image similarity metrics play an important role in computer vision applications, as they are used in image processing, computer vision and machine learning. Furthermore, those metrics enable tasks such as image retrieval, object recognition and quality assessment, essential in fields like healthcare, astronomy and surveillance. Existing metrics, such as PSNR, MSE, SSIM, ISSM and FSIM, often face limitations in terms of either speed, complexity or sensitivity to small changes in images. To address these challenges, a novel image similarity metric, namely CSIM, that combines real-time while being sensitive to subtle image variations is investigated in this paper. The novel metric uses Gaussian Copula from probability theory to transform an image into vectors of pixel distribution associated to local image patches. These vectors contain, in addition to intensities and pixel positions, information on the dependencies between pixel values, capturing the structural relationships within the image. By leveraging the properties of Copulas, CSIM effectively models the joint distribution of pixel intensities, enabling a more nuanced comparison of image patches making it more sensitive to local changes compared to other metrics. Experimental results demonstrate that CSIM outperforms existing similarity metrics in various image distortion scenarios, including noise, compression artifacts and blur. The metric's ability to detect subtle differences makes it suitable for applications requiring high precision, such as medical imaging, where the detection of minor anomalies can be of a high importance. The results obtained in this work can be reproduced from this Github repository: https://github.com/safouaneelg/copulasimilarity.

Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for jumps in conditional means when outcomes lie in a non-Euclidean metric space. Using local Fr\'echet regressionx2014which generalizes standard regression to metric-space valued datax2014the method estimates a mean path on either side of a candidate cutoff, extending existing k-sample tests to a flexible regression setting. Key theoretical contributions include a central limit theorem for the local estimator of the conditional Fr\'echet variance and the asymptotic validity and consistency of the proposed test. Simulations confirm nominal size control and robust power in finite samples. Two applications demonstrate the method's value by revealing effects invisible to scalar-based tests. First, I detect a sharp change in work-from-home compositions at Washington State's income threshold for non-compete enforceability during COVID-19, highlighting remote work's role as a bargaining margin. Second, I find that countries restructure their input-output networks after losing preferential US trade access. These findings underscore that analyzing regression functions within their native metric spaces can reveal structural discontinuities that scalar summaries would miss.

Requirement traceability is the process of identifying the inter-dependencies between requirements. It poses a significant challenge when conducted manually, especially when dealing with requirements at various levels of abstraction. In this work, we propose a novel approach to automate the task of linking high-level business requirements with more technical system requirements. The proposed approach begins by representing each requirement using a Bag of-Words (BOW) model combined with the Term Frequency-Inverse Document Frequency (TF-IDF) scoring function. Then, we suggested an enhanced cosine similarity that uses recent advances in word embedding representation to correct traditional cosine similarity function limitations. To evaluate the effectiveness of our approach, we conducted experiments on three well-known datasets: COEST, WARC(NFR), and WARC(FRS). The results demonstrate that our approach significantly improves efficiency compared to existing methods. We achieved better results with an increase of approximately 18.4% in one of the datasets, as measured by the F2 score.

Dense retrieval compresses texts into single embeddings ranked by cosine similarity. While efficient for recall, this interface is brittle for identity-level matching: minimal compositional edits (negation, role swaps) flip meaning yet retain high similarity. Motivated by geometric results for unit-sphere cosine spaces (Kang et al., 2025), we test this retrieval-composition tension in text-only retrieval. Across four dual-encoder backbones, adding structure-targeted negatives consistently reduces zero-shot NanoBEIR retrieval (8-9% mean nDCG@10 drop on small backbones; up to 40% on medium ones), while only partially improving pooled-space separation. Treating pooled cosine as a recall interface, we then benchmark verifiers scoring token--token cosine maps. MaxSim (late interaction) excels at reranking but fails to reject structural near-misses, whereas a small Transformer over similarity maps reliably separates near-misses under end-to-end training.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

Riemannian geometry has been applied to Brain Computer Interface (BCI) for brain signals classification yielding promising results. Studying electroencephalographic (EEG) signals from their associated covariance matrices allows a mitigation of common sources of variability (electronic, electrical, biological) by constructing a representation which is invariant to these perturbations. While working in Euclidean space with covariance matrices is known to be error-prone, one might take advantage of algorithmic advances in information geometry and matrix manifold to implement methods for Symmetric Positive-Definite (SPD) matrices. This paper proposes a comprehensive review of the actual tools of information geometry and how they could be applied on covariance matrices of EEG. In practice, covariance matrices should be estimated, thus a thorough study of all estimators is conducted on real EEG dataset. As a main contribution, this paper proposes an online implementation of a classifier in the Riemannian space and its subsequent assessment in Steady-State Visually Evoked Potential (SSVEP) experimentations.

The paper considers a new quantitative-qualitative proximity measure for the features of information objects, where data enters a common information resource from several sources independently. The goal is to determine the possibility of their relation to the same physical object (observation object). The proposed measure accounts for the possibility of differences in individual feature values - both quantitative and qualitative - caused by existing determination errors. To analyze the proximity of quantitative feature values, the author employs a probabilistic measure; for qualitative features, a measure of possibility is used. The paper demonstrates the feasibility of the proposed measure by checking its compliance with the axioms required of any measure. Unlike many known measures, the proposed approach does not require feature value transformation to ensure comparability. The work also proposes several variants of measures to determine the proximity of information objects (IO) based on a group of diverse features.

A central aspiration of mechanistic interpretability is controllability: if we know where a behavior is represented in a model's activations, we should be able to modify it. This rests on a hidden premise -- that the direction which detects a behavior and the direction which controls it are the same, or close. We test this geometrically: what is the angle between the direction that best detects a behavior and the one that best causes it? If detection implies control the cosine is near 1; otherwise it quantifies a detection-intervention gap. On Gemma 2-2B-it, output format (clean JSON vs markdown fencing) collapses both roles onto one axis. Hallucination does not: the model detects fake entities with perfect linear separability (AUC = 1.000 from layer 5), yet that direction sits at cos = 0.12 (about 83 degrees) from the direction producing a refusal -- a small, reproducible alignment, far from the cos = 1 that "detection is control" would require. A detector built from activations, with no chosen tokens, likewise fails to align (cos = -0.06). The gap generalizes: across four models from three families and two scales (1B-9B), cos stays in [0.12, 0.20], identical before and after instruction tuning (0.1197 vs 0.1200), placing its origin in pretraining. A 15-degree rotation toward the refusal direction partially bridges it -- 73% and 60% refusal on two held-out fake-entity categories at 1.8% false positives. We then ask whether this cosine predicts steerability, and it does not: detection is a high-dimensional class, not a single direction, and what separates the steerable case is functional, not readable from a static angle. The cosine is a weight-computable signature of the dissociation between knowing and steering, not a predictor of it.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

This paper describes the design and simulation of an 8-bit dedicated processor for calculating the Sine and Cosine of an Angle using CORDIC Algorithm (COordinate Rotation DIgital Computer), a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. We have proposed a dedicated processor system, modeled by writing appropriate programs in VHDL, for calculating the Sine and Cosine of an angle. System simulation was carried out using ModelSim 6.3f and Xilinx ISE Design Suite 12.3. A maximum frequency of 81.353 MHz was reached with a minimum period of 12.292 ns. 126 (3%) slices were used. This paper attempts to survey the existing CORDIC algorithm with an eye towards implementation in Field Programmable Gate Arrays (FPGAs). A brief description of the theory behind the algorithm and the derivation of the Sine and Cosine of an angle using the CORDIC algorithm has been presented. The system can be implemented using Spartan3 XC3S400 with Xilinx ISE 12.3 and VHDL.

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods.

Testing equality of two high-dimensional covariance matrices is challenging when many entries differ only slightly. Dependence among sample covariance entries can also affect the finite-sample size and power of tests that aggregate their differences. We propose a studentized ell_2-type statistic that averages squared, marginally standardized differences between corresponding entries of the two sample covariance matrices. Before constructing the statistic, we apply the same nonsingular linear transformation to both samples. In the transformed coordinates, the covariance-equality hypothesis is unchanged, whereas the standardized differences and correlations among their estimators generally change. The transformation can therefore incorporate structural or scientific information without reducing dimension. We approximate the null distribution using a Gaussian multiplier bootstrap that uses coordinatewise studentization and avoids forming or inverting the full covariance matrix of the vectorized sample covariance entries. For deterministic transformations, we derive nonasymptotic Gaussian and bootstrap approximation bounds and establish asymptotic size validity and power consistency. We also show that replacing a population transformation by a same-sample estimator leaves the statistic and bootstrap critical value asymptotically unchanged in relative terms under an operator-norm convergence condition. Simulations show that suitable transformations improve size accuracy and power under weak dependence. An analysis of breast cancer gene-expression data illustrates the method.

Prevalent text-to-video retrieval systems mainly adopt embedding models for feature extraction and compute cosine similarities for ranking. However, this design presents two limitations. Low-quality text-video data pairs could compromise the retrieval, yet are hard to identify and examine. Cosine similarity alone provides no explanation for the ranking results, limiting the interpretability. We ask that can we interpret the ranking results, so as to assess the retrieval models and examine the text-video data? This work proposes X-CoT, an explainable retrieval framework upon LLM CoT reasoning in place of the embedding model-based similarity ranking. We first expand the existing benchmarks with additional video annotations to support semantic understanding and reduce data bias. We also devise a retrieval CoT consisting of pairwise comparison steps, yielding detailed reasoning and complete ranking. X-CoT empirically improves the retrieval performance and produces detailed rationales. It also facilitates the model behavior and data quality analysis. Code and data are available at: https://github.com/PrasannaPulakurthi/X-CoT.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

We identify the task of measuring data to quantitatively characterize the composition of machine learning data and datasets. Similar to an object's height, width, and volume, data measurements quantify different attributes of data along common dimensions that support comparison. Several lines of research have proposed what we refer to as measurements, with differing terminology; we bring some of this work together, particularly in fields of computer vision and language, and build from it to motivate measuring data as a critical component of responsible AI development. Measuring data aids in systematically building and analyzing machine learning (ML) data towards specific goals and gaining better control of what modern ML systems will learn. We conclude with a discussion of the many avenues of future work, the limitations of data measurements, and how to leverage these measurement approaches in research and practice.

Conversational interviews are commonly used to complement structured surveys by eliciting rich and contextualized responses, which are typically analyzed qualitatively. However, their potential contribution to quantitative measurement remains underexplored. In this paper, we introduce ConvScale, an AI-supported approach that transforms psychometric scales into natural conversational interviews while preserving the original measurement structure. Based on interview data, ConvScale predicts item-level scores and aggregates them to derive scale-based assessments. In a within-subjects study with 18 participants, our results show that ConvScale-derived scores align closely with participants' self-report scores at both the item and construct levels, while maintaining moderate internal reliability; however, the structural validity was inadequate. In light of this, we discussed the potential of supporting quantitative measurement through interviews and proposed implications for future designs.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

RANSAC-based algorithms are the standard techniques for robust estimation in computer vision. These algorithms are iterative and computationally expensive; they alternate between random sampling of data, computing hypotheses, and running inlier counting. Many authors tried different approaches to improve efficiency. One of the major improvements is having a guided sampling, letting the RANSAC cycle stop sooner. This paper presents a new adaptive sampling process for RANSAC. Previous methods either assume no prior information about the inlier/outlier classification of data points or use some previously computed scores in the sampling. In this paper, we derive a dynamic Bayesian network that updates individual data points' inlier scores while iterating RANSAC. At each iteration, we apply weighted sampling using the updated scores. Our method works with or without prior data point scorings. In addition, we use the updated inlier/outlier scoring for deriving a new stopping criterion for the RANSAC loop. We test our method in multiple real-world datasets for several applications and obtain state-of-the-art results. Our method outperforms the baselines in accuracy while needing less computational time.

Reading measurement instruments is effortless for humans and requires relatively little domain expertise, yet it remains surprisingly challenging for current vision-language models (VLMs) as we find in preliminary evaluation. In this work, we introduce MeasureBench, a benchmark on visual measurement reading covering both real-world and synthesized images of various types of measurements, along with an extensible pipeline for data synthesis. Our pipeline procedurally generates a specified type of gauge with controllable visual appearance, enabling scalable variation in key details such as pointers, scales, fonts, lighting, and clutter. Evaluation on popular proprietary and open-weight VLMs shows that even the strongest frontier VLMs struggle measurement reading in general. A consistent failure mode is indicator localization: models can read digits or labels but misidentify the key positions of pointers or alignments, leading to big numeric errors despite plausible textual reasoning. We have also conducted preliminary experiments with reinforcement learning over synthetic data, and find encouraging results on in-domain synthetic subset but less promising for real-world images. Our analysis highlights a fundamental limitation of current VLMs in fine-grained spatial grounding. We hope this resource can help future advances on visually grounded numeracy and precise spatial perception of VLMs, bridging the gap between recognizing numbers and measuring the world.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Despite the success of deep learning, training deep networks in biologically plausible and hardware-efficient ways remains an open challenge. Feedback alignment (FA) methods address this by replacing backpropagation's symmetric backward weights with fixed random matrices, but their effectiveness depends critically on whether they can be accurately evaluated. The standard evaluation relies on two quantities: task accuracy and cosine similarity between the method's credit signal and the backpropagation gradient. We show that this reporting pair is insufficient by identifying two independent failure modes, both silent under current reporting: (1) measurement degeneracy, where the BP reference gradient collapses to the numerical floor in terminal-LayerNorm residual architectures, rendering cosine uninterpretable; and (2) aggregation collapse, where the aggregate cosine masks layerwise heterogeneity that concentrates credit at one end of the network. To address these limitations, we propose a diagnostic evaluation protocol based on three checks -- scale stability, reference validity, and depth utility -- together with per-layer rather than aggregate cosine reporting. Across multiple architectures and methods, the standard reporting pair gives no signal of failure in any audited case, while our protocol identifies all failures with wide calibration margins. The two failure modes are causally independent: a per-block scale penalty alleviates Mode 1 (residual scale explosion driving reference collapse) without affecting Mode 2 (cosine ranking that contradicts every functional metric we measured). Identifying these silent failures prevents researchers from building on non-functional credit assignment and provides actionable guidance for developing FA methods that genuinely train deep layers.

Histograms provide a powerful means of summarizing large data sets by representing their distribution in a compact, binned form. The HistogramTools R package enhances R built-in histogram functionality, offering advanced methods for manipulating and analyzing histograms, especially in large-scale data environments. Key features include the ability to serialize histograms using Protocol Buffers for distributed computing tasks, tools for merging and modifying histograms, and techniques for measuring and visualizing information loss in histogram representations. The package is particularly suited for environments utilizing MapReduce, where efficient storage and data sharing are critical. This paper presents various methods of histogram bin manipulation, distance measures, quantile approximation, and error estimation in cumulative distribution functions (CDFs) derived from histograms. Visualization techniques and efficient storage representations are also discussed alongside applications for large data processing and distributed computing tasks.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

This paper develops a hierarchical clustering algorithm for weighted projective spaces P_{q}, utilizing a Finsler metric d_F([z], [w]) and its rational analogue d_{F,Q}([z], [w]) to define distances that preserve the non-Euclidean geometry of these quotient manifolds. Defined via geodesic integrals of a scaling invariant Finsler norm weighted by the grades q = (q_0, q_1, dots, q_n), these metrics satisfy true metric properties including the triangle inequality, overcoming the limitations of the non-metric dissimilarity measure from prior work.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Current metric learning approaches for image retrieval are usually based on learning a space of informative latent representations where simple approaches such as the cosine distance will work well. Recent state of the art methods such as HypViT move to more complex embedding spaces that may yield better results but are harder to scale to production environments. In this work, we first construct a simpler model based on triplet loss with hard negatives mining that performs at the state of the art level but does not have these drawbacks. Second, we introduce a novel approach for image retrieval postprocessing called Siamese Transformer for Image Retrieval (STIR) that reranks several top outputs in a single forward pass. Unlike previously proposed Reranking Transformers, STIR does not rely on global/local feature extraction and directly compares a query image and a retrieved candidate on pixel level with the usage of attention mechanism. The resulting approach defines a new state of the art on standard image retrieval datasets: Stanford Online Products and DeepFashion In-shop. We also release the source code at https://github.com/OML-Team/open-metric-learning/tree/main/pipelines/postprocessing/ and an interactive demo of our approach at https://dapladoc-oml-postprocessing-demo-srcappmain-pfh2g0.streamlit.app/

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

We propose the Fréchet Audio Distance (FAD), a novel, reference-free evaluation metric for music enhancement algorithms. We demonstrate how typical evaluation metrics for speech enhancement and blind source separation can fail to accurately measure the perceived effect of a wide variety of distortions. As an alternative, we propose adapting the Fréchet Inception Distance (FID) metric used to evaluate generative image models to the audio domain. FAD is validated using a wide variety of artificial distortions and is compared to the signal based metrics signal to distortion ratio (SDR), cosine distance and magnitude L2 distance. We show that, with a correlation coefficient of 0.52, FAD correlates more closely with human perception than either SDR, cosine distance or magnitude L2 distance, with correlation coefficients of 0.39, -0.15 and -0.01 respectively.

Flying Triangulation sensors enable a free-hand and motion-robust 3D data acquisition of complex shaped objects. The measurement principle is based on a multi-line light-sectioning approach and uses sophisticated algorithms for real-time registration (S. Ettl et al., Appl. Opt. 51 (2012) 281-289). As "single-shot principle", light sectioning enables the option to get surface data from one single camera exposure. But there is a drawback: A pixel-dense measurement is not possible because of fundamental information-theoretical reasons. By "pixel-dense" we understand that each pixel displays individually measured distance information, neither interpolated from its neighbour pixels nor using lateral context information. Hence, for monomodal single-shot principles, the 3D data generated from one 2D raw image display a significantly lower space-bandwidth than the camera permits. This is the price one must pay for motion robustness. Currently, our sensors project about 10 lines (each with 1000 pixels), reaching an considerable lower data efficiency than theoretically possible for a single-shot sensor. Our aim is to push Flying Triangulation to its information-theoretical limits. Therefore, the line density as well as the measurement depth needs to be significantly increased. This causes serious indexing ambiguities. On the road to a single-shot 3D movie camera, we are working on solutions to overcome the problem of false line indexing by utilizing yet unexploited information. We will present several approaches and will discuss profound information-theoretical questions about the information efficiency of 3D sensors.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Adapting standard methods from geometric measure theory, we provide an example of a polynomial-valued measure mu on tame sets in R^d which satisfies many desirable properties. Among these is strict monotonicity: the measure of a proper subset is strictly less than the measure of the whole set. Using techniques from non-standard analysis, we display that the domain of mu can be extended to all subsets of R^d (up to equivalence modulo infinitesimals). The resulting extension is a numerosity function that encodes the i-dimensional Hausdorff measure for all iin N, as well as the i-th intrinsic volume functions.

Data assimilation is the process of estimating the time-evolving state of a dynamical system by integrating model predictions and noisy observations. It is commonly formulated as Bayesian filtering, but classical filters often struggle with accuracy or computational feasibility in high dimensions. Recently, score-based generative models have emerged as a scalable approach for high-dimensional data assimilation, enabling accurate modeling and sampling of complex distributions. However, existing score-based filters often specify the forward process independently of the data assimilation. As a result, the measurement-update step depends on heuristic approximations of the likelihood score, which can accumulate errors and degrade performance over time. Here, we propose a measurement-aware score-based filter (MASF) that defines a measurement-aware forward process directly from the measurement equation. This construction makes the likelihood score analytically tractable: for linear measurements, we derive the exact likelihood score and combine it with a learned prior score to obtain the posterior score. Numerical experiments covering a range of settings, including high-dimensional datasets, demonstrate improved accuracy and stability over existing score-based filters.

Recent 4D Gaussian Splatting (4DGS) methods achieve impressive dynamic scene reconstruction but often rely on piecewise linear velocity approximations and short temporal windows. This disjointed modeling leads to severe temporal fragmentation, forcing primitives to be repeatedly eliminated and regenerated to track complex nonlinear dynamics. This makeshift approximation eliminates the long-term temporal identity of objects and causes an inevitable proliferation of Gaussians, hindering scalability to extended video sequences. To address this, we propose TRiGS, a novel 4D representation that utilizes unified, continuous geometric transformations. By integrating SE(3) transformations, hierarchical Bezier residuals, and learnable local anchors, TRiGS models geometrically consistent rigid motions for individual primitives. This continuous formulation preserves temporal identity and effectively mitigates unbounded memory growth. Extensive experiments demonstrate that TRiGS achieves high fidelity rendering on standard benchmarks while uniquely scaling to extended video sequences (e.g., 600 to 1200 frames) without severe memory bottlenecks, significantly outperforming prior works in temporal stability.

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Scene graph generation has emerged as a prominent research field in computer vision, witnessing significant advancements in the recent years. However, despite these strides, precise and thorough definitions for the metrics used to evaluate scene graph generation models are lacking. In this paper, we address this gap in the literature by providing a review and precise definition of commonly used metrics in scene graph generation. Our comprehensive examination clarifies the underlying principles of these metrics and can serve as a reference or introduction to scene graph metrics. Furthermore, to facilitate the usage of these metrics, we introduce a standalone Python package called SGBench that efficiently implements all defined metrics, ensuring their accessibility to the research community. Additionally, we present a scene graph benchmarking web service, that enables researchers to compare scene graph generation methods and increase visibility of new methods in a central place. All of our code can be found at https://lorjul.github.io/sgbench/.

The "maximum similarity correlation" definition introduced in this study is motivated by the seminal work of Szekely et al on "distance covariance" (Ann. Statist. 2007, 35: 2769-2794; Ann. Appl. Stat. 2009, 3: 1236-1265). Instead of using Euclidean distances "d" as in Szekely et al, we use "similarity", which can be defined as "exp(-d/s)", where the scaling parameter s>0 controls how rapidly the similarity falls off with distance. Scale parameters are chosen by maximizing the similarity correlation. The motivation for using "similarity" originates in spectral clustering theory (see e.g. Ng et al 2001, Advances in Neural Information Processing Systems 14: 849-856). We show that a particular form of similarity correlation is asymptotically equivalent to distance correlation for large values of the scale parameter. Furthermore, we extend similarity correlation to coherence between complex valued vectors, including its partitioning into real and imaginary contributions. Several toy examples are used for comparing distance and similarity correlations. For instance, points on a noiseless straight line give distance and similarity correlation values equal to 1; but points on a noiseless circle produces near zero distance correlation (dCorr=0.02) while the similarity correlation is distinctly non zero (sCorr=0.36). In distinction to the distance approach, similarity gives more importance to small distances, which emphasizes the local properties of functional relations. This paper represents a preliminary empirical study, showing that the novel similarity association has some distinct practical advantages over distance based association.For the sake of reproducible research, the software code implementing all methods here (using lazarus free-pascal "www.lazarus.freepascal.org"), including all test data, are freely available at: "sites.google.com/site/pascualmarqui/home/similaritycovariance".

Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and machine learning. The dominant geometric paradigm for such applications has consisted of a few Riemannian geometries associated with spectral computations that are costly at high scale and in high dimensions. We present a route to a scalable geometric framework for the analysis and processing of SPD-valued data based on the efficient computation of extreme generalized eigenvalues through the Hilbert and Thompson geometries of the semidefinite cone. We explore a particular geodesic space structure based on Thompson geometry in detail and establish several properties associated with this structure. Furthermore, we define a novel iterative mean of SPD matrices based on this geometry and prove its existence and uniqueness for a given finite collection of points. Finally, we state and prove a number of desirable properties that are satisfied by this mean.

Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is different than other unconstrained data, but this point is often neglected by researchers, which results in fallacious statistical analysis. This article studies three prevalent fallacies in group MCDM along with solutions based on compositional data analysis to avoid misusing statistical operations. First, we use a compositional approach to aggregate the priorities of a group of DMs and show that the outcome of the compositional analysis is identical to the normalized geometric mean, meaning that the arithmetic mean should be avoided. Furthermore, a new aggregation method is developed, which is a robust surrogate for the geometric mean. We also discuss the errors in computing measures of dispersion, including standard deviation and distance functions. Discussing the fallacies in computing the standard deviation, we provide a probabilistic criteria ranking by developing proper Bayesian tests, where we calculate the extent to which a criterion is more important than another. Finally, we explain the errors in computing the distance between priorities, and a clustering algorithm is specially tailored based on proper distance metrics.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Firm characteristics are commonly represented as fixed vectors, even though evidence about firms' operations arrives as heterogeneous collections of articles reports. We study how distances between distributions of firm characteristics restrict systematic covariance. For given latent exposure laws, quadratic Wasserstein geometry yields sharp covariance endpoints over admissible couplings. Under a common randomized bi-Lipschitz characteristic-to-exposure map, bounded risk-coordinate slack, and a maintained return-covariance bridge, characteristic-side distance yields a conditional interval for the covariance ceiling. Greater separation then leaves less scope for aligned systematic exposures when these assumptions are tight, while a non-negative transport excess term records the gap between realized and maximum-covariance arrangements. The resulting envelope is scenario analysis rather than an expected-return, no-arbitrage, or identified structural model. Empirically, we proxy characteristic distributions with encoder-only language-model embeddings of financial news articles, disclosures, and analyst reports for Nasdaq firms over 2018-2022. In a dyadic regression with symmetric firm effects, greater pairwise article-embedding W2 distance is associated with weaker return co-movement: the coefficient is 1.920, with 95% interval [1.412, 2.468]. The estimate retains the same sign when returns are measured in a later window, although the feature construction is not point-in-time and the evidence remains reduced form.

We propose a modified moment matching algorithm to avoid catastrophic failures for sources with a low signal to noise ratio (SNR). The proposed modifications include a method to eliminate non-physical negative pixel values and a forced single iteration with an initial guess derived from co-add measurements when iterative methods are unstable. We correct for all biases in measurements introduced by the method. We find that the proposed modifications allow the algorithm to avoid catastrophic failures in nearly 100\% of the cases, especially at low signal to noise ratio. Additionally, with a reasonable guess from co-add measurements, the algorithm measures the flux, centroid, size, shape and ellipticity with bias statistically consistent with zero. We show the proposed method allows us to measure sources seven times fainter than traditional methods when applied to images obtained from WIYN-ODI. We also present a scheme to find uncertainties in measurements when using the new method to measure astronomical sources.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

We extend conformal prediction methodology beyond the case of exchangeable data. In particular, we show that a weighted version of conformal prediction can be used to compute distribution-free prediction intervals for problems in which the test and training covariate distributions differ, but the likelihood ratio between these two distributions is known---or, in practice, can be estimated accurately with access to a large set of unlabeled data (test covariate points). Our weighted extension of conformal prediction also applies more generally, to settings in which the data satisfies a certain weighted notion of exchangeability. We discuss other potential applications of our new conformal methodology, including latent variable and missing data problems.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation of formulas for mathematical constants because each such formula must be correct for infinite digits of precision, with "near-true" formulas providing no insight toward the correct ones. Consequently, formula discovery lacks a clear distance metric needed to guide automated discovery in this realm. In this work, we propose a systematic methodology for categorization, characterization, and pattern identification of such formulas. The key to our methodology is introducing metrics based on the convergence dynamics of the formulas, rather than on the numerical value of the formula. These metrics enable the first automated clustering of mathematical formulas. We demonstrate this methodology on Polynomial Continued Fraction formulas, which are ubiquitous in their intrinsic connections to mathematical constants, and generalize many mathematical functions and structures. We test our methodology on a set of 1,768,900 such formulas, identifying many known formulas for mathematical constants, and discover previously unknown formulas for pi, ln(2), Gauss', and Lemniscate's constants. The uncovered patterns enable a direct generalization of individual formulas to infinite families, unveiling rich mathematical structures. This success paves the way towards a generative model that creates formulas fulfilling specified mathematical properties, accelerating the rate of discovery of useful formulas.

Modern deep residual networks perform substantial redundant computation by evaluating all residual blocks for every input, even when identity mappings suffice. We introduce CosineGate, an end-to-end differentiable architecture for dynamic routing in residual networks that uses cosine incompatibility between identity and residual feature representations as a self-supervised skip signal. CosineGate measures semantic redundancy through the Cosine Incompatibility Ratio (CIR), defined as 1 - cos(x, F(x)), and uses Gumbel-Softmax relaxation to enable per-sample, per-block gating during training. A progressive FLOPs regularization term controls average compute usage without destabilizing optimization. On CIFAR-10, CosineGate spans the accuracy-efficiency Pareto frontier: an aggressive configuration achieves 89.9 percent accuracy with 24.1 percent FLOPs savings, a balanced configuration achieves 91.3 percent accuracy with 28.5 percent savings at epoch 160, and a conservative configuration reaches a peak of 93.2 percent accuracy with minimal compute reduction. These results match or exceed ResNet-20 (91.3 percent) while reducing computation, without auxiliary supervision, distillation, or task-specific heuristics. Our results demonstrate that simple geometric measures of feature incompatibility provide a principled and effective signal for dynamic residual routing.

Nonlinear sufficient dimension reductionlibing_generalSDR, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean random objects, which are frequently encountered in many recent statistical applications. In this paper, we introduce a new statistical dependence measure termed Fr\'echet Cumulative Covariance (FCCov) and develop a novel nonlinear SDR framework based on FCCov. Our approach is not only applicable to complex non-Euclidean data, but also exhibits robustness against outliers. We further incorporate Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to estimate nonlinear sufficient directions in the sample level. Theoretically, we prove that our method with squared Frobenius norm regularization achieves unbiasedness at the sigma-field level. Furthermore, we establish non-asymptotic convergence rates for our estimators based on FNNs and ResNet-type CNNs, which match the minimax rate of nonparametric regression up to logarithmic factors. Intensive simulation studies verify the performance of our methods in both Euclidean and non-Euclidean settings. We apply our method to facial expression recognition datasets and the results underscore more realistic and broader applicability of our proposal.

Recently, self-supervised learning has attracted great attention, since it only requires unlabeled data for model training. Contrastive learning is one popular method for self-supervised learning and has achieved promising empirical performance. However, the theoretical understanding of its generalization ability is still limited. To this end, we define a kind of (sigma,delta)-measure to mathematically quantify the data augmentation, and then provide an upper bound of the downstream classification error rate based on the measure. It reveals that the generalization ability of contrastive self-supervised learning is related to three key factors: alignment of positive samples, divergence of class centers, and concentration of augmented data. The first two factors are properties of learned representations, while the third one is determined by pre-defined data augmentation. We further investigate two canonical contrastive losses, InfoNCE and cross-correlation, to show how they provably achieve the first two factors. Moreover, we conduct experiments to study the third factor, and observe a strong correlation between downstream performance and the concentration of augmented data.

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.

Recent studies show that paddings in convolutional neural networks encode absolute position information which can negatively affect the model performance for certain tasks. However, existing metrics for quantifying the strength of positional information remain unreliable and frequently lead to erroneous results. To address this issue, we propose novel metrics for measuring (and visualizing) the encoded positional information. We formally define the encoded information as PPP (Position-information Pattern from Padding) and conduct a series of experiments to study its properties as well as its formation. The proposed metrics measure the presence of positional information more reliably than the existing metrics based on PosENet and a test in F-Conv. We also demonstrate that for any extant (and proposed) padding schemes, PPP is primarily a learning artifact and is less dependent on the characteristics of the underlying padding schemes.

As an adaptive method, Shampoo employs a structured second-moment estimation, and its effectiveness has attracted growing attention. Prior work has primarily analyzed its estimation scheme through the Frobenius norm. Motivated by the natural connection between the second moment and a covariance matrix, we propose studying Shampoo's estimation as covariance estimation through the lens of Kullback-Leibler (KL) minimization. This alternative perspective reveals a previously hidden limitation, motivating improvements to Shampoo's design. Building on this insight, we develop a practical estimation scheme, termed KL-Shampoo, that eliminates Shampoo's reliance on Adam for stabilization, thereby removing the additional memory overhead introduced by Adam. Preliminary results show that KL-Shampoo improves Shampoo's performance, enabling it to stabilize without Adam and even outperform its Adam-stabilized variant, SOAP, in neural network pretraining.

We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold. The estimator fuses samples from a hierarchy of data sources of differing fidelities and costs for variance reduction while guaranteeing definiteness, in contrast with previous approaches. The new estimator makes covariance estimation tractable in applications where simulation or data collection is expensive; to that end, we develop an optimal sample allocation scheme that minimizes the mean-squared error of the estimator given a fixed budget. Guaranteed definiteness is crucial to metric learning, data assimilation, and other downstream tasks. Evaluations of our approach using data from physical applications (heat conduction, fluid dynamics) demonstrate more accurate metric learning and speedups of more than one order of magnitude compared to benchmarks.

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

Block-based video codecs select coding parameters based on the input by optimizing a rate-distortion trade-off. The conventional distortion choice, the sum of squared errors (SSE), simplifies parameter selection: the SSE is the sum of block-wise SSEs, so rate-distortion optimization (RDO) can treat blocks independently. Alternatively, full-reference image quality assessment (FR-IQA) metrics such as MS-SSIM or LPIPS often align better with the human visual system than SSE, but they cannot be used in-loop: they do not decompose block-wise and typically require the fully decoded image as input. Building on existing results in metric quadratization, we approximate a broad class of FR-IQA metrics by an input-dependent quadratic distortion (IDQD), whose quadratic form matrix is derived from the Hessian of the metric evaluated at the source video. To make the distortion computable block-wise, we propose two approximations of the Hessian matrix: 1) keeping the block-diagonal, and 2) keeping only its diagonal. We propose estimators for both that require only matrix-vector products with the Hessian obtained by automatic differentiation. Across five metrics for Kodak and CLIC in VVC, IDQD-RDO achieves 14.2-36.7 % BD-rate savings under the target metric with no decoder changes and incurs 10-30 % encoding complexity overhead.

Using Large Language Models for complex mathematical reasoning is difficult, primarily due to the complexity of multi-step reasoning. The main challenges of this process include (1) selecting critical intermediate results to advance the procedure, and (2) limited exploration of potential solutions. To address these issues, we introduce a novel algorithm, namely Stepwise Self-Consistent Chain-of-Thought (SSC-CoT). SSC-CoT employs a strategy of selecting intermediate steps based on the intersection of various reasoning chains. Additionally, SSC-CoT enables the model to discover critical intermediate steps by querying a knowledge graph comprising relevant domain knowledge. To validate SSC-CoT, we present a new dataset, TriMaster100, tailored for complex trigonometry problems. This dataset contains 100 questions, with each solution broken down into scored intermediate steps, facilitating a comprehensive evaluation of the mathematical reasoning process. On TriMaster100, SSC-CoT triples the effectiveness of the state-of-the-art methods. Furthermore, we benchmark SSC-CoT on the widely recognized complex mathematical question dataset, MATH level 5, and it surpasses the second-best method by 7.2% in accuracy. Code and the TriMaster100 dataset can be found at: https://github.com/zhao-zilong/ssc-cot.

In order to read meter values from a camera on an autonomous inspection robot with positional errors, it is necessary to detect meter regions from the image. In this study, we developed shape-based, texture-based, and background information-based methods as meter area detection techniques and compared their effectiveness for meters of different shapes and sizes. As a result, we confirmed that the background information-based method can detect the farthest meters regardless of the shape and number of meters, and can stably detect meters with a diameter of 40px.

We develop a robust quaternion recurrent neural network (QRNN) for real-time processing of 3D and 4D data with outliers. This is achieved by combining the real-time recurrent learning (RTRL) algorithm and the maximum correntropy criterion (MCC) as a loss function. While both the mean square error and maximum correntropy criterion are viable cost functions, it is shown that the non-quadratic maximum correntropy loss function is less sensitive to outliers, making it suitable for applications with multidimensional noisy or uncertain data. Both algorithms are derived based on the novel generalised HR (GHR) calculus, which allows for the differentiation of real functions of quaternion variables and offers the product and chain rules, thus enabling elegant and compact derivations. Simulation results in the context of motion prediction of chest internal markers for lung cancer radiotherapy, which includes regular and irregular breathing sequences, support the analysis.

Searching for approximate nearest neighbors (ANN) in the high-dimensional Euclidean space is a pivotal problem. Recently, with the help of fast SIMD-based implementations, Product Quantization (PQ) and its variants can often efficiently and accurately estimate the distances between the vectors and have achieved great success in the in-memory ANN search. Despite their empirical success, we note that these methods do not have a theoretical error bound and are observed to fail disastrously on some real-world datasets. Motivated by this, we propose a new randomized quantization method named RaBitQ, which quantizes D-dimensional vectors into D-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations. Extensive experiments on real-world datasets confirm that (1) our method outperforms PQ and its variants in terms of accuracy-efficiency trade-off by a clear margin and (2) its empirical performance is well-aligned with our theoretical analysis.

The present paper attempts to modify the way of constructing a measure in the Alternative Set Theory setting originally devised by Martin Kalina. Introducing a system of cuts of rational numbers extended with some special ones, it is proved that the measure which is nondecreasing, nonnegative and "depending on the way of measurement" as same as Kalina's, but exhibits σ-superadditivity is obtained.

We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Loève transform, and several others along with their continuous counterparts (Fourier transform, Fourier series, spherical harmonics, fractional Fourier transform) under one representation-theoretic principle: each is the eigenbasis of every covariance invariant under a specific finite or compact group, with columns constructed from the irreducible matrix elements of the group via the Peter-Weyl theorem. The unification rests on the Algebraic Diversity (AD) framework, which identifies the matched group of a covariance as the foundational object of second-order signal processing. The data-dependent KLT emerges as the trivial-matched-group limit; classical transforms emerge as the cyclic, dihedral, elementary abelian, iterated wreath, and hybrid wreath cases. Composition rules cover direct, wreath, and semidirect products. The Reed-Muller and arithmetic transforms appear as related change-of-basis transforms on the matched group of Walsh-Hadamard. A polynomial-time algorithm for matched-group discovery, the DAD-CAD relaxation cast as a generalized eigenvalue problem in double-commutator form, closes the operational loop: the matched group of any empirical covariance is discovered without expert judgment, with noise-aware variants via the commutativity residual δ and algebraic coloring index α for finite-SNR settings. The fractional Fourier transform is treated as the metaplectic SO(2) case with Hermite-Gauss matched basis, and a structural principle relates matched group size inversely to transform resolution. Modern applications (massive-MIMO, graph neural networks, transformer attention, point cloud and 3D vision, brain connectivity, single-cell genomics, quantum informatics) are sketched with their matched groups.

The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Lo\`eve transform (KLT), which is the optimal transform in terms of retained transform coefficients and data decorrelation. In this paper, we introduce 16-, 32-, and 64-point low-complexity DCT approximations by minimizing individually the angle between the rows of the exact DCT matrix and the matrix induced by the approximate transforms. According to some classical figures of merit, the proposed transforms outperformed the approximations for the DCT already known in the literature. Fast algorithms were also developed for the low-complexity transforms, asserting a good balance between the performance and its computational cost. Practical applications in image encoding showed the relevance of the transforms in this context. In fact, the experiments showed that the proposed transforms had better results than the known approximations in the literature for the cases of 16, 32, and 64 blocklength.

Limited data is a common problem in remote sensing due to the high cost of obtaining annotated samples. In the few-shot segmentation task, models are typically trained on base classes with abundant annotations and later adapted to novel classes with limited examples. However, this often necessitates specialized model architectures or complex training strategies. Instead, we propose a simple approach that leverages diffusion models to generate diverse variations of novel-class objects within a given scene, conditioned by the limited examples of the novel classes. By framing the problem as an image inpainting task, we synthesize plausible instances of novel classes under various environments, effectively increasing the number of samples for the novel classes and mitigating overfitting. The generated samples are then assessed using a cosine similarity metric to ensure semantic consistency with the novel classes. Additionally, we employ Segment Anything Model (SAM) to segment the generated samples and obtain precise annotations. By using high-quality synthetic data, we can directly fine-tune off-the-shelf segmentation models. Experimental results demonstrate that our method significantly enhances segmentation performance in low-data regimes, highlighting its potential for real-world remote sensing applications.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Classical CUSUM relies on the log-likelihood ratio of the underlying distributions, which cannot generally be computed from finite pre- and post-change samples alone. We propose diffusion-integrated score CUSUM (DI-SCUSUM), a training-free detector. We add Gaussian noise to the samples to form two smooth density estimates and calculate their Hyvärinen scores exactly, without training a score network. For each incoming observation, we sample a diffusion time, perturb the observation, and use the importance-weighted score difference as an increment in the DI-SCUSUM recursion. Under the assumption that observations follow the fixed empirical distributions, the post-change mean increment is proportional to the Kullback-Leibler (KL) divergence from the smoothed post-change to the smoothed pre-change empirical distribution. We establish exponential false-alarm scaling and a first-order delay bound that, for a fixed threshold and increment scaling, is inversely proportional to the KL divergence. In the calibrated anisotropic Gaussian simulation, DI-SCUSUM nearly matches likelihood-ratio CUSUM and reduces the measured detection delay by about 91% relative to score-based CUSUM. On MNIST and Oxford-IIIT Pet, DI-SCUSUM also has lower empirical conditional detection delay than SCUSUM at comparable false-alarm levels.

We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

We address the task of estimating camera parameters from a set of images depicting a scene. Popular feature-based structure-from-motion (SfM) tools solve this task by incremental reconstruction: they repeat triangulation of sparse 3D points and registration of more camera views to the sparse point cloud. We re-interpret incremental structure-from-motion as an iterated application and refinement of a visual relocalizer, that is, of a method that registers new views to the current state of the reconstruction. This perspective allows us to investigate alternative visual relocalizers that are not rooted in local feature matching. We show that scene coordinate regression, a learning-based relocalization approach, allows us to build implicit, neural scene representations from unposed images. Different from other learning-based reconstruction methods, we do not require pose priors nor sequential inputs, and we optimize efficiently over thousands of images. Our method, ACE0 (ACE Zero), estimates camera poses to an accuracy comparable to feature-based SfM, as demonstrated by novel view synthesis. Project page: https://nianticlabs.github.io/acezero/

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where eta:=M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X,Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to R\'{e}nyi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of gamma-H\"{o}lder smooth functions, the estimator achieves the MSE rate of O(N^{-2gamma/(gamma+d)}). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

Quantized neural networks employ reduced precision representations for both weights and activations. This quantization process significantly reduces the memory requirements and computational complexity of the network. Binary Neural Networks (BNNs) are the extreme quantization case, representing values with just one bit. Since the sign function is typically used to map real values to binary values, smooth approximations are introduced to mimic the gradients during error backpropagation. Thus, the mismatch between the forward and backward models corrupts the direction of the gradient, causing training inconsistency problems and performance degradation. In contrast to current BNN approaches, we propose to employ a binary periodic (BiPer) function during binarization. Specifically, we use a square wave for the forward pass to obtain the binary values and employ the trigonometric sine function with the same period of the square wave as a differentiable surrogate during the backward pass. We demonstrate that this approach can control the quantization error by using the frequency of the periodic function and improves network performance. Extensive experiments validate the effectiveness of BiPer in benchmark datasets and network architectures, with improvements of up to 1% and 0.69% with respect to state-of-the-art methods in the classification task over CIFAR-10 and ImageNet, respectively. Our code is publicly available at https://github.com/edmav4/BiPer.

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation. In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

Room acoustics analysis plays a central role in architectural design, audio engineering, speech intelligibility assessment, and hearing research. Despite the availability of standardized metrics such as reverberation time, clarity, and speech transmission index, accessible tools that combine rigorous signal processing with intuitive visualization remain scarce. This paper presents AcoustiVision Pro, an open-source web-based platform for comprehensive room impulse response (RIR) analysis. The system computes twelve distinct acoustic parameters from uploaded or dataset-sourced RIRs, provides interactive 3D visualizations of early reflections, generates frequency-dependent decay characteristics through waterfall plots, and checks compliance against international standards including ANSI S12.60 and ISO 3382. We introduce the accompanying RIRMega and RIRMega Speech datasets hosted on Hugging Face, containing thousands of simulated room impulse responses with full metadata. The platform supports real-time auralization through FFT-based convolution, exports detailed PDF reports suitable for engineering documentation, and provides CSV data export for further analysis. We describe the mathematical foundations underlying each acoustic metric, detail the system architecture, and present preliminary case studies demonstrating the platform's utility across diverse application domains including classroom acoustics, healthcare facility design, and recording studio evaluation.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

Many real-world machine learning problems involve inherently hierarchical data, yet traditional approaches rely on Euclidean metrics that fail to capture the discrete, branching nature of hierarchical relationships. We present a theoretical foundation for machine learning in p-adic metric spaces, which naturally respect hierarchical structure. Our main result proves that an n-dimensional plane minimizing the p-adic sum of distances to points in a dataset must pass through at least n + 1 of those points -- a striking contrast to Euclidean regression that highlights how p-adic metrics better align with the discrete nature of hierarchical data. As a corollary, a polynomial of degree n constructed to minimise the p-adic sum of residuals will pass through at least n + 1 points. As a further corollary, a polynomial of degree n approximating a higher degree polynomial at a finite number of points will yield a difference polynomial that has distinct rational roots. We demonstrate the practical significance of this result through two applications in natural language processing: analyzing hierarchical taxonomies and modeling grammatical morphology. These results suggest that p-adic metrics may be fundamental to properly handling hierarchical data structures in machine learning. In hierarchical data, interpolation between points often makes less sense than selecting actual observed points as representatives.

This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of k+1 reference points. As this definition relies on points and not on tangent vectors, it can also be extended to geodesic spaces which are not Riemannian. For instance, in stratified spaces, it naturally allows principal subspaces that span several strata, which is impossible in previous generalizations of PCA. We show that barycentric subspaces locally define a submanifold of dimension k which generalizes geodesic subspaces.Second, we rephrase PCA in Euclidean spaces as an optimization on flags of linear subspaces (a hierarchy of properly embedded linear subspaces of increasing dimension). We show that the Euclidean PCA minimizes the Accumulated Unexplained Variances by all the subspaces of the flag (AUV). Barycentric subspaces are naturally nested, allowing the construction of hierarchically nested subspaces. Optimizing the AUV criterion to optimally approximate data points with flags of affine spans in Riemannian manifolds lead to a particularly appealing generalization of PCA on manifolds called Barycentric Subspaces Analysis (BSA).

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

Objective speech-quality metrics are widely used to assess codec performance. However, for neural codecs, it is often unclear which metrics provide reliable quality estimates. To address this, we evaluated 45 objective metrics by correlating their scores with subjective listening scores for clean speech across 17 codec conditions. Neural-based metrics such as scoreq and utmos achieved the highest Pearson correlations with subjective scores. Further analysis across different subjective quality ranges revealed that non-intrusive metrics tend to saturate at high subjective quality levels.

Evaluation metrics are central to binary target segmentation because they determine how progress is measured, compared, and interpreted. In this paper, target denotes the task-defined positive region to be segmented rather than a generic foreground object. It may be salient, camouflaged, transparent, glass-like, mirror-like, shadow-like, lesion-like, or defined by other application-specific semantics. We treat existing metrics as compositions of modular design choices rather than isolated formulas. The proposed framework decomposes each metric into five stages covering prediction representation, target extraction, target matching, score computation, and metric reporting. We use this framework to analyze representative metrics and show how newer metrics address specific limits in earlier protocols. The stage choices keep each metric's assumptions visible. We then discuss the design space opened by the framework and its implications for task-aware evaluation protocols. Reference code is available at https://github.com/lartpang/PySODMetrics.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The harmonic loss is a distance-based alternative grounded in Euclidean geometry that improves interpretability and mitigates phenomena such as grokking, or delayed generalization on the test set. However, the study of harmonic loss remains narrow: only Euclidean distance is explored, and no systematic evaluation of computational efficiency or sustainability was conducted. We extend harmonic loss by systematically investigating a broad spectrum of distance metrics as replacements for the Euclidean distance. We comprehensively evaluate distance-tailored harmonic losses on both vision backbones and large language models. Our analysis is framed around a three-way evaluation of model performance, interpretability, and sustainability. On vision tasks, cosine distances provide the most favorable trade-off, consistently improving accuracy while lowering carbon emissions, whereas Bray-Curtis and Mahalanobis further enhance interpretability at varying efficiency costs. On language models, cosine-based harmonic losses improve gradient and learning stability, strengthen representation structure, and reduce emissions relative to cross-entropy and Euclidean heads. Our code is available at: https://anonymous.4open.science/r/rethinking-harmonic-loss-5BAB/.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the well-known Pearson correlation coefficient, the most important is that distance correlation equals zero if and only if the random vectors are independent. There are two different estimators of the distance correlation available in the literature. The first one, proposed by Székely et al. (2007), is based on an asymptotically unbiased estimator of the distance covariance which turns out to be a V-statistic. The second one builds on an unbiased estimator of the distance covariance proposed in Székely et al. (2014), proved to be an U-statistic by Székely and Huo (2016). This study evaluates their efficiency (mean squared error) and compares computational times for both methods under different dependence structures. Under conditions of independence or near-independence, the V-estimates are biased, while the U-estimator frequently cannot be computed due to negative values. To address this challenge, a convex linear combination of the former estimators is proposed and studied, yielding good results regardless of the level of dependence.

Intrinsic dimension (ID) is an important tool in modern LLM analysis, informing studies of training dynamics, scaling behavior, and dataset structure, yet its textual determinants remain underexplored. We provide the first comprehensive study grounding ID in interpretable text properties through cross-encoder analysis, linguistic features, and sparse autoencoders (SAEs). In this work, we establish three key findings. First, ID is complementary to entropy-based metrics: after controlling for length, the two are uncorrelated, with ID capturing geometric complexity orthogonal to prediction quality. Second, ID exhibits robust genre stratification: scientific prose shows low ID (~8), encyclopedic content medium ID (~9), and creative/opinion writing high ID (~10.5) across all models tested. This reveals that contemporary LLMs find scientific text "representationally simple" while fiction requires additional degrees of freedom. Third, using SAEs, we identify causal features: scientific signals (formal tone, report templates, statistics) reduce ID; humanized signals (personalization, emotion, narrative) increase it. Steering experiments confirm these effects are causal. Thus, for contemporary models, scientific writing appears comparatively "easy", whereas fiction, opinion, and affect add representational degrees of freedom. Our multi-faceted analysis provides practical guidance for the proper use of ID and the sound interpretation of ID-based results.

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 and initial weights of each layer consistently translate into better generalization performance of the final model. Interestingly, this relation admits a network independent optimum: training procedures during which all layers' weights reach a cosine distance of 1 from their initialization consistently outperform other configurations -by up to 30% test accuracy. Moreover, we show that layer rotations are easily monitored and controlled (helpful for hyperparameter tuning) and potentially provide a unified framework to explain the impact of learning rate tuning, weight decay, learning rate warmups and adaptive gradient methods on generalization and training speed. In an attempt to explain the surprising properties of layer rotation, we show on a 1-layer MLP trained on MNIST that layer rotation correlates with the degree to which features of intermediate layers have been trained.

Devising indicative evaluation metrics for the image generation task remains an open problem. The most widely used metric for measuring the similarity between real and generated images has been the Fr\'echet Inception Distance (FID) score. Because it does not differentiate the fidelity and diversity aspects of the generated images, recent papers have introduced variants of precision and recall metrics to diagnose those properties separately. In this paper, we show that even the latest version of the precision and recall metrics are not reliable yet. For example, they fail to detect the match between two identical distributions, they are not robust against outliers, and the evaluation hyperparameters are selected arbitrarily. We propose density and coverage metrics that solve the above issues. We analytically and experimentally show that density and coverage provide more interpretable and reliable signals for practitioners than the existing metrics. Code: https://github.com/clovaai/generative-evaluation-prdc.

Reliable pattern recognition systems should exhibit consistent behavior across similar inputs, and their explanations should remain stable. However, most Explainable AI evaluations remain instance centric and do not explicitly quantify whether attribution patterns are consistent across samples that share the same class or represent small variations of the same input. In this work, we propose a novel metric aimed at assessing the consistency of model explanations, ensuring that models consistently reflect the intended objectives and consistency under label-preserving perturbations. We implement this metric using a pre-trained BERT model on the SST-2 sentiment analysis dataset, with additional robustness tests on RoBERTa, DistilBERT, and IMDB, applying SHAP to compute feature importance for various test samples. The proposed metric quantifies the cosine similarity of SHAP values for inputs with the same label, aiming to detect inconsistent behaviors, such as biased reliance on certain features or failure to maintain consistent reasoning for similar predictions. Through a series of experiments, we evaluate the ability of this metric to identify misaligned predictions and inconsistencies in model explanations. These experiments are compared against standard fidelity metrics to assess whether the new metric can effectively identify when a model's behavior deviates from its intended objectives. The proposed framework provides a deeper understanding of model behavior by enabling more robust verification of rationale stability, which is critical for building trustworthy AI systems. By quantifying whether models rely on consistent attribution patterns for similar inputs, the proposed approach supports more robust evaluation of model behavior in practical pattern recognition pipelines. Our code is publicly available at https://github.com/anmspro/ESS-XAI-Stability.

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data, and on estimating local Hessian matrices of neural network loss landscapes.

AI models are increasingly used for data analysis and visualization, yet benchmarks rarely address scatterplot-specific tasks, limiting insight into performance. To address this gap for one of the most common chart types, we introduce a synthetic, annotated dataset of over 18,000 scatterplots from six data generators and 17 chart designs, and a benchmark based on it. We evaluate proprietary models from OpenAI and Google using N-shot prompting on five distinct tasks derived from annotations of cluster bounding boxes, their center coordinates, and outlier coordinates. OpenAI models and Gemini 2.5 Flash, especially when prompted with examples, are viable options for counting clusters and, in Flash's case, outliers (90%+ Accuracy). However, the results for localization-related tasks are unsatisfactory: Precision and Recall are near or below 50%, except for Flash in outlier identification (65.01%). Furthermore, the impact of chart design on performance appears to be a secondary factor, but it is advisable to avoid scatterplots with wide aspect ratios (16:9 and 21:9) or those colored randomly. Supplementary materials are available at https://github.com/feedzai/biy-paper.

Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which limits the suitability of the algorithm for larger values of k depending on the size of the collection. Optimizations targeted at the Euclidean k-Means algorithm largely do not apply because the cosine distance is not a metric. We therefore propose an efficient indexing structure to improve the scalability of Spherical k-Means with respect to k. Our approach exploits the sparsity of the input vectors and the convergence behavior of k-Means to reduce the number of comparisons on each iteration significantly.

Traditional fish farming practices often lead to inefficient feeding, resulting in environmental issues and reduced productivity. We developed an innovative system combining computer vision and IoT technologies for precise Tilapia feeding. Our solution uses real-time IoT sensors to monitor water quality parameters and computer vision algorithms to analyze fish size and count, determining optimal feed amounts. A mobile app enables remote monitoring and control. We utilized YOLOv8 for keypoint detection to measure Tilapia weight from length, achieving 94\% precision on 3,500 annotated images. Pixel-based measurements were converted to centimeters using depth estimation for accurate feeding calculations. Our method, with data collection mirroring inference conditions, significantly improved results. Preliminary estimates suggest this approach could increase production up to 58 times compared to traditional farms. Our models, code, and dataset are open-source~\footnote{The code, dataset, and models are available upon reasonable request.

Image Quality Assessment (IQA) measures and predicts perceived image quality by human observers. Although recent studies have highlighted the critical influence that variations in the scale of an image have on its perceived quality, this relationship has not been systematically quantified. To bridge this gap, we introduce the Image Intrinsic Scale (IIS), defined as the largest scale where an image exhibits its highest perceived quality. We also present the Image Intrinsic Scale Assessment (IISA) task, which involves subjectively measuring and predicting the IIS based on human judgments. We develop a subjective annotation methodology and create the IISA-DB dataset, comprising 785 image-IIS pairs annotated by experts in a rigorously controlled crowdsourcing study. Furthermore, we propose WIISA (Weak-labeling for Image Intrinsic Scale Assessment), a strategy that leverages how the IIS of an image varies with downscaling to generate weak labels. Experiments show that applying WIISA during the training of several IQA methods adapted for IISA consistently improves the performance compared to using only ground-truth labels. We will release the code, dataset, and pre-trained models upon acceptance.