Mariano Tepper

Mariano Tepper, Guillermo Sapiro

Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a (weighted) L2 norm while the latter ensures smoothness. Thus, when dealing with grid data, the optimization can be solved very efficiently using the DCT. In this work we propose to replace the L2 norm in the fitting term with an L1 norm, leading to automatic robustness to outliers. To solve the resulting minimization problem we propose an extremely simple and efficient numerical scheme based on split-Bregman iteration combined with DCT. Experimental validation shows the high-quality results obtained in short processing times.

Romain Cosentino, Anirvan Sengupta, Salman Avestimehr et al.

Self-supervised learning (SSL) is currently one of the premier techniques to create data representations that are actionable for transfer learning in the absence of human annotations. Despite their success, the underlying geometry of these representations remains elusive, which obfuscates the quest for more robust, trustworthy, and interpretable models. In particular, mainstream SSL techniques rely on a specific deep neural network architecture with two cascaded neural networks: the encoder and the projector. When used for transfer learning, the projector is discarded since empirical results show that its representation generalizes more poorly than the encoder's. In this paper, we investigate this curious phenomenon and analyze how the strength of the data augmentation policies affects the data embedding. We discover a non-trivial relation between the encoder, the projector, and the data augmentation strength: with increasingly larger augmentation policies, the projector, rather than the encoder, is more strongly driven to become invariant to the augmentations. It does so by eliminating crucial information about the data by learning to project it into a low-dimensional space, a noisy estimate of the data manifold tangent plane in the encoder representation. This analysis is substantiated through a geometrical perspective with theoretical and empirical results.

Cecilia Aguerrebere, Ishwar Bhati, Mark Hildebrand et al.

Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications. Graph-based indices are currently the best performing techniques for billion-scale similarity search. However, their random-access memory pattern presents challenges to realize their full potential. In this work, we present new techniques and systems for creating faster and smaller graph-based indices. To this end, we introduce a novel vector compression method, Locally-adaptive Vector Quantization (LVQ), that uses per-vector scaling and scalar quantization to improve search performance with fast similarity computations and a reduced effective bandwidth, while decreasing memory footprint and barely impacting accuracy. LVQ, when combined with a new high-performance computing system for graph-based similarity search, establishes the new state of the art in terms of performance and memory footprint. For billions of vectors, LVQ outcompetes the second-best alternatives: (1) in the low-memory regime, by up to 20.7x in throughput with up to a 3x memory footprint reduction, and (2) in the high-throughput regime by 5.8x with 1.4x less memory.

Cecilia Aguerrebere, Mark Hildebrand, Ishwar Singh Bhati et al.

Retrieving the most similar vector embeddings to a given query among a massive collection of vectors has long been a key component of countless real-world applications. The recently introduced Retrieval-Augmented Generation is one of the most prominent examples. For many of these applications, the database evolves over time by inserting new data and removing outdated data. In these cases, the retrieval problem is known as streaming similarity search. While Locally-Adaptive Vector Quantization (LVQ), a highly efficient vector compression method, yields state-of-the-art search performance for non-evolving databases, its usefulness in the streaming setting has not been yet established. In this work, we study LVQ in streaming similarity search. In support of our evaluation, we introduce two improvements of LVQ: Turbo LVQ and multi-means LVQ that boost its search performance by up to 28% and 27%, respectively. Our studies show that LVQ and its new variants enable blazing fast vector search, outperforming its closest competitor by up to 9.4x for identically distributed data and by up to 8.8x under the challenging scenario of data distribution shifts (i.e., where the statistical distribution of the data changes over time). We release our contributions as part of Scalable Vector Search, an open-source library for high-performance similarity search.

Seyed Saman Saboksayr, Gonzalo Mateos, Mariano Tepper

We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the $\textit{unknown}$ SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from the exogenous noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE ($\textbf{Co}$ncomitant $\textbf{Li}$near $\textbf{D}$AG $\textbf{E}$stimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of noise variances in heteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger and the noise level profile is heterogeneous. We also find CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of our novel linear DAG estimator.

Mariano Tepper, Ishwar Singh Bhati, Cecilia Aguerrebere et al.

Modern deep learning models have the ability to generate high-dimensional vectors whose similarity reflects semantic resemblance. Thus, similarity search, i.e., the operation of retrieving those vectors in a large collection that are similar to a given query, has become a critical component of a wide range of applications that demand highly accurate and timely answers. In this setting, the high vector dimensionality puts similarity search systems under compute and memory pressure, leading to subpar performance. Additionally, cross-modal retrieval tasks have become increasingly common, e.g., where a user inputs a text query to find the most relevant images for that query. However, these queries often have different distributions than the database embeddings, making it challenging to achieve high accuracy. In this work, we present LeanVec, a framework that combines linear dimensionality reduction with vector quantization to accelerate similarity search on high-dimensional vectors while maintaining accuracy. We present LeanVec variants for in-distribution (ID) and out-of-distribution (OOD) queries. LeanVec-ID yields accuracies on par with those from recently introduced deep learning alternatives whose computational overhead precludes their usage in practice. LeanVec-OOD uses two novel techniques for dimensionality reduction that consider the query and database distributions to simultaneously boost the accuracy and the performance of the framework even further (even presenting competitive results when the query and database distributions match). All in all, our extensive and varied experimental results show that LeanVec produces state-of-the-art results, with up to 3.7x improvement in search throughput and up to 4.9x faster index build time over the state of the art.

Alexandria Leto, Cecilia Aguerrebere, Ishwar Bhati et al.

Retrieval-augmented generation (RAG) is a promising method for addressing some of the memory-related challenges associated with Large Language Models (LLMs). Two separate systems form the RAG pipeline, the retriever and the reader, and the impact of each on downstream task performance is not well-understood. Here, we work towards the goal of understanding how retrievers can be optimized for RAG pipelines for common tasks such as Question Answering (QA). We conduct experiments focused on the relationship between retrieval and RAG performance on QA and attributed QA and unveil a number of insights useful to practitioners developing high-performance RAG pipelines. For example, lowering search accuracy has minor implications for RAG performance while potentially increasing retrieval speed and memory efficiency.

Mariano Tepper, Ted Willke

Embedding vectors are widely used for representing unstructured data and searching through it for semantically similar items. However, the large size of these vectors, due to their high-dimensionality, creates problems for modern vector search techniques: retrieving large vectors from memory/storage is expensive and their footprint is costly. In this work, we present NVQ (non-uniform vector quantization), a new vector compression technique that is computationally and spatially efficient in the high-fidelity regime. The core in NVQ is to use novel parsimonious and computationally efficient nonlinearities for building non-uniform vector quantizers. Critically, these quantizers are \emph{individually} learned for each indexed vector. Our experimental results show that NVQ exhibits improved accuracy compared to the state of the art with a minimal computational cost.

Mariano Tepper, Ted Willke

The most popular graph indices for vector search use principles from computational geometry to build the graph. Hence, their formal graph navigability guarantees are only valid in Euclidean space. In this work, we show that machine learning can be used to build graph indices for vector search in metric and non-metric vector spaces (e.g., for inner product similarity). From this novel perspective, we introduce the Support Vector Graph (SVG), a new type of graph index that leverages kernel methods to establish the graph connectivity and that comes with formal navigability guarantees valid in metric and non-metric vector spaces. In addition, we interpret the most popular graph indices, including HNSW and DiskANN, as particular specializations of SVG and show that new indices can be derived from the principles behind this specialization. Finally, we propose SVG-L0 that incorporates an $\ell_0$ sparsity constraint into the SVG kernel method to build graphs with a bounded out-degree. This yields a principled way of implementing this practical requirement, in contrast to the traditional heuristic of simply truncating the out edges of each node. Additionally, we show that SVG-L0 has a self-tuning property that avoids the heuristic of using a set of candidates to find the out-edges of each node and that keeps its computational complexity in check.

Mariano Tepper, Ishwar Singh Bhati, Cecilia Aguerrebere et al.

Embedding models can generate high-dimensional vectors whose similarity reflects semantic affinities. Thus, accurately and timely retrieving those vectors in a large collection that are similar to a given query has become a critical component of a wide range of applications. In particular, cross-modal retrieval (e.g., where a text query is used to find images) is gaining momentum rapidly. Here, it is challenging to achieve high accuracy as the queries often have different statistical distributions than the database vectors. Moreover, the high vector dimensionality puts these search systems under compute and memory pressure, leading to subpar performance. In this work, we present new linear and nonlinear methods for dimensionality reduction to accelerate high-dimensional vector search while maintaining accuracy in settings with in-distribution (ID) and out-of-distribution (OOD) queries. The linear LeanVec-Sphering outperforms other linear methods, trains faster, comes with no hyperparameters, and allows to set the target dimensionality more flexibly. The nonlinear Generalized LeanVec (GleanVec) uses a piecewise linear scheme to further improve the search accuracy while remaining computationally nimble. Initial experimental results show that LeanVec-Sphering and GleanVec push the state of the art for vector search.

Mariano Tepper, Dipanjan Sengupta, Ted Willke

Hashing is one of the most popular methods for similarity search because of its speed and efficiency. Dense binary hashing is prevalent in the literature. Recently, insect olfaction was shown to be structurally and functionally analogous to sparse hashing [6]. Here, we prove that this biological mechanism is the solution to a well-posed optimization problem. Furthermore, we show that orthogonality increases the accuracy of sparse hashing. Next, we present a novel method, Procrustean Orthogonal Sparse Hashing (POSH), that unifies these findings, learning an orthogonal transform from training data compatible with the sparse hashing mechanism. We provide theoretical evidence of the shortcomings of Optimal Sparse Lifting (OSL) [22] and BioHash [30], two related olfaction-inspired methods, and propose two new methods, Binary OSL and SphericalHash, to address these deficiencies. We compare POSH, Binary OSL, and SphericalHash to several state-of-the-art hashing methods and provide empirical results for the superiority of the proposed methods across a wide range of standard benchmarks and parameter settings.

Mariano Tepper

We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve this broader goal. We formally derive a biologically-inspired neural network from Nyström kernel approximations and empirically demonstrate that the network successfully approximates transition distributions. The proposed network yields representations that, just like place cells, soft-tile the input space with highly sparse and localized receptive fields. Additionally, we show that the proposed computational motif can be extended to handle supervised problems, creating class-specific place cells while exhibiting low sample complexity.

Mariano Tepper, Anirvan M. Sengupta, Dmitri Chklovskii

In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular semidefinite relaxation of K-means clustering which yields the same solution as the non-convex original formulation for well segregated datasets. We report an unexpected finding: when data contains (greater than zero-dimensional) manifolds, the SDP solution captures such geometrical structures. Unlike traditional manifold embedding techniques, our approach does not rely on manually defining a kernel but rather enforces locality via a nonnegativity constraint. We thus call our approach NOnnegative MAnifold Disentangling, or NOMAD. To build an intuitive understanding of its manifold learning capabilities, we develop a theoretical analysis of NOMAD on idealized datasets. While NOMAD is convex and the globally optimal solution can be found by generic SDP solvers with polynomial time complexity, they are too slow for modern datasets. To address this problem, we analyze a non-convex heuristic and present a new, convex and yet efficient, algorithm, based on the conditional gradient method. Our results render NOMAD a versatile, understandable, and powerful tool for manifold learning.

Mariano Tepper, Guillermo Sapiro

In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are interesting as, compared to traditional NMF, they present additional sparsity and part-based behavior, explaining unique data features. To show these features in practice, we first present an application to the analysis of climate data. We then present an NMU-based algorithm to robustly fit multiple parametric models to a dataset. The proposed approach delivers state-of-the-art results for the estimation of multiple fundamental matrices and homographies, outperforming other alternatives in the literature and exemplifying the use of efficient NMU computations.

Mariano Tepper, Guillermo Sapiro

In this work we introduce a comprehensive algorithmic pipeline for multiple parametric model estimation. The proposed approach analyzes the information produced by a random sampling algorithm (e.g., RANSAC) from a machine learning/optimization perspective, using a \textit{parameterless} biclustering algorithm based on L1 nonnegative matrix factorization (L1-NMF). The proposed framework exploits consistent patterns that naturally arise during the RANSAC execution, while explicitly avoiding spurious inconsistencies. Contrarily to the main trends in the literature, the proposed technique does not impose non-intersecting parametric models. A new accelerated algorithm to compute L1-NMFs allows to handle medium-sized problems faster while also extending the usability of the algorithm to much larger datasets. This accelerated algorithm has applications in any other context where an L1-NMF is needed, beyond the biclustering approach to parameter estimation here addressed. We accompany the algorithmic presentation with theoretical foundations and numerous and diverse examples.

Mariano Tepper, Guillermo Sapiro

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor to this is the increasingly growing size of the datasets available and needed in the information sciences. To address this, in this work we propose to use structured random compression, that is, random projections that exploit the data structure, for two NMF variants: classical and separable. In separable NMF (SNMF) the left factors are a subset of the columns of the input matrix. We present suitable formulations for each problem, dealing with different representative algorithms within each one. We show that the resulting compressed techniques are faster than their uncompressed variants, vastly reduce memory demands, and do not encompass any significant deterioration in performance. The proposed structured random projections for SNMF allow to deal with arbitrarily shaped large matrices, beyond the standard limit of tall-and-skinny matrices, granting access to very efficient computations in this general setting. We accompany the algorithmic presentation with theoretical foundations and numerous and diverse examples, showing the suitability of the proposed approaches.

Mariano Tepper, Guillermo Sapiro

We consider grouping as a general characterization for problems such as clustering, community detection in networks, and multiple parametric model estimation. We are interested in merging solutions from different grouping algorithms, distilling all their good qualities into a consensus solution. In this paper, we propose a bi-clustering framework and perspective for reaching consensus in such grouping problems. In particular, this is the first time that the task of finding/fitting multiple parametric models to a dataset is formally posed as a consensus problem. We highlight the equivalence of these tasks and establish the connection with the computational Gestalt program, that seeks to provide a psychologically-inspired detection theory for visual events. We also present a simple but powerful bi-clustering algorithm, specially tuned to the nature of the problem we address, though general enough to handle many different instances inscribed within our characterization. The presentation is accompanied with diverse and extensive experimental results in clustering, community detection, and multiple parametric model estimation in image processing applications.

Thiago V. Spina, Mariano Tepper, Amy Esler et al.

Video object segmentation is a challenging problem due to the presence of deformable, connected, and articulated objects, intra- and inter-object occlusions, object motion, and poor lighting. Some of these challenges call for object models that can locate a desired object and separate it from its surrounding background, even when both share similar colors and textures. In this work, we extend a fuzzy object model, named cloud system model (CSM), to handle video segmentation, and evaluate it for body pose estimation of toddlers at risk of autism. CSM has been successfully used to model the parts of the brain (cerebrum, left and right brain hemispheres, and cerebellum) in order to automatically locate and separate them from each other, the connected brain stem, and the background in 3D MR-images. In our case, the objects are articulated parts (2D projections) of the human body, which can deform, cause self-occlusions, and move along the video. The proposed CSM extension handles articulation by connecting the individual clouds, body parts, of the system using a 2D stickman model. The stickman representation naturally allows us to extract 2D body pose measures of arm asymmetry patterns during unsupported gait of toddlers, a possible behavioral marker of autism. The results show that our method can provide insightful knowledge to assist the specialist's observations during real in-clinic assessments.

Jordan Hashemi, Thiago Vallin Spina, Mariano Tepper et al.

The early detection of developmental disorders is key to child outcome, allowing interventions to be initiated that promote development and improve prognosis. Research on autism spectrum disorder (ASD) suggests behavioral markers can be observed late in the first year of life. Many of these studies involved extensive frame-by-frame video observation and analysis of a child's natural behavior. Although non-intrusive, these methods are extremely time-intensive and require a high level of observer training; thus, they are impractical for clinical and large population research purposes. Diagnostic measures for ASD are available for infants but are only accurate when used by specialists experienced in early diagnosis. This work is a first milestone in a long-term multidisciplinary project that aims at helping clinicians and general practitioners accomplish this early detection/measurement task automatically. We focus on providing computer vision tools to measure and identify ASD behavioral markers based on components of the Autism Observation Scale for Infants (AOSI). In particular, we develop algorithms to measure three critical AOSI activities that assess visual attention. We augment these AOSI activities with an additional test that analyzes asymmetrical patterns in unsupported gait. The first set of algorithms involves assessing head motion by tracking facial features, while the gait analysis relies on joint foreground segmentation and 2D body pose estimation in video. We show results that provide insightful knowledge to augment the clinician's behavioral observations obtained from real in-clinic assessments.

Mariano Tepper, Pablo Musé, Andrés Almansa

Mathematical Morphology proposes to extract shapes from images as connected components of level sets. These methods prove very suitable for shape recognition and analysis. We present a method to select the perceptually significant (i.e., contrasted) level lines (boundaries of level sets), using the Helmholtz principle as first proposed by Desolneux et al. Contrarily to the classical formulation by Desolneux et al. where level lines must be entirely salient, the proposed method allows to detect partially salient level lines, thus resulting in more robust and more stable detections. We then tackle the problem of combining two gestalts as a measure of saliency and propose a method that reinforces detections. Results in natural images show the good performance of the proposed methods.

Zhongwei Tang, Alexey Castrodad, Mariano Tepper et al.

A framework for unsupervised group activity analysis from a single video is here presented. Our working hypothesis is that human actions lie on a union of low-dimensional subspaces, and thus can be efficiently modeled as sparse linear combinations of atoms from a learned dictionary representing the action's primitives. Contrary to prior art, and with the primary goal of spatio-temporal action grouping, in this work only one single video segment is available for both unsupervised learning and analysis without any prior training information. After extracting simple features at a single spatio-temporal scale, we learn a dictionary for each individual in the video during each short time lapse. These dictionaries allow us to compare the individuals' actions by producing an affinity matrix which contains sufficient discriminative information about the actions in the scene leading to grouping with simple and efficient tools. With diverse publicly available real videos, we demonstrate the effectiveness of the proposed framework and its robustness to cluttered backgrounds, changes of human appearance, and action variability.