arXiv subjects

Emanuele Rodolà

Publications and source records attributed to Emanuele Rodolà.

At least 91 records · Page 5Linked to original sources

arXiv2023

Fluid Dynamics Network: Topology-Agnostic 4D Reconstruction via Fluid Dynamics Priors

Representing 3D surfaces as level sets of continuous functions over $\mathbb{R}^3$ is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision tasks. In order to represent 3D motion within this framework, it is often assumed (either explicitly or implicitly) that the transformations which a surface may undergo are homeomorphic: this is not necessarily true, for instance, in the case of fluid dynamics. In order to represent more general classes of deformations, we propose to apply this theoretical framework as regularizers for the optimization of simple 4D implicit functions (such as signed distance fields). We show that our representation is capable of capturing both homeomorphic and topology-changing deformations, while also defining correspondences over the continuously-reconstructed surfaces.

cs.CV↗

arXiv2023

Relative representations enable zero-shot latent space communication

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

cs.LG↗

arXiv2023

Spectral Maps for Learning on Subgraphs

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and modified graphs. Classically, these maps are represented as binary node-to-node correspondence matrices and used as-is to transfer node-wise features between the graphs. In this paper, we argue that simply changing this map representation can bring notable benefits to graph learning tasks. Drawing inspiration from recent progress in geometry processing, we introduce a spectral representation for maps that is easy to integrate into existing graph learning models. This spectral representation is a compact and straightforward plug-in replacement and is robust to topological changes of the graphs. Remarkably, the representation exhibits structural properties that make it interpretable, drawing an analogy with recent results on smooth manifolds. We demonstrate the benefits of incorporating spectral maps in graph learning pipelines, addressing scenarios where a node-to-node map is not well defined, or in the absence of exact isomorphism. Our approach bears practical benefits in knowledge distillation and hierarchical learning, where we show comparable or improved performance at a fraction of the computational cost.

cs.LG↗

arXiv2023

Latent Autoregressive Source Separation

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

cs.LG↗

arXiv2022

Learning Spectral Unions of Partial Deformable 3D Shapes

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.

cs.GR↗

arXiv2022

KiloNeuS: A Versatile Neural Implicit Surface Representation for Real-Time Rendering

NeRF-based techniques fit wide and deep multi-layer perceptrons (MLPs) to a continuous radiance field that can be rendered from any unseen viewpoint. However, the lack of surface and normals definition and high rendering times limit their usage in typical computer graphics applications. Such limitations have recently been overcome separately, but solving them together remains an open problem. We present KiloNeuS, a neural representation reconstructing an implicit surface represented as a signed distance function (SDF) from multi-view images and enabling real-time rendering by partitioning the space into thousands of tiny MLPs fast to inference. As we learn the implicit surface locally using independent models, resulting in a globally coherent geometry is non-trivial and needs to be addressed during training. We evaluate rendering performance on a GPU-accelerated ray-caster with in-shader neural network inference, resulting in an average of 46 FPS at high resolution, proving a satisfying tradeoff between storage costs and rendering quality. In fact, our evaluation for rendering quality and surface recovery shows that KiloNeuS outperforms its single-MLP counterpart. Finally, to exhibit the versatility of KiloNeuS, we integrate it into an interactive path-tracer taking full advantage of its surface normals. We consider our work a crucial first step toward real-time rendering of implicit neural representations under global illumination.

cs.CV↗

arXiv2022

Sparse Vicious Attacks on Graph Neural Networks

Graph Neural Networks (GNNs) have proven to be successful in several predictive modeling tasks for graph-structured data. Amongst those tasks, link prediction is one of the fundamental problems for many real-world applications, such as recommender systems. However, GNNs are not immune to adversarial attacks, i.e., carefully crafted malicious examples that are designed to fool the predictive model. In this work, we focus on a specific, white-box attack to GNN-based link prediction models, where a malicious node aims to appear in the list of recommended nodes for a given target victim. To achieve this goal, the attacker node may also count on the cooperation of other existing peers that it directly controls, namely on the ability to inject a number of ``vicious'' nodes in the network. Specifically, all these malicious nodes can add new edges or remove existing ones, thereby perturbing the original graph. Thus, we propose SAVAGE, a novel framework and a method to mount this type of link prediction attacks. SAVAGE formulates the adversary's goal as an optimization task, striking the balance between the effectiveness of the attack and the sparsity of malicious resources required. Extensive experiments conducted on real-world and synthetic datasets demonstrate that adversarial attacks implemented through SAVAGE indeed achieve high attack success rate yet using a small amount of vicious nodes. Finally, despite those attacks require full knowledge of the target model, we show that they are successfully transferable to other black-box methods for link prediction.

cs.LG↗

arXiv2022

Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach

Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of well-localized functional parts with specific geometric features. Often, these features are strongly correlated -- a modification of facial traits in a quadruped should induce changes to the body structure. However, in shape modelling applications, these types of edits are among the hardest ones; they require high precision, but also a global awareness of the entire shape. Even in the deep learning era, obtaining manipulable representations that satisfy such requirements is an open problem posing significant constraints. In this work, we address this problem by defining a data-driven model upon a family of linear operators (variants of the mesh Laplacian), whose spectra capture global and local geometric properties of the shape at hand. Modifications to these spectra are translated to semantically valid deformations of the corresponding surface. By explicitly decoupling the global from the local surface features, our pipeline allows to perform local edits while simultaneously maintaining a global stylistic coherence. We empirically demonstrate how our learning-based model generalizes to shape representations not seen at training time, and we systematically analyze different choices of local operators over diverse shape categories.

cs.CV↗

arXiv2022

Smoothness and effective regularizations in learned embeddings for shape matching

Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the different shapes in high-dimensional space where the matching is easier to solve is a well-trodden path that has given many outstanding solutions. Recently, a new trend has shown advantages in learning such representations. This novel idea motivated us to investigate which properties differentiate these data-driven embeddings and which ones promote state-of-the-art results. In this study, we analyze, for the first time, properties that arise in data-driven learned embedding and their relation to the shape-matching task. Our discoveries highlight the close link between matching and smoothness, which naturally emerge from training. Also, we demonstrate the relation between the orthogonality of the embedding and the bijectivity of the correspondence. Our experiments show exciting results, overcoming well-established alternatives and shedding a different light on relevant contexts and properties for learned embeddings.

cs.CV↗

arXiv2022

Unsupervised Source Separation via Bayesian Inference in the Latent Domain

State of the art audio source separation models rely on supervised data-driven approaches, which can be expensive in terms of labeling resources. On the other hand, approaches for training these models without any direct supervision are typically high-demanding in terms of memory and time requirements, and remain impractical to be used at inference time. We aim to tackle these limitations by proposing a simple yet effective unsupervised separation algorithm, which operates directly on a latent representation of time-domain signals. Our algorithm relies on deep Bayesian priors in the form of pre-trained autoregressive networks to model the probability distributions of each source. We leverage the low cardinality of the discrete latent space, trained with a novel loss term imposing a precise arithmetic structure on it, to perform exact Bayesian inference without relying on an approximation strategy. We validate our approach on the Slakh dataset arXiv:1909.08494, demonstrating results in line with state of the art supervised approaches while requiring fewer resources with respect to other unsupervised methods.

cs.LG↗

arXiv2022

3D Human Pose Estimation Using Möbius Graph Convolutional Networks

3D human pose estimation is fundamental to understanding human behavior. Recently, promising results have been achieved by graph convolutional networks (GCNs), which achieve state-of-the-art performance and provide rather light-weight architectures. However, a major limitation of GCNs is their inability to encode all the transformations between joints explicitly. To address this issue, we propose a novel spectral GCN using the Möbius transformation (MöbiusGCN). In particular, this allows us to directly and explicitly encode the transformation between joints, resulting in a significantly more compact representation. Compared to even the lightest architectures so far, our novel approach requires 90-98% fewer parameters, i.e. our lightest MöbiusGCN uses only 0.042M trainable parameters. Besides the drastic parameter reduction, explicitly encoding the transformation of joints also enables us to achieve state-of-the-art results. We evaluate our approach on the two challenging pose estimation benchmarks, Human3.6M and MPI-INF-3DHP, demonstrating both state-of-the-art results and the generalization capabilities of MöbiusGCN.

cs.CV↗

arXiv2022

Certification of Gaussian Boson Sampling via graph theory

Gaussian Boson Sampling is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a specific computational model. Indeed, thanks to the implementation in photonics-based processors, the latest Gaussian Boson Sampling experiments have reached a level of complexity where the quantum apparatus has solved the task faster than currently up-to-date classical strategies. In addition, recent studies have identified possible applications beyond the inherent sampling task. In particular, a direct connection between photon counting of a genuine Gaussian Boson Sampling device and the number of perfect matchings in a graph has been established. In this work, we propose to exploit such a connection to benchmark Gaussian Boson Sampling experiments. We interpret the properties of the feature vectors of the graph encoded in the device as a signature of correct sampling from the true input state. Within this framework, two approaches that exploit the distributions of graph feature vectors and graph kernels are presented. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.

quant-ph↗

arXiv2022

Explanatory Learning: Beyond Empiricism in Neural Networks

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

cs.LG↗

arXiv2022

Efficient Globally Optimal 2D-to-3D Deformable Shape Matching

We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem as finding the shortest circular path on the product 3-manifold of the surface and the curve. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of $O(mn^2\log(n))$, where $m$ and $n$ denote the number of vertices on the template curve and the 3D shape respectively. We also demonstrate that in practice the runtime is essentially linear in $m\!\cdot\! n$ making it an efficient method for shape analysis and shape retrieval. Quantitative evaluation confirms that the method provides excellent results for sketch-based deformable 3D shape retrieval.

cs.CV↗

arXiv2022

Fish sounds: towards the evaluation of marine acoustic biodiversity through data-driven audio source separation

The marine ecosystem is changing at an alarming rate, exhibiting biodiversity loss and the migration of tropical species to temperate basins. Monitoring the underwater environments and their inhabitants is of fundamental importance to understand the evolution of these systems and implement safeguard policies. However, assessing and tracking biodiversity is often a complex task, especially in large and uncontrolled environments, such as the oceans. One of the most popular and effective methods for monitoring marine biodiversity is passive acoustics monitoring (PAM), which employs hydrophones to capture underwater sound. Many aquatic animals produce sounds characteristic of their own species; these signals travel efficiently underwater and can be detected even at great distances. Furthermore, modern technologies are becoming more and more convenient and precise, allowing for very accurate and careful data acquisition. To date, audio captured with PAM devices is frequently manually processed by marine biologists and interpreted with traditional signal processing techniques for the detection of animal vocalizations. This is a challenging task, as PAM recordings are often over long periods of time. Moreover, one of the causes of biodiversity loss is sound pollution; in data obtained from regions with loud anthropic noise, it is hard to separate the artificial from the fish sound manually. Nowadays, machine learning and, in particular, deep learning represents the state of the art for processing audio signals. Specifically, sound separation networks are able to identify and separate human voices and musical instruments. In this work, we show that the same techniques can be successfully used to automatically extract fish vocalizations in PAM recordings, opening up the possibility for biodiversity monitoring at a large scale.

cs.SD↗

arXiv2021

Multimodal Feature Fusion and Knowledge-Driven Learning via Experts Consult for Thyroid Nodule Classification

Computer-aided diagnosis (CAD) is becoming a prominent approach to assist clinicians spanning across multiple fields. These automated systems take advantage of various computer vision (CV) procedures, as well as artificial intelligence (AI) techniques, to formulate a diagnosis of a given image, e.g., computed tomography and ultrasound. Advances in both areas (CV and AI) are enabling ever increasing performances of CAD systems, which can ultimately avoid performing invasive procedures such as fine-needle aspiration. In this study, a novel end-to-end knowledge-driven classification framework is presented. The system focuses on multimodal data generated by thyroid ultrasonography, and acts as a CAD system by providing a thyroid nodule classification into the benign and malignant categories. Specifically, the proposed system leverages cues provided by an ensemble of experts to guide the learning phase of a densely connected convolutional network (DenseNet). The ensemble is composed by various networks pretrained on ImageNet, including AlexNet, ResNet, VGG, and others. The previously computed multimodal feature parameters are used to create ultrasonography domain experts via transfer learning, decreasing, moreover, the number of samples required for training. To validate the proposed method, extensive experiments were performed, providing detailed performances for both the experts ensemble and the knowledge-driven DenseNet. As demonstrated by the results, the proposed system achieves relevant performances in terms of qualitative metrics for the thyroid nodule classification task, thus resulting in a great asset when formulating a diagnosis.

eess.IV↗

arXiv2021

Efficiently Parallelizable Strassen-Based Multiplication of a Matrix by its Transpose

The multiplication of a matrix by its transpose, $A^T A$, appears as an intermediate operation in the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm (ATA) for computing this product, based upon the classical Strassen algorithm as a sub-routine. In particular, we decrease the computational cost to $\frac{2}{3}$ the time required by Strassen's algorithm, amounting to $\frac{14}{3}n^{\log_2 7}$ floating point operations. ATA works for generic rectangular matrices, and exploits the peculiar symmetry of the resulting product matrix for saving memory. In addition, we provide an extensive implementation study of ATA in a shared memory system, and extend its applicability to a distributed environment. To support our findings, we compare our algorithm with state-of-the-art solutions specialized in the computation of $A^T A$. Our experiments highlight good scalability with respect to both the matrix size and the number of involved processes, as well as favorable performance for both the parallel paradigms and the sequential implementation, when compared with other methods in the literature.

cs.DC↗

arXiv2021

Learning disentangled representations via product manifold projection

We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.

cs.LG↗