Automatic Music Transcription using Convolutional Neural Networks and Constant-Q transform

Automatic music transcription (AMT) is the problem of analyzing an audio recording of a musical piece and detecting notes that are being played. AMT is a challenging problem, particularly when it comes to polyphonic music. The goal of AMT is to produce a score representation of a music piece, by analyzing a sound signal containing multiple notes played simultaneously. In this work, we design a processing pipeline that can transform classical piano audio files in .wav format into a music score representation. The features from the audio signals are extracted using the constant-Q transform, and the resulting coefficients are used as an input to the convolutional neural network (CNN) model.

Learning and Transferring Physical Models through Derivatives

We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that effectively transfers knowledge from a pre-trained to a student model. We provide theoretical guarantees that our approach can learn the true physical system, being consistent with the underlying physical laws, even when using empirical derivatives. DERL outperforms state-of-the-art methods in generalizing an ODE to unseen initial conditions and a parametric PDE to unseen parameters. We finally propose a method based on DERL to transfer physical knowledge across models by extending them to new portions of the physical domain and new range of PDE parameters. We believe this is the first attempt at building physical models incrementally in multiple stages.

Deferring Concept Bottleneck Models: Learning to Defer Interventions to Inaccurate Experts

Concept Bottleneck Models (CBMs) are machine learning models that improve interpretability by grounding their predictions on human-understandable concepts, allowing for targeted interventions in their decision-making process. However, when intervened on, CBMs assume the availability of humans that can identify the need to intervene and always provide correct interventions. Both assumptions are unrealistic and impractical, considering labor costs and human error-proneness. In contrast, Learning to Defer (L2D) extends supervised learning by allowing machine learning models to identify cases where a human is more likely to be correct than the model, thus leading to deferring systems with improved performance. In this work, we gain inspiration from L2D and propose Deferring CBMs (DCBMs), a novel framework that allows CBMs to learn when an intervention is needed. To this end, we model DCBMs as a composition of deferring systems and derive a consistent L2D loss to train them. Moreover, by relying on a CBM architecture, DCBMs can explain why defer occurs on the final task. Our results show that DCBMs achieve high predictive performance and interpretability at the cost of deferring more to humans.

Towards Efficient Molecular Property Optimization with Graph Energy Based Models

Optimizing chemical properties is a challenging task due to the vastness and complexity of chemical space. Here, we present a generative energy-based architecture for implicit chemical property optimization, designed to efficiently generate molecules that satisfy target properties without explicit conditional generation. We use Graph Energy Based Models and a training approach that does not require property labels. We validated our approach on well-established chemical benchmarks, showing superior results to state-of-the-art methods and demonstrating robustness and efficiency towards de novo drug design.

I Know How: Combining Prior Policies to Solve New Tasks

Multi-Task Reinforcement Learning aims at developing agents that are able to continually evolve and adapt to new scenarios. However, this goal is challenging to achieve due to the phenomenon of catastrophic forgetting and the high demand of computational resources. Learning from scratch for each new task is not a viable or sustainable option, and thus agents should be able to collect and exploit prior knowledge while facing new problems. While several methodologies have attempted to address the problem from different perspectives, they lack a common structure. In this work, we propose a new framework, I Know How (IKH), which provides a common formalization. Our methodology focuses on modularity and compositionality of knowledge in order to achieve and enhance agent's ability to learn and adapt efficiently to dynamic environments. To support our framework definition, we present a simple application of it in a simulated driving environment and compare its performance with that of state-of-the-art approaches.

Long Range Propagation on Continuous-Time Dynamic Graphs

Learning Continuous-Time Dynamic Graphs (C-TDGs) requires accurately modeling spatio-temporal information on streams of irregularly sampled events. While many methods have been proposed recently, we find that most message passing-, recurrent- or self-attention-based methods perform poorly on long-range tasks. These tasks require correlating information that occurred "far" away from the current event, either spatially (higher-order node information) or along the time dimension (events occurred in the past). To address long-range dependencies, we introduce Continuous-Time Graph Anti-Symmetric Network (CTAN). Grounded within the ordinary differential equations framework, our method is designed for efficient propagation of information. In this paper, we show how CTAN's (i) long-range modeling capabilities are substantiated by theoretical findings and how (ii) its empirical performance on synthetic long-range benchmarks and real-world benchmarks is superior to other methods. Our results motivate CTAN's ability to propagate long-range information in C-TDGs as well as the inclusion of long-range tasks as part of temporal graph models evaluation.

Learning Causal Abstractions of Linear Structural Causal Models

The need for modelling causal knowledge at different levels of granularity arises in several settings. Causal Abstraction provides a framework for formalizing this problem by relating two Structural Causal Models at different levels of detail. Despite increasing interest in applying causal abstraction, e.g. in the interpretability of large machine learning models, the graphical and parametrical conditions under which a causal model can abstract another are not known. Furthermore, learning causal abstractions from data is still an open problem. In this work, we tackle both issues for linear causal models with linear abstraction functions. First, we characterize how the low-level coefficients and the abstraction function determine the high-level coefficients and how the high-level model constrains the causal ordering of low-level variables. Then, we apply our theoretical results to learn high-level and low-level causal models and their abstraction function from observational data. In particular, we introduce Abs-LiNGAM, a method that leverages the constraints induced by the learned high-level model and the abstraction function to speedup the recovery of the larger low-level model, under the assumption of non-Gaussian noise terms. In simulated settings, we show the effectiveness of learning causal abstractions from data and the potential of our method in improving scalability of causal discovery.

Injecting Hamiltonian Architectural Bias into Deep Graph Networks for Long-Range Propagation

The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce (port-)Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.

Tackling Graph Oversquashing by Global and Local Non-Dissipativity

A common problem in Message-Passing Neural Networks is oversquashing -- the limited ability to facilitate effective information flow between distant nodes. Oversquashing is attributed to the exponential decay in information transmission as node distances increase. This paper introduces a novel perspective to address oversquashing, leveraging properties of global and local non-dissipativity, that enable the maintenance of a constant information flow rate. Namely, we present SWAN, a uniquely parameterized model GNN with antisymmetry both in space and weight domains, as a means to obtain non-dissipativity. Our theoretical analysis asserts that by achieving these properties, SWAN offers an enhanced ability to transmit information over extended distances. Empirical evaluations on synthetic and real-world benchmarks that emphasize long-range interactions validate the theoretical understanding of SWAN, and its ability to mitigate oversquashing.

Temporal Graph ODEs for Irregularly-Sampled Time Series

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous dynamics and sporadic observations. To address this limitation, we introduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework, which learns both the temporal and spatial dynamics from graph streams where the intervals between observations are not regularly spaced. We empirically validate the proposed approach on several graph benchmarks, showing that TG-ODE can achieve state-of-the-art performance in irregular graph stream tasks.