Marcio Gameiro

M. A. Gameiro

This study addresses the challenge of integrating complex, high-dimensional deep semantic features with simple, interpretable structural cues for lyrical content classification. We introduce a novel Synergistic Fusion Layer (SFL) architecture, a deep learning model utilizing a gated mechanism to modulate Sentence-BERT embeddings (Fdeep) using low-dimensional auxiliary features (Fstruct). The task, derived from clustering UMAP-reduced lyrical embeddings, is reframed as binary classification, distinguishing a dominant, homogeneous cluster (Class 0) from all other content (Class 1). The SFL model achieved an accuracy of 0.9894 and a Macro F1 score of 0.9894, outperforming a comprehensive Random Forest (RF) baseline that used feature concatenation (Accuracy = 0.9868). Crucially, the SFL model demonstrated vastly superior reliability and calibration, exhibiting a 93% reduction in Expected Calibration Error (ECE = 0.0035) and a 2.5x lower Log Loss (0.0304) compared to the RF baseline (ECE = 0.0500; Log Loss = 0.0772). This performance validates the architectural hypothesis that non-linear gating is superior to simple feature concatenation, establishing the SFL model as a robust and trustworthy system for complex multimodal lyrical analysis.

Ewerton R. Vieira, Edgar Granados, Aravind Sivaramakrishnan et al.

Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing more effective hybrid controllers. This paper proposes a topological framework to analyze the global dynamics of robot controllers, even data-driven ones, in an effective and explainable way. It builds a combinatorial representation representing the underlying system's state space and non-linear dynamics, which is summarized in a directed acyclic graph, the Morse graph. The approach only probes the dynamics locally by forward propagating short trajectories over a state-space discretization, which needs to be a Lipschitz-continuous function. The framework is evaluated given either numerical or data-driven controllers for classical robotic benchmarks. It is compared against established analytical and recent machine learning alternatives for estimating the RoAs of such controllers. It is shown to outperform them in accuracy and efficiency. It also provides deeper insights as it describes the global dynamics up to the discretization's resolution. This allows to use the Morse graph to identify how to synthesize controllers to form improved hybrid solutions or how to identify the physical limitations of a robotic system.

Mohammed Eslami, Hamed Eramian, Marcio Gameiro et al.

Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states which produce inconsistent predictions of the same test data points. This calls for techniques to be able to empirically quantify the difference in the trajectories and highlight problematic regions. While much focus is placed on discovering what models learn, the question of how a model learns is less studied beyond theoretical landscape characterizations and local geometric approximations near optimal conditions. Here, we present a toolkit for the Dynamical Organization Of Deep Learning Loss Landscapes, or DOODL3. DOODL3 formulates the training of neural networks as a dynamical system, analyzes the learning process, and presents an interpretable global view of trajectories in the loss landscape. Our approach uses the coarseness of topology to capture the granularity of geometry to mitigate against states of instability or elongated training. Overall, our analysis presents an empirical framework to extract the global dynamics of a model and to use that information to guide the training of neural networks.

R. Castelli, M. Gameiro, J. -P. Lessard

In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach), to obtain rigorous proofs of existence of the periodic orbits in a weighted $\ell^1$ Banach space of space-time Fourier coefficients with geometric decay. We present several computer-assisted proofs of existence of periodic orbits at different parameter values.