Graph Neural Networks (GNNs) have recently shown promise as solvers for Boolean Satisfiability Problems (SATs) by operating on graph representations of logical formulas. However, their performance degrades sharply on harder instances, raising the question of whether this reflects fundamental architectural limitations. In this work, we provide a geometric explanation through the lens of graph Ricci Curvature (RC), which quantifies local connectivity bottlenecks. We prove that bipartite graphs derived from random k-SAT formulas are inherently negatively curved, and that this curvature decreases with instance difficulty. Building on this, we show that GNN-based SAT solvers are affected by oversquashing, a phenomenon where long-range dependencies become impossible to compress into fixed-length representations. We validate our claims empirically across different SAT benchmarks and confirm that curvature is both a strong indicator of problem complexity and can be used to predict performance. Finally, we connect our findings to design principles of existing solvers and outline promising directions for future work.

Psychological biases, such as confirmation bias, make individuals particularly vulnerable to believing and spreading fake news on social media, leading to significant consequences in domains such as public health and politics. Machine learning-based fact-checking systems have been widely studied to mitigate this problem. Among them, ensemble methods are particularly effective in combining multiple classifiers to improve robustness. However, their performance heavily depends on the diversity of the constituent classifiers-selecting genuinely diverse models remains a key challenge, especially when models tend to learn redundant patterns. In this work, we propose a novel automatic classifier selection approach that prioritizes diversity, also extended by performance. The method first computes pairwise diversity between classifiers and applies hierarchical clustering to organize them into groups at different levels of granularity. A HierarchySelect then explores these hierarchical levels to select one pool of classifiers per level, each representing a distinct intra-pool diversity. The most diverse pool is identified and selected for ensemble construction from these. The selection process incorporates an evaluation metric reflecting each classifiers's performance to ensure the ensemble also generalises well. We conduct experiments with 40 heterogeneous classifiers across six datasets from different application domains and with varying numbers of classes. Our method is compared against the Elbow heuristic and state-of-the-art baselines. Results show that our approach achieves the highest accuracy on two of six datasets. The implementation details are available on the project's repository: https://github.com/SaraBCoutinho/HSFN .

--In recent years, with the large-scale expansion of graph data, there has been an increased focus on Riemannian manifold data spaces other than Euclidean space. In particular, the development of hyperbolic spaces has been remarkable, and they have high expressive power for graph data with hierarchical structures. Normalized Maximum Likelihood (NML) is employed in regret minimization and model selection. However, existing formulations of NML have been developed primarily in Euclidean spaces and are inherently dependent on the choice of coordinate systems, making it non-trivial to extend NML to Riemannian manifolds. In this study, we define a new NML that reflects the geometric structure of Riemannian manifolds, called the Riemannian manifold NML (Rm-NML). This Rm-NML is invariant under coordinate transformations and coincides with the conventional NML under the natural parameterization in Euclidean space. We extend existing computational techniques for NML to the setting of Riemannian manifolds. Furthermore, we derive a method to simplify the computation of Rm-NML on Riemannian symmetric spaces, which encompass data spaces of growing interest such as hyperbolic spaces. T o illustrate the practical application of our proposed method, we explicitly computed the Rm-NML for normal distributions on hyperbolic spaces. With the recent increase in the scale of graph data, Riemannian manifold data spaces other than Euclidian spaces are attracting attention as latent spaces suitable for graph embedding [1, 2]. For example, hyperbolic spaces have been demonstrated to possess high expressive power for graph data with hierarchical structures [3]. Spherical spaces are particularly effective in representing graph data with cyclic structures [4]. Notably, research on hyperbolic spaces has been particularly remarkable[3]. Specifically, in the field of representation learning, methods that embed hierarchical structures into hyperbolic space have successfully represented such relationships using significantly lower-dimensional space compared to conventional methods based on Euclidean space, while preserving the essential relational information[2].

We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate estimators to each subset. It attains near-optimal rates for this estimator class and remains valid even when the mixture components come from different distribution families. As an application, we develop MV-PMODE, which scales a previously theoretical approach to high-dimensional density estimation to settings with thousands of dimensions. Despite its simplicity, it performs competitively against deep baselines on CIFAR-10 anomaly detection.

One key insight widely accepted in the machine learning community is the idea that wide basins (regions around a local minimum where the loss increases gradually) promote better generalization by offering greater stability to small changes in input data or model parameters. In contrast, sharp minima are typically more sensitive and less stable. Motivated by two key empirical observations - the inherent heavy-tailed distribution of gradient noise in stochastic gradient descent and the Edge of Stability phenomenon during neural network training, in which curvature grows before settling at a plateau, we introduce Adaptive Heavy Tailed Stochastic Gradient Descent (AHTSGD). The algorithm injects heavier-tailed noise into the optimizer during the early stages of training to enhance exploration and gradually transitions to lighter-tailed noise as sharpness stabilizes. By dynamically adapting to the sharpness of the loss landscape throughout training, AHTSGD promotes accelerated convergence to wide basins. AHTSGD is the first algorithm to adjust the nature of injected noise into an optimizer based on the Edge of Stability phenomenon. AHTSGD consistently outperforms SGD and other noise-based methods on benchmarks like MNIST and CIFAR-10, with marked gains on noisy datasets such as SVHN. It ultimately accelerates early training from poor initializations and improves generalization across clean and noisy settings, remaining robust to learning rate choices.

Detecting domain shifts in myoelectric activations poses a significant challenge due to the inherent non-stationarity of electromyography (EMG) signals. This paper explores the detection of domain shifts using data stream (DS) learning techniques, focusing on the DB6 dataset from the Ninapro database. We define domains as distinct time-series segments based on different subjects and recording sessions, applying Kernel Principal Component Analysis (KPCA) with a cosine kernel to pre-process and highlight these shifts. By evaluating multiple drift detection methods such as CUSUM, Page-Hinckley, and ADWIN, we reveal the limitations of current techniques in achieving high performance for real-time domain shift detection in EMG signals. Our results underscore the potential of streaming-based approaches for maintaining stable EMG decoding models, while highlighting areas for further research to enhance robustness and accuracy in real-world scenarios.

Evaluation of machine learning models typically emphasizes final accuracy, overlooking the cost of adaptation: the cumulative errors incurred while learning from scratch. Guess-and- Learn (G&L) v1.0 addresses this gap by measuring cold-start adaptability - the total mistakes a model makes while sequentially labeling an unlabeled dataset. At each step, the learner selects an instance, predicts its label, receives the ground truth, and updates parameters under either online (per-sample) or batch (delayed) mode. The resulting error trajectory exposes adaptation speed, selection quality, and bias - dynamics invisible to endpoint metrics. G&L defines four tracks (Scratch/Pretrained $\times$ Online/Batch) to disentangle the effects of initialization and update frequency. We formalize the protocol, relate it to classical mistake-bound theory, and estimate a heuristic "oracle reference band" for MNIST as a plausibility reference. Baseline experiments on MNIST and AG News, spanning classical methods (Perceptron, k-NN), convolutional architectures (CNN, ResNet-50), and pretrained transformers (ViT-B/16, BERT-base), reveal systematic differences in early-phase efficiency: smaller models can adapt with fewer initial errors, while pretraining benefits vary by domain. Across settings, current models remain well above the oracle band, highlighting an adaptability gap. By quantifying the mistake cost of early learning, G&L complements conventional benchmarks and provides a reproducible framework for developing learners that are not only accurate in the limit but also reliable from the first examples.

Numerous methods have been proposed to enhance Keyword Spotting (KWS) in adult speech, but children's speech presents unique challenges for KWS systems due to its distinct acoustic and linguistic characteristics. This paper introduces a zero-shot KWS approach that leverages state-of-the-art self-supervised learning (SSL) models, including Wav2Vec2, HuBERT and Data2Vec. Features are extracted layer-wise from these SSL models and used to train a Kaldi-based DNN KWS system. The WSJCAM0 adult speech dataset was used for training, while the PFSTAR children's speech dataset was used for testing, demonstrating the zero-shot capability of our method. Our approach achieved state-of-the-art results across all keyword sets for children's speech. Notably, the Wav2Vec2 model, particularly layer 22, performed the best, delivering an ATWV score of 0.691, a MTWV score of 0.7003 and probability of false alarm and probability of miss of 0.0164 and 0.0547 respectively, for a set of 30 keywords. Furthermore, age-specific performance evaluation confirmed the system's effectiveness across different age groups of children. To assess the system's robustness against noise, additional experiments were conducted using the best-performing layer of the best-performing Wav2Vec2 model. The results demonstrated a significant improvement over traditional MFCC-based baseline, emphasizing the potential of SSL embeddings even in noisy conditions. To further generalize the KWS framework, the experiments were repeated for an additional CMU dataset. Overall the results highlight the significant contribution of SSL features in enhancing Zero-Shot KWS performance for children's speech, effectively addressing the challenges associated with the distinct characteristics of child speakers.

Decoding in large language models is often described as scoring tokens and normalizing with softmax. We give a minimal, self-contained account of this step as a constrained variational principle on the probability simplex. The discrete, normalization-respecting ascent is the classical multiplicative-weights (entropic mirror) update; its continuous-time limit is the replicator flow. From these ingredients we prove that, for a fixed context and temperature, the next-token distribution follows a smooth trajectory inside the simplex and converges to the softmax equilibrium. This formalizes the common ``manifold traversal'' intuition at the output-distribution level. The analysis yields precise, practice-facing consequences: temperature acts as an exact rescaling of time along the same trajectory, while top-k and nucleus sampling restrict the flow to a face with identical guarantees. We also outline a controlled account of path-dependent score adjustments and their connection to loop-like, hallucination-style behavior. We make no claims about training dynamics or internal representations; those are deferred to future work.

This paper presents a novel cascaded observer architecture that combines optical flow and IMU measurements to perform continuous monocular visual-inertial odometry (VIO). The proposed solution estimates body-frame velocity and gravity direction simultaneously by fusing velocity direction information from optical flow measurements with gyro and accelerometer data. This fusion is achieved using a globally exponentially stable Riccati observer, which operates under persistently exciting translational motion conditions. The estimated gravity direction in the body frame is then employed, along with an optional magnetometer measurement, to design a complementary observer on $\mathbf{SO}(3)$ for attitude estimation. The resulting interconnected observer architecture is shown to be almost globally asymptotically stable. To extract the velocity direction from sparse optical flow data, a gradient descent algorithm is developed to solve a constrained minimization problem on the unit sphere. The effectiveness of the proposed algorithms is validated through simulation results.