arXiv:2603.06651v1 Announce Type: cross Abstract: Euclidean gradient descent algorithms barely capture the geometry of objective function-induced hypersurfaces and risk driving update trajectories off the hypersurfaces. Riemannian gradient descent algorithms address these issues but fail to represent complex hypersurfaces via a single classic manifold. We propose geodesic gradient descent (GGD), a generic and learning-rate-free Riemannian gradient descent algorithm. At each iteration, GGD uses an n-dimensional sphere to approximate a local neighborhood on the objective function-induced hypersurface, adapting to arbitrarily complex geometries. A tangent vector derived from the Euclidean gradient is projected onto the sphere to form a geodesic, ensuring the update trajectory stays on the hypersurface. Parameter updates are performed using the endpoint of the geodesic. The maximum step size of the gradient in GGD is equal to a quarter of the arc length on the n-dimensional sphere, thus eliminating the need for a learning rate. Experimental results show that compared with the classic Adam algorithm, GGD achieves test MSE reductions ranging from 35.79% to 48.76% for fully connected networks on the Burgers' dataset, and cross-entropy loss reductions ranging from 3.14% to 11.59% for convolutional neural networks on the MNIST dataset.

arXiv:2603.07545v1 Announce Type: cross Abstract: Learned world models excel at interpolative generalization but fail at extrapolative generalization to novel physical properties. This limitation arises because they learn statistical correlations rather than the environment's underlying generative rules, such as physical invariances and conservation laws. We argue that learning these invariances is key to robust extrapolation. To achieve this, we first introduce \textbf{Symmetry Exploration}, an unsupervised exploration strategy where an agent is intrinsically motivated by a Hamiltonian-based curiosity bonus to actively probe and challenge its understanding of conservation laws, thereby collecting physically informative data. Second, we design a Hamiltonian-based world model that learns from the collected data, using a novel self-supervised contrastive objective to identify the invariant physical state from raw, view-dependent pixel observations. Our framework, \textbf{DreamSAC}, trained on this actively curated data, significantly outperforms state-of-the-art baselines in 3D physics simulations on tasks requiring extrapolation.

arXiv:2603.08034v1 Announce Type: cross Abstract: Emotion recognition in real-world environments is hindered by partial occlusions, missing modalities, and severe class imbalance. To address these issues, particularly for the Affective Behavior Analysis in-the-wild (ABAW) Expression challenge, we propose a multimodal framework that dynamically fuses visual and audio representations. Our approach uses a dual-branch Transformer architecture featuring a safe cross-attention mechanism and a modality dropout strategy. This design allows the network to rely on audio-based predictions when visual cues are absent. To mitigate the long-tail distribution of the Aff-Wild2 dataset, we apply focal loss optimization, combined with a sliding-window soft voting strategy to capture dynamic emotional transitions and reduce frame-level classification jitter. Experiments demonstrate that our framework effectively handles missing modalities and complex spatiotemporal dependencies, achieving an accuracy of 60.79% and an F1-score of 0.5029 on the Aff-Wild2 validation set.