#01Oct 30, 2026
cs.LG
Gradient Descent on Two ReLU Neurons: Global Landscape and Bifurcation Dynamics
Binghua Li, Mengzhe Li, Denny Wu and 1 more
Understanding how gradient descent learns features remains a central challenge in neural network theory. We study this question in a minimal multi-index setting that already exhibits rich multi-phase gradient dynamics: a well-specified two-neuron ReLU teacher-student model under isotropic Gaussian inputs, trained by population gradient flow from small initialization. We show that the dynamics are organized by two directions: the "easy" bisector direction, which carries the leading signal, and the "hard" splitting direction, which governs specialization. To characterize the loss structure and learning behavior, we analyze the population squared-loss landscape and show that every critical point with both student weights nonzero is either a global minimum or a saddle. We then track the gradient-flow trajectory, showing that student neurons first collapse toward a bisector saddle before escaping and specializing to teacher neurons. Our results provide both a landscape and dynamics account of the multi-phase symmetry-breaking behavior that arises in a simple multi-index model and under standard algorithmic and architectural choices.
#02Oct 30, 2026
cs.LG
CausalXRL: Explainable Reinforcement Learning through Causal Graph Reasoning
Yanming Zhang, Eric Papenhausen, Klaus Mueller
Reinforcement learning is a powerful paradigm for training autonomous agents and has achieved impressive performance in complex environments. However, this success often comes at the cost of interpretability, diminishing trust and complicating efforts to debug and improve agent behavior. To address these challenges, we introduce CausalXRL, a novel framework for explainable reinforcement learning (XRL). A key feature of CausalXRL is its use of causal graph reasoning, which provides transparent, structured, multi-level explanations of agent decision-making. We validate CausalXRL through comprehensive case studies and a two-part evaluation: (1) a quantitative analysis of explanation fidelity and causal-structure learning efficiency in benchmark RL environments, and (2) a qualitative expert study assessing explainability in the real-time strategy (RTS) benchmark MicroRTS. The quantitative results show that CausalXRL can provide faithful explanations while efficiently learning causal structures, and the qualitative expert study suggests that participants found CausalXRL useful for inspecting high-level RTS strategies.
#03Oct 30, 2026
cs.LG
Towards Understanding the Impact of Plasticity Loss on Reinforcement Learning in Stochastic Environments
Philipp Bordne, André Biedenkapp
Deep reinforcement learning (RL) is a powerful framework for sequential decision-making. Despite many high-profile successes in recent years, deep RL is known to be brittle. An emerging line of research attributes this brittleness to a loss of plasticity in neural networks. However, plasticity loss has so far been understudied in stochastic environments. We study this interplay systematically, training SAC agents on three DeepMind Control tasks augmented with controlled levels of observation and action noise. We find that plasticity-preserving methods increase learning robustness on the two harder tasks, with their advantage growing as observation noise increases, while combining resets with layer normalization underperforms resets alone at every observation noise level tested. Further, stochasticity can accelerate the loss of plasticity in harder environments, whereas in easier settings noise can act as a regularizer that sustains plasticity. Lastly, plasticity loss is most pronounced in the early stages of training. In the most challenging stochastic settings, TD instability rather than gradual plasticity loss becomes the dominant failure mode.
#04Oct 30, 2026
cs.LG
When Does Jacobian Fine-Tuning Stabilize Neural PDE Emulators?
Shreeyam Bangera, Manya Gupta
Neural emulators of chaotic PDEs are trained on one-step prediction but deployed autoregressively, where their errors compound. Jacobian-based regularisers aim to curb this growth, but in a chaotic system part of the growth is physical and cannot be trained away. We separate the two sources of this error with a first-order decomposition. We compare the emulator's error with a counterfactual that propagates the same one-step mistakes through the solver's Jacobian, giving an amplification ratio: the factor by which the model's own dynamics amplify its errors. We study 21 configurations across four PDEs, five architectures and two model sizes (8-10k and 33k parameters), with errors measured at one Lyapunov time. Jacobian fine-tuning reduced the error by more than 10% for 1 of 34 seeds whose amplification ratio was at most 1.25, and for all 20 seeds whose ratio was at least four; for the latter, the error fell by a factor of 8 (small models) and 55 (33k models) in geometric mean over seeds. The gain approximately equals the one-step accuracy cost of fine-tuning divided by the amplification ratio. Matching the solver's Jacobian along the model's own error direction (EDJM) outperformed random directions at the same cost on 28 of 35 seeds; input-noise injection performed comparably to EDJM.
#05Oct 30, 2026
physics.ao-ph
SATFRONT: Detecting Atmospheric Fronts with Satellite Data using Machine Learning
Ioannis Dravilas, Miruna Stoicescu, Roope Tervo and 5 more
Atmospheric fronts are associated with much of the high-impact weather in the mid-latitudes, yet their identification and classification remain largely manual and subjective. Existing deep learning approaches rely primarily on gridded reanalysis or forecast data, limiting their applicability to satellite observations available for time-critical applications. We introduce SATFRONT, a machine learning framework for detecting cold, warm, and occluded fronts over Europe from geostationary satellite observations, with reanalysis data as an optional additional input. The model is trained on frontal analyses from five European national meteorological services and evaluated against UK Met Office analyses for 2024. Using satellite observations alone, SATFRONT achieves a Critical Success Index (CSI) of 0.428 at a 150 km tolerance, within the range of agreement between analyses from different meteorological services (0.277-0.501) and higher than that of an operational rule-based front detector that uses satellite data (0.133). Adding ERA5 reanalysis increases the CSI to 0.591. ERA5 substantially improves the placement of individual fronts, although its effect on their annual spatial distribution varies by front type. These results demonstrate that cold, warm, and occluded fronts can be detected directly from geostationary satellite observations, providing a basis for automated frontal analyses at the high temporal frequency required for time-critical applications.