#01Nov 6, 2026
stat.ML
Beyond the Lower-Star Filtration: Alternative Filtration Methods for Persistent Homology
Innocent Abaa, Umar Islambekov
In the lower-star filtration (LSF), simplices are assigned filtration values according to the maximum-vertex rule, with each simplex entering the filtration when its highest-valued vertex appears. A limitation of this construction is that some higher-dimensional simplices may enter simultaneously with their boundary faces, causing certain topological features to be filled immediately upon formation and thus not appear in the resulting persistence diagram. To address this limitation, we propose three alternative filtration methods: the \(\varepsilon\)-lower-star filtration (ELSF), the \(L_p\) filtration (LpF), and the softmax filtration (SMF). {ELSF introduces a dimension-dependent delay to the maximum-vertex rule,} allowing higher-dimensional simplices to enter the filtration after their boundary faces, whereas {LpF and SMF use aggregation functions that depend on all vertex values rather} than solely on their maximum. By modifying how filtration values are assigned, these methods allow simplices to enter the filtration more progressively, so that topological features such as loops and voids may persist over longer filtration intervals rather than being filled immediately. Consequently, the resulting persistence diagrams may include persistence features that are not observed under LSF, potentially providing useful information for distinguishing data populations. Experimental results on simulated and real-world datasets demonstrate that the proposed filtration methods are computationally efficient and can provide greater sensitivity to structural differences in the data than LSF.
#02Nov 6, 2026
cs.LG
Learning to Restart: Differentiable Restart Policies for Optimization Dynamics
Yiman Fong, Zhonglin Xie, Zaiwen Wen
Adaptive restart mechanisms, which reset the momentum or other auxiliary state of an iterative optimizer, play a central role in the empirical performance of accelerated first-order methods, yet existing restart rules remain almost entirely hand-designed. The obstruction to learning restart policies is that, unlike the typical Learning to Optimize (L2O) setting, the discrete restart events make the resulting trajectory non-differentiable in the algorithm parameters and thus block gradient-based optimization of the restart policy. We resolve this obstruction by developing a differentiable framework for restart policies through their continuous-time limit. We introduce surrogate gradients for the restart events and optimization trajectories that are efficient to compute and provably converge to their continuous-time counterparts. We validate the effectiveness of our surrogate gradients in L2O settings, training restart policies that improve upon standard handcrafted adaptive restart criteria on quadratic and linear programs, and that transfer zero-shot from synthetic quadratics to logistic regression on real datasets.
#03Nov 5, 2026
cs.LG
On the Few-Shot Adaptation of Vision-Language Models: A Few Gradient Signs Are All You Need
Nairouz Mrabah, Ismail Ben Ayed, Mahdi S. Hosseini and 1 more
The limited supervision available for the few-shot adaptation of vision-language models makes gradient estimation particularly noisy. We find that the gradient magnitudes are severely miscalibrated, while the signs of a small top-magnitude subset remain informative. This motivates SignSparseSGD and DynSignSparseSGD, two state-free optimizers that use gradient magnitudes only to select where to update and fixed-magnitude signs to decide how to update. The static variant fixes the support after the first minibatch. The dynamic variant refreshes it at every step. Across 11 datasets, three CLIP backbones, and five shot levels, the proposed methods are competitive with or outperform parameter-efficient and optimization-based baselines on average, while exhibiting markedly lower sensitivity to long training schedules. They introduce no task-specific modules, maintain no first- or second-moment optimizer states, and use one shared configuration across datasets, backbones, and shot levels. Our code is included in the supplementary materials and will be released upon publication.
#04Nov 6, 2026
cs.RO
STRIDE: Learning Humanoid Locomotion in Minutes with Acceleration-Based Rewards
Nico Bohlinger, Jan Peters
Learning locomotion directly on a humanoid robot is a promising direction to avoid the sim-to-real gap. However, locomotion rewards in Reinforcement Learning (RL) typically track the base velocity, which cannot be measured onboard without an external motion capture system or well-calibrated state estimator. This is why we introduce \method{}, which learns humanoid locomotion from minutes of samples with a reward that only requires the onboard Inertial Measurement Unit (IMU). Instead of tracking the base velocity, STRIDE rewards the robot for following a commanded acceleration profile. To learn efficiently from this reward, we use the off-policy RL algorithm XQC and combine a high gain setting for the joint position controllers with left-right symmetry augmentation. In simulation, STRIDE learns to walk on the Unitree G1 and Booster T1 humanoids within 14 minutes of samples. Compared to learning without these two components, it reduces the falls during training by 81%, while without them the robot learns only in over an hour.
#05Nov 6, 2026
cs.LG
SSF-Net: A Spatial-Spectral Fusion Network for Accurate PDE Operator Learning
Siqi Zhao, Flora D. Salim
Machine learning methods for solving partial differential equations (PDEs) significantly improve computational efficiency over traditional numerical solvers such as finite element method (FEM). However, PDE dynamics inherently span both local and global dynamics: disturbances propagate and decay gradually through the domain, while global coupling effects can influence the whole system simultaneously. Capturing both types of dynamics with a low complexity model remains a key challenge. To address this, we propose the Spatial-Spectral Fusion Network (SSF-Net), built around a dual-branch Spatial-Spectral Fusion (SSF) block comprising a spatial branch and a spectral branch. The spatial branch employs a multi-directional Mamba, which mitigates its inherent causal, single-direction scanning bias and capture local interactions with reduced directional bias at linear complexity. The spectral branch leverages a Fourier transform with a block-diagonal MLP to efficiently capture global spectral features with reduced parameter count and complexity. The SSF block is embedded in a multiresolution convolutional encoder-decoder, which extracts multi-scale features. We evaluate SSF-Net on a comprehensive PDE benchmark spanning multiple task types and assess its long-horizon stability. Compared with attention-based and convolution-based baselines, SSF-Net achieves lower prediction error with fewer parameters while retaining near-linear asymptotic complexity in the number of spatial tokens.