Leveraging Energy Features for Surface Classification with Deep Learning: A Comparative Analysis Across Three Independent Datasets

Deep learning models dependency on large-scale inertial datasets presents a significant bottleneck in inertial sensor-based classification tasks, such as human activity recognition and smartphone location recognition. In these domains, data collection requires massive recording campaigns that are complex, time-consuming, and difficult to scale. Currently, data-driven guidelines for determining the minimum sample size required to reach a desired accuracy level do not exist. To address this gap, this study presents a systematic empirical evaluation of learning curve convergence rates in inertial classification. We introduce a unified framework that analyzes classification performance under both binary and multi-class scenarios, and derive an empirical formula to estimate performance relative to dataset size. Testing across six diverse, real-world datasets totaling 102.7 hours of inertial measurements demonstrates that accuracy follows a consistent logarithmic growth pattern, regardless of task complexity. Leveraging this finding, we propose a quantitative stability point metric, defined as the sample size required for the learning curve to stabilize within a predefined mean absolute percentage deviation of its asymptotic maximum. Our analysis reveals that models often reach practical stability with substantially fewer samples than traditional heuristics suggest. Ultimately, we offer a generalizable framework to extrapolate total data requirements from small-scale pilot studies, optimizing the tradeoff between recording effort and model reliability. These findings shift the prevailing paradigm from maximizing data volume toward optimizing data efficiency, offering concrete, data-backed guidelines for planning recording campaigns in inertial sensing applications.

We present OctoSense, an open-source sensor platform with stereo RGB and event cameras, LiDAR, a thermal camera, an inertial measurement unit, RTK-corrected global positioning system, and proprioception (CAN bus data from a car, and joint angles for a quadruped robot). The eponymous OctoSense dataset contains 59 hours of time-synchronized driving data across different types of environments at different times of the day, including situations with highly degraded sensors. We demonstrate multi-modal self-supervised learning using such real-world robotics data, where sensors have different representations, frequencies, latencies and noise. Our approach, a "late-fusion" masked autoencoder, (i) uses modality-specific tokenizers to account for different spatiotemporal characteristics of these sensors, and (ii) caches modality-specific tokens at inference time to process new measurements as they come. This architecture (i) is fast (6.68 ms and 112 ms on NVIDIA 5090 and Orin NX respectively, to compute the representation), (ii) performs better than existing image-only foundation models on tasks such as estimation of optical flow, depth, semantic segmentation, and ego-motion (translation, rotation, and steering angle), and (iii) predicts robustly at nighttime or in situations where sensory data is degraded. See our project page for links to the dataset, code, and supplementary videos: https://abisulco.com/octosense/.

Modern machine learning optimizes for accuracy without explicit treatment of internal computational cost, even though physical and biological systems operate under intrinsic energy constraints. We evaluate energy-aware learning across 2,203 experiments spanning vision, text, neuromorphic, and physiological datasets with 10 seeds per configuration and factorial statistical analysis. Three findings emerge. First, architecture alone explains negligible variance in accuracy (partial eta^2 = 0.001), while the architecture x dataset interaction is large (partial eta^2 = 0.44, p < 0.001), demonstrating that optimal architecture depends critically on task modality and rejecting the assumption of a universal best architecture. Second, a controlled lambda-sweep across lambda in {0, 1e-5, 1e-4, 1e-3, 1e-2} validates a single-parameter energy-regularized objective L = L_CE + lambda * E(theta, x): across this range, internal activation energy decreases by approximately three orders of magnitude relative to the unregularized lambda=0 baseline, with negligible accuracy change (<0.5 percentage points) on both MNIST and Fashion-MNIST. Third, energy-first architectures inspired by an action-principle framework yield 5-33% within-modality training-efficiency gains over conventional baselines. These results emerge from a research program that interprets learning through a structural correspondence between the action functional in classical mechanics, free energy in statistical physics, and KL-regularized objectives in variational inference. We frame this correspondence as a design hypothesis, not a derivation.