Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for continuous symmetry of manifold geometry. Thereby we achieve learnable and stable dynamics on the underlying manifold for general Lie group, and we are able to utilize the powerful representation capability of Lie group such as SO(3) and SE(3) to solve real world engineering problems in areas such as robotics, graphics, and control. Two core challenges are: (i) General Lie groups are incompatible with addition arithmetic, which is necessary for neural network interactions. (ii) The dynamics evolve in the nonlinear representation space of special algebra rather than the normal Euclidean space, which violates the paradigm of common neural ODEs. To address these two challenges, we firstly introduce adjoint Lie group action on the Lie algebra, which induces a linear mapping and transfer to the block-wise structure of weight matrices, such that addition could operate on the Lie algebra as a vector space. Then we parameterize the Lie algebra and the adjoint action as linear transformation so that the architecture is aligned with neural network perceptrons. Explicitly, this embedding appears as block-wise manifold constraints on weights, and we develop algorithms to learn the equilibrium with stability guarantees of the temporal neural network dynamics. Experiments are implemented on a specific Lie group SE(3), with the application scenario of telescopic manipulators.

Interpretability by Design for Efficient Multi-Objective Reinforcement Learning

Multi-objective reinforcement learning (MORL) aims at optimising several, often conflicting goals in order to improve flexibility and reliability of RL in practical tasks. This can be achieved by finding diverse policies that are optimal for some objective preferences and non-dominated by optimal policies for other preferences so that they form a Pareto front in the multi-objective performance space. The relation between the multi-objective performance space and the parameter space that represents the policies is generally non-unique. Using a training scheme that is based on a locally linear map between the parameter space and the performance space, we show that an approximate Pareto front can provide an interpretation of the current parameter vectors in terms of the objectives which enables an effective search within contiguous solution domains. Experiments are conducted with and without retraining across different domains, and the comparison with previous methods demonstrates the efficiency of our approach.

Differentiable Radio Frequency Ray Tracing for Millimeter-Wave Sensing

Millimeter wave (mmWave) sensing is an emerging technology with applications in 3D object characterization and environment mapping. However, realizing precise 3D reconstruction from sparse mmWave signals remains challenging. Existing methods rely on data-driven learning, constrained by dataset availability and difficulty in generalization. We propose DiffSBR, a differentiable framework for mmWave-based 3D reconstruction. DiffSBR incorporates a differentiable ray tracing engine to simulate radar point clouds from virtual 3D models. A gradient-based optimizer refines the model parameters to minimize the discrepancy between simulated and real point clouds. Experiments using various radar hardware validate DiffSBR's capability for fine-grained 3D reconstruction, even for novel objects unseen by the radar previously. By integrating physics-based simulation with gradient optimization, DiffSBR transcends the limitations of data-driven approaches and pioneers a new paradigm for mmWave sensing.

Multimodal Indoor Localization Using Crowdsourced Radio Maps

Indoor Positioning Systems (IPS) traditionally rely on odometry and building infrastructures like WiFi, often supplemented by building floor plans for increased accuracy. However, the limitation of floor plans in terms of availability and timeliness of updates challenges their wide applicability. In contrast, the proliferation of smartphones and WiFi-enabled robots has made crowdsourced radio maps - databases pairing locations with their corresponding Received Signal Strengths (RSS) - increasingly accessible. These radio maps not only provide WiFi fingerprint-location pairs but encode movement regularities akin to the constraints imposed by floor plans. This work investigates the possibility of leveraging these radio maps as a substitute for floor plans in multimodal IPS. We introduce a new framework to address the challenges of radio map inaccuracies and sparse coverage. Our proposed system integrates an uncertainty-aware neural network model for WiFi localization and a bespoken Bayesian fusion technique for optimal fusion. Extensive evaluations on multiple real-world sites indicate a significant performance enhancement, with results showing ~ 25% improvement over the best baseline

Robust Human Detection under Visual Degradation via Thermal and mmWave Radar Fusion

The majority of human detection methods rely on the sensor using visible lights (e.g., RGB cameras) but such sensors are limited in scenarios with degraded vision conditions. In this paper, we present a multimodal human detection system that combines portable thermal cameras and single-chip mmWave radars. To mitigate the noisy detection features caused by the low contrast of thermal cameras and the multi-path noise of radar point clouds, we propose a Bayesian feature extractor and a novel uncertainty-guided fusion method that surpasses a variety of competing methods, either single-modal or multi-modal. We evaluate the proposed method on real-world data collection and demonstrate that our approach outperforms the state-of-the-art methods by a large margin.