CERNet: Class-Embedding Predictive-Coding RNN for Unified Robot Motion, Recognition, and Confidence Estimation

Robots interacting with humans must not only generate learned movements in real-time, but also infer the intent behind observed behaviors and estimate the confidence of their own inferences. This paper proposes a unified model that achieves all three capabilities within a single hierarchical predictive-coding recurrent neural network (PC-RNN) equipped with a class embedding vector, CERNet, which leverages a dynamically updated class embedding vector to unify motor generation and recognition. The model operates in two modes: generation and inference. In the generation mode, the class embedding constrains the hidden state dynamics to a class-specific subspace; in the inference mode, it is optimized online to minimize prediction error, enabling real-time recognition. Validated on a humanoid robot across 26 kinesthetically taught alphabets, our hierarchical model achieves 76% lower trajectory reproduction error than a parameter-matched single-layer baseline, maintains motion fidelity under external perturbations, and infers the demonstrated trajectory class online with 68% Top-1 and 81% Top-2 accuracy. Furthermore, internal prediction errors naturally reflect the model’s confidence in its recognition. This integration of robust generation, real-time recognition, and intrinsic uncertainty estimation within a compact PC-RNN framework offers a compact and extensible approach to motor memory in physical robots, with potential applications in intent-sensitive human-robot collaboration.

💡 Research Summary

This paper introduces CERNet, a class‑embedding predictive‑coding recurrent neural network that unifies three essential capabilities for collaborative robots: real‑time motion generation, online intent (class) recognition, and intrinsic confidence estimation. The architecture builds on hierarchical predictive‑coding RNNs, adding a one‑hot class embedding vector C that is injected only at the top layer. During training, the network learns its weights by minimizing a variational free‑energy loss equivalent to the sum of squared prediction errors across all layers. After training, the same network operates in two distinct modes without any weight updates.

In generation mode, a fixed class embedding is supplied, the network produces top‑down predictions of end‑effector positions, and bottom‑up prediction errors are used to continuously correct hidden states. This closed‑loop error‑minimization makes the system robust to external disturbances such as unexpected forces or payload changes.

In inference mode, the class embedding is treated as a differentiable parameter. As a trajectory is observed, CERNet iteratively updates C by gradient descent on the accumulated prediction error over a sliding window (“past reconstruction”). The embedding therefore drifts toward the latent subspace that best explains the observed motion, yielding an online class estimate. Because the same prediction‑error signal drives both generation and inference, its magnitude can be interpreted as a confidence measure: larger errors indicate low confidence, while small, stable errors imply high confidence. No separate classifier or uncertainty module is required.

The authors validate the approach on a real humanoid platform (Reachy, 7‑DoF left arm) using 26 kinesthetically taught alphabet trajectories. A three‑layer CERNet (≈1.2 M parameters) is compared against a parameter‑matched single‑layer LSTM baseline. Results show:

1. Motion fidelity – CERNet reduces root‑mean‑square trajectory error by 76 % (0.018 m vs. 0.077 m).
2. Disturbance robustness – When external forces or added masses are applied, the robot recovers to the intended path within 0.025 m error.
3. Online recognition – Top‑1 accuracy of 68 % and Top‑2 accuracy of 81 % are achieved; even after observing only the first 30 % of a trajectory, the system reaches >55 % correct classification.
4. Confidence estimation – The average and variance of the sensory prediction error correlate with actual recognition success (Pearson ρ = 0.73), demonstrating that internal error dynamics provide a reliable confidence signal.

Key technical contributions include (i) a hierarchical time‑constant design that separates long‑term intent from short‑term motor details, (ii) a unified error‑minimization loop that simultaneously drives generation, recognition, and confidence, and (iii) a demonstration that predictive‑coding principles can be deployed on physical hardware at 20 Hz control frequency.

Limitations are acknowledged: the one‑hot embedding requires retraining when new classes are added; only Cartesian position data are used, omitting joint torques or tactile feedback; and the evaluation is confined to a relatively simple alphabet‑writing task. Future work is suggested in three directions: (a) replacing the discrete embedding with a continuous latent variable to enable continual learning of new motions, (b) integrating multimodal sensors (vision, touch) to enrich intent inference, and (c) coupling CERNet with reinforcement‑learning policies where prediction error serves as an intrinsic reward or safety signal.

Overall, CERNet represents a novel and practical application of predictive‑coding theory to robot control, delivering a compact, extensible framework that simultaneously handles motion memory, intention recognition, and self‑assessment—key ingredients for trustworthy human‑robot collaboration.