When Does Legacy Data Start to Help? Emergent Transfer in Cross-Configuration Robot Learning

Robotic hardware evolves over time, but demonstration data is often tied to a specific sensor and actuator configuration. This raises a practical and underexplored question: when does legacy data begin to benefit an upgraded robot? We study this question on a wheeled humanoid platform across two hardware generations, where both the camera and gripper are changed while the overall morphology remains fixed. Contrary to the common assumption that more cross-configuration data is always helpful, we observe a grokking-like transition: legacy data remains ineffective until the upgraded configuration acquires a minimum level of task competence, after which co-training gains rise sharply before diminishing near saturation. We hypothesize that this task-dependent transition is governed by a transfer threshold and characterize the resulting three-phase pattern. Across real-robot manipulation tasks, we observe all three phases: no measurable benefit at low competence ($10.0\% \rightarrow 10.0\%$), a sharp gain after crossing the threshold ($23.3\% \rightarrow 86.7\%$ on flower insertion), and diminishing returns at high competence ($85.0\% \rightarrow 93.3\%$ on pen insertion). We provide a theoretical account based on gradient alignment and residual policy uncertainty, and derive a phase-aware rule for deciding when to collect more new-hardware data and when to reuse legacy demonstrations. We further validate this three-phase pattern on a mobile dual-arm watering task, with results consistent with our predictions.

Derivation and analysis of power offset in fiber-longitudinal power profile estimation using pre-FEC hard-decision data

Utilizing the precise reference waveform regenerated by post-forward error correction (FEC) data, the fiber-longitudinal power profile estimation based on the minimum-mean-square-error method (MMSE-PPE) has been validated as an effective tool for absolute power monitoring. However, when post-FEC data is unavailable, it becomes necessary to rely on pre-FEC hard-decision data, which inevitably introduces hard-decision errors. These hard-decision errors will result in a power offset that undermines the accuracy of absolute power monitoring. In this paper, we present the first analytical expression for power offset in MMSE-PPE when using pre-FEC hard-decision data, achieved by introducing a virtual hard-decision nonlinear perturbation term. Based on this analytical expression, we also establish the first nonlinear relationship between the power offset and the symbol error rate (SER) of M-ary quadrature amplitude modulation (M-QAM) formats based on Gaussian assumptions. Verified in a numerical 130-GBaud single-wavelength coherent optical fiber transmission system, the correctness of the analytical expression of power offset has been confirmed with 4-QAM, 16-QAM, and 64-QAM formats under different SER situations. Furthermore, the nonlinear relationship between the power offset and SER of $M$-QAM formats has also been thoroughly validated under both linear scale (measured in mW) and logarithmic scale (measured in dB). These theoretical insights offer significant contributions to the design of potential power offset mitigation strategies in MMSE-PPE, thereby enhancing its real-time application.