## 1 Introduction
These reported NIR glucose sensors commonly have very few NIR channels and broad-spectrum bandwidths caused by simple LED sources, which leads to rough NIR multi-wavelength light information and large measurement errors, limiting their use in terms of accurate glucose sensing. As a result, their predicted network algorithms must become increasingly complex, typically requiring large datasets and a long time to predict human glucose. The critical parameters of typical NIR glucose sensors are summarized and compared in Table 1. These traditional sensors suffer from limited NIR multi-wavelength light information and complex predicted networks, meaning they fall short in terms of the development trends of real-time, highly accurate, and highly sensitive daily glucose monitoring. A non-invasive NIR glucose sensor with more efficient multi-wavelength light optical information and using a predicted algorithm shows promise for application in these regards; however, this remains an open question. In this paper, we propose a non-invasive and highly accurate multi-wavelength light NIR glucose sensor using a multilevel metric learning-back propagation network, i.e., an \"HMML-BP\" network, based on the multi-wavelength light narrowband NIR sensing system. The HMML-BP network is composed of multilevel metric learning modules and a BP network, meaning it can remove complex sensing backgrounds and predict human blood glucose concentration. Our method distinguishes itself from prior approaches through its physics-informed design and hierarchical processing, offering unique advantages for non-invasive glucose monitoring. Most reported glucose sensing methods rely on single-step predictive models with direct preprocessing [29; 32; 33; 34; 36; 37]. These models often require increasingly complex architectures, large datasets, and extended training times due to the intrinsic NIR absorption spectra of glucose heavily overlapping with those of other biomolecules, as well as the high complexity of sensing backgrounds in vivo. Our method leverages the distinct absorption properties of human tissue and blood glucose; low tissue absorption regions (850 nm and 950 nm channels) serve as reference signals to mitigate background noise and glucose absorption bands (1300 nm, 1400 nm, 1550 nm, and 1650 nm) containing target-specific information. By systematically integrating multilevel metric learning with a BP network, our method achieves high accuracy while maintaining physical interpretability. Different from conventional approaches that directly process overlapped glucose absorption spectra, our hierarchical design enables the independent verification of the embedding space's physical consistency, as well as the convenient extraction of effective information from complex backgrounds. In addition, these physics-aware architectures show more transparency, reduced joint optimization information loss, and better computational efficiency, all of which are critical for practical daily human blood glucose sensing. Our highly accurate narrowband multi-wavelength light NIR sensing system consists of six-channel NIR filters with center wavelengths of 850 nm, 940 nm, 1300 nm, 1400 nm, 1550 nm, and 1650 nm and a spectral resolution below 12 nm. The measured information is entered into the multilevel metric learning modules to build 3D multi-wavelength light data. The multilevel metric learning module is made of the first-level metric learning elements of 1D tissue absorption and 3D glucose absorption data, which are further connected to the second-level metric learning element to remove complex sensing backgrounds. Several metric learning algorithms of stochastic neighbor embedding (SNE) [38], diffusion maps [39], and factor analysis [40] are used to optimize 3D multi-wavelength light data. Furthermore, these data are input into the BP network to predict blood glucose concentration.