Current methods for training Binarized Neural Networks (BNNs) heavily rely on the heuristic straight-through estimator (STE), which crucially enables the application of SGD-based optimizers to the combinatorial training problem. Although the STE heuristics and their variants have led to significant improvements in BNN performance, their theoretical underpinnings remain unclear and relatively understudied. In this paper, we propose a theoretically motivated optimization framework for BNN training based on Gaussian variational inference. In its simplest form, our approach yields a non-convex linear programming formulation whose variables and associated gradients motivate the use of latent weights and STE gradients. More importantly, our framework allows us to formulate semidefinite programming (SDP) relaxations to the BNN training task. Such formulations are able to explicitly models pairwise correlations between weights during training, leading to a more accurate optimization characterization of the training problem. As the size of such formulations grows quadratically in the number of weights, quickly becoming intractable for large networks, we apply the Burer-Monteiro approach and only optimize over linear-size low-rank SDP solutions. Our empirical evaluation on CIFAR-10, CIFAR-100, Tiny-ImageNet and ImageNet datasets shows our method consistently outperforming all state-of-the-art algorithms for training BNNs.

Sun-induced chlorophyll fluorescence (SIF) is a promising remote sensing signal for early stress detection due to its close link with photosynthesis. Canopy SIF signals are controlled by leaf physiology, canopy structure, radiation intensity and sun-observer geometry. Variations in SIF observations are affected by variations in these controlling factors besides water stress. Mitigating the interference of non-drought factors on the variations in canopy SIF to accurately evaluate drought degree is still challenging. In this study, we explore the response of apparent SIF yield (SIFy) to progressive drought in maize. With experimental evidence, we show that the difference between noon and morning SIFy was a better indicator of drought than mono-temporal SIFy measurements. We proposed the noon-to-morning ratio (NMR) to characterize diurnal dynamics and assess the severity of drought. The results show that midday measurements of SIFy were the most affected by water stress, and morning measurements were the least. The NMR of SIFy successfully revealed water stress by tracking the timing of the transition from light-limited to water-limited conditions of SIF within a day. Hence, the NMRs of SIFy were considerably more sensitive to drought than their mono-temporal values, and traditional vegetation indices, especially during the early phase of drought. This demonstrates that the use of multi-temporal or diurnal SIF measurements is more reliable than mono-temporal observations for stress detection.