In this paper, we propose a novel optimizer state compression algorithm, namely π-Quant, which leverages the properties of irrational numbers (e.g., π) for memoryefficient training. The core idea is based on our mathematical findings, which show that a pair of parameters can be represented by a single rotation angle using the complex rotation scheme. Building on this insight, we map the parameters into a complex space and perform quantization using the corresponding rotation angles. To efficiently integrate it into optimization process, we develop an efficient system of geometric equations that computes the precise rotation angles with linear complexity. We evaluate π-Quant on a wide range of tasks. Our experiments show that it can reduce the bit-width of parameters to 3.32-bit, achieving a 41.8% decrease in GPU memory usage, all while maintaining full accuracy.

Many real-world data can be modeled as 3D graphs, but learning representations that incorporates 3D information completely and efficiently is challenging. Existing methods either use partial 3D information, or suffer from excessive computational cost. To incorporate 3D information completely and efficiently, we propose a novel message passing scheme that operates within 1-hop neighborhood.

To study the accuracy of the predicted rotation angles by TARGET-VAE, we calculate the mean standard deviation ofthepredicted rotations, introduced in[1]. This metric basically measures the mean square error between the rotation ofthe object inthe input image and the predicted rotation forthatobject. Wefind that the model correctly identifies and reconstructs the objects (Figure 3). Eachshape is rotated by one of 40 values linearly spaced in [0, 2π], translated across bothx and y dimensions, and scaled using one of six linearly spaced values in [0.5, 1]. Weobserved that, as expected, eliminating inference on the discretized rotation dimension has a significant negative effect on identifying transformation-invariant representations and the clustering accuracy on MNIST(U) is only33.8%(Table2).

To incorporate 3D information completely and efficiently, we propose a novel message passing scheme that operates within 1-hop neighborhood.

-- A robust and compact magneto - optical rotary encoder for the characterisation of robotic rotary joints is demonstrated. The system employs magnetic field - induced optical attenuation in a double - pass configuration using rotating nonuniform magnets around an optical circulator operating in reflection . The encoder tracks continuous 360 rotation with rotation sweep rates from ν = 135 /s to ν = 3 70 /s, and an angular resolution of Δ θ = 0. 3 . I NTRODUCTION OTARY encoders convert rotation into electromagnetic signals, most commonly electrical. Examples include precision monitoring and control of steering wheels [1], [2], motors of autopilot vehicles [2], [3], robot ics [4], [5], and prosthetic arms [6] . In robotics, the encoder is a crucial part of the positional feedback needed to perform precision movements.