Recommendation systems represent one of the largest machine learning applications on the planet -- industry-scale recommendation models are trained with petabytes of data and serve billions of users every day. To utilize the rich user signals in the long user history, these models have been scaled up to unprecedented complexity, up to trillions of floating-point operations (TFLOPs) per example. This scale, coupled with the huge amount of training data, necessitates new storage and training algorithms to efficiently improve the quality of these complex recommendation systems.

Visual representations play a crucial role in developing generalist robotic policies. Previous vision encoders, typically pre-trained with single-image reconstruction or two-image contrastive learning, tend to capture static information, often neglecting the dynamic aspects vital for embodied tasks. Recently, video diffusion models (VDMs) demonstrate the ability to predict future frames and showcase a strong understanding of physical world. We hypothesize that VDMs inherently produce visual representations that encompass both current static information and predicted future dynamics, thereby providing valuable guidance for robot action learning. Based on this hypothesis, we propose the Video Prediction Policy (VPP), which learns implicit inverse dynamics model conditioned on predicted future representations inside VDMs. To predict more precise future, we fine-tune pre-trained video foundation model on robot datasets along with internet human manipulation data. In experiments, VPP achieves a 18.6% relative improvement on the Calvin ABC-D generalization benchmark compared to the previous state-of-the-art, and demonstrates a 31.6% increase in success rates for complex real-world dexterous manipulation tasks. For your convenience, videos can be found at https://video-prediction-policy.github.io/

The elementary function approximation using piecewise quadratic polynomial interpolation requires larger area of the look-up table (LUT) and circuit. To solve the problem, this paper presents an algorithm for elementary function approximation in single-precision floating-point format, which is based on minimax piecewise cubic polynomial approximation. The algorithm can efficiently achieve the approximation of reciprocal, square root, square root reciprocal, exponentials, logarithm, and trigonometric function in single-precision floating-point format. According to the algorithm the range of parameters is narrowed first, then we get the optimal truncated bit width of coefficients through errors analyzing and dividing the interval into subsections. Meanwhile Remes algorithm is used to perform the successive optimization, so as to reduce the area of LUT and circuit. At last the intermediate parameters of the circuit are optimally truncated, and the overall framework of hardware circuit is designed. The analysis and experimental results show that comparing with piecewise quadratic polynomial approximation the circuit delay is reduced by 17.25%, the area of LUT is decreased by 53.60% and total area of circuits is reduced by 19.73%. The comparisons with the polynomial approximation of degree-1, degree-2, degree-4 are also made, the results show that the piecewise cubic polynomial interpolation algorithm proposed by this paper can achieve optimal performance and minimized cost of hardware implementation.