Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12, 500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.Code and the MATH dataset can be found at github.com/hendrycks/math/.
Recent progress in the performance of intermediate temperature (500–600°C) protonic ceramic fuel cells (PCFCs) has demonstrated both fuel flexibility and increasing power density that approach commercial application requirements. Under the U.S. DOE ARPA-E REBELS program, the Colorado School of Mines (Mines), in collaboration with Fuel Cell Energy (FCE), is developing durable, kW-scale PCFC stacks and system concepts. Results from cell scale-up efforts are reviewed. Several cells have been tested for over 6,000 hours, and we demonstrate excellent performance and exceptional durability (<1.5%/1,000 hours in most cases) across all fuels without any modifications in the cell composition or architecture. The success of scale-up efforts towards commercially viable, kW-scale cell platforms is given, inclusive of short stack test results. System-level work shows that trade-offs between lower cell power densities (due to lower operating temperature), lower-cost materials, manufacturing processes, and balance-of-stack components exist which can offer competitive advantage for PCFCs in various stationary power applications.
Versa Power Systems (VPS) is a developer of solid oxide fuel cells (SOFCs) for clean power generation. VPS has been working with its development partner FuelCell Energy within the U.S. Department of Energy (DOE) Office of Fossil Energy's Solid State Energy Conversion Alliance (SECA) program to apply SOFC technology in large-scale, multi-megawatt power plant systems that utilize coal in a clean and efficient manner. As a result, new initiatives such as scale-up of the cell and stack are now being actively pursued for these applications.
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