Recent advances in Large Language Models (LLMs) have raised interest in their formal reasoning capabilities, particularly in mathematics. While closed LLMs like GPT-4 perform well on mathematical benchmarks, e.g., GSM8K, it remains unclear whether small to medium-sized open LLMs can achieve similar performance, questioning their reliability. To close this gap, we propose a post-training approach leveraging a mixture of opinions (MoO) from weaker ancillary LLMs to enhance a (relatively) stronger LLM's reasoning. For that, each post-training sample is augmented with Chain-of-Thought (CoT) reasoning steps and answers from ancillary LLMs, enabling the main LLM to learn from diverse perspectives. We compare MoO with standard supervised fine-tuning (SFT), few-shot prompting, and the Mixture of Agents (MoA) method on mathematical reasoning benchmarks. Our results show that incorporating weaker LLMs' opinions improves mathematical reasoning by an average of 5%, highlighting the value of diverse perspectives in reasoning tasks.

Employees from AeroVironment allegedly brought a drone with explosives attached to it in a carry-on bag, on a Delta flight in April 2015. As Bloomberg reports, the flight had 230 passengers and when another employee, Mark Anderson, discovered this and reported it to the Department of Defense a month later, he said he was punished, stripped of his responsibilities and then fired without a severance package. AeroVironment counts the US government as a major customer, Bloomberg notes. It's supplied the Navy with submarine-launched spy drones and made robo-hummingbirds for DARPA, for example. A recent report from the company said that over half of its income is from being a government contractor. It's pretty easy, if not more than a little predictable, to see why the company reacted to Anderson's claims the way it did.

NEW YORK – AeroVironment Inc. was accused of trying to conceal that employees transported a drone rigged with explosives on a commercial flight and retaliating against a manager who told the government. In April 2015, AeroVironment workers traveled to Los Angeles from Salt Lake City on a Delta Air Lines Inc. There were about 230 civilian passengers aboard, the lawsuit states. The plaintiff, Mark Anderson, who oversaw security for the drone-maker's top-secret government programs, learned of the incident in May 2015, according to the complaint. After reporting it to the U.S. Department of Defense, he was reprimanded, stripped of his responsibilities and ultimately fired without severance, Anderson alleges.