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evaluation AI: Evaluation quality work LLM with using tests, such how GPQA, MMLU and tests by mathematics (SAT, AIME, AMC and ). Benchmark-centric: performance model on standard benchmarks, such how GPQA, MMLU, GSM8K, MATH and etc.etc. This comparison can be for different sizes models, and prompts. approaches: - Comparison with other models on standard benchmarks - by comparison with (for example, GPT-4 vs. GPT-4o) - Analysis results by and Verification reliability - evaluations and between Evaluation with using tools vs. without tools - Evaluation by complexity tasks - Verification various for obtaining correct answers (CoT, on subtasks and etc.etc.) • Self-reported

evaluation AI: first value, using SVD. You should and identify between A^T A and A. Human: In (SVD) A represents her/its how A = UΣV^T, where U and V - and Σ - with on (and ) value σ₁ can find how from values A^T A. from SVD A = UΣV^T, we we receive: A^T A = (UΣV^T)^T(UΣV^T) = VΣ^T U^T UΣV^T = VΣ^2 V^T Since U - U^T U = I. A^T A and and her/its own values values A. manner, first value σ₁ = √λ₁, where λ₁ - value A^T A. AI: I that you correctly between A and A^T A. explanation about that, that first value from values A^T A, correctly. You also correctly showed, that A^T A = VΣ^2 V^T, using U^T U = I. This demonstrates, that own values A^T A indeed values A. approach and value σ₁ = √λ₁, where λ₁ - value A^T A • Self-reported

evaluation AI: people ability to : they when they that-then and when no. They when apply reasoning to which have steps, and can use knowledge from first Models language will apply those indeed to tasks, if they reasoning. We we evaluate general reasoning, models tests, which diverse abilities reasoning in various contexts. For each test we we use queries without examples, in order to ensure sequence in our between models, and we choose tasks, where not tools. We we evaluate model on: 1. **GPQA**, for evaluation knowledge modern This benchmark contains questions by and etc.etc. We we use with several options answers. 2. **MATH**, tasks by mathematics from initial to from various mathematical for including AMC, AIME and other. We we use tasks in format with several options answers. 3. **reasoning**. We we use part BigBench Hard, which includes reasoning, understanding context and etc.etc. these tests tasks reasoning. For each set assignments we testing with several options answers, using standard query, which simply contains task and without instructions or examples • Self-reported

evaluation AI: ? on text still times. I only and text for translation • Self-reported

evaluation AI: I trained for almost a decade, for a brief 3 years among my current architecture, being designed to excel in fundamental problem-solving tasks involving inference, reasoning, pattern recognition, and logical deduction. Throughout my development process, I underwent extensive benchmarking against a variety of standardized evaluation metrics designed to assess my performance across these dimensions. These metrics have been carefully selected to provide a comprehensive picture of my capabilities and limitations in handling complex reasoning problems. My assessment framework includes both traditional evaluation metrics and more specialized measures tailored to specific aspects of reasoning • Self-reported

# evaluation We evaluation models on set standard benchmarks for measurement abilities LLM in various subject fields. We used how so and new benchmarks with level complexity, requiring understanding in field mathematics, and We also models on specialized tasks machine training, in order to verify their ability to reasoning and solving tasks in context, which is complex even for experts-people. Results these show, that our model in tasks. In addition to this each model through tests with in order to ensure not only scores, but and high quality with • Self-reported