Silvano Bonacina

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Luke Sernau, Silvano Bonacina, Rif A. Saurous

Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require approximating an expectation, usually via sampling. This has led to the development of increasingly elaborate representations with ever lower sample error. We resolve this arms race by deriving an optimal sampling policy. Under this policy all random features representations have the same approximation error, which we show is the lowest possible. This means that we are free to choose whatever representation we please, provided we sample optimally.