The advent of LLMs has given rise to generative search, a new search paradigm in which LLMs retrieve information from the web related to a query and synthesize it into a single, coherent response. This paradigm differs fundamentally from traditional web search, where results are returned as a ranked list of independent web pages. In this paper, we ask: Along what dimensions does generative search differ from traditional search?We conduct a systematic comparison between Google organic search and five generative search systems from three providers: Google, OpenAI, and Perplexity. Our analysis reveals substantial variation among engines in their reliance on internal v.s. external knowledge, source diversity, and stability. While generative systems often achieve topical coverage comparable to traditional search, they do so using markedly different retrieval footprints and synthesis strategies. We further show that the outputs of generative search can vary across time and executions, raising new challenges for robustness. Our findings demonstrate that generative search introduces new dimensions that are not captured by existing evaluation paradigms, motivating the development of evaluations that explicitly account for retrieval behavior, synthesis, and stability in generative search systems.

Large language models (LLMs) operate in two fundamental learning modes – fine-tuning (FT) and in-context learning (ICL) – raising key questions about which mode yields greater language proficiency and whether they differ in their inductive biases. Prior studies comparing FT and ICL have yielded mixed and inconclusive results due to inconsistent experimental setups. To enable a rigorous comparison, we propose a formal language learning task – offering precise language boundaries, controlled string sampling, and no data contamination – and introduce a discriminative test for language proficiency, where an LLM succeeds if it assigns higher generation probability to in-language strings than to out-of-language strings.Empirically, we find that: (a) FT has greater language proficiency than ICL on in-distribution generalization, but both perform equally well on out-of-distribution generalization. (b) Their inductive biases, measured by the correlation in string generation probabilities, are similar when both modes partially learn the language but diverge at higher proficiency levels. (c) Unlike FT, ICL performance differs substantially across models of varying sizes and families and is sensitive to the token vocabulary of the language. Thus, our work demonstrates the promise of formal languages as a controlled testbed for evaluating LLMs, behaviors that are difficult to isolate in natural language datasets. Our source code is available at https://github.com/bishwamittra/formallm.