Noah Fleming, Mika Göös, Ziyi Guan, Oliver Korten, Daniel Mitropolsky, Toniann Pitassi, Artur Riazanov, Dmitry Sokolov 等 10 位作者
AI 速览：作者在随机预言机模型（Romantica）中刻画了主要 TFNP 类的平均情形困难性，并给出 PPAD 困难、EoPL 与 UEoPL 可解性分离等结果。
We determine which major $\TFNP$ classes are hard in the random oracle model (ROM). Prior work establishes average-case hardness of highly structured subclasses of $\TFNP$ from strong cryptographic assumptions such as LWE and indistinguishability obfuscation. It is not known whether weaker assumptions such as one-way functions imply hardness of any of the standard $\TFNP$ subclasses, even in the worst case. The ROM, where all parties have query access to a random function, lies, morally, between these two regimes: a random function is one-way, but public-key cryptography cannot be built from it in a black-box way. We refer to this setting as \emph{Romantica}. Our first result settles a long-standing open problem: $\PPAD$, the class of total search problems reducible to finding a Nash equilibrium, is hard on average in Romantica. Combined with the known hardness of PLS (local search), this gives average-case hardness of $\EoPL = \PPAD \cap \PLS$. In contrast, we show that $\UEoPL$ can be solved in Romantica with polynomially many oracle queries by a computationally unbounded solver, a sharp distinction between $\EoPL$ and $\UEoPL$. This resolves the black-box hardness landscape of all major $\TFNP$ classes in Romantica. Finally, we initiate the study of separations between $\TFNP$ subclasses in Romantica: $\PWPP$ and $\PPA$ do not reduce to $\PLS$ under \emph{public-coin} reductions.
Ziyi Guan, Yael Tauman Kalai, Ron Rothblum, Zoe Xi
AI 速览：提出可回卷交互证明（RIPs），利用验证者可回卷AI证明者状态的能力，在无需诚实证明者假设且不使用密码学的前提下实现更高效的可扩展监督。
Scalable oversight asks how a weak verifier can check the outputs of computations performed by more powerful AI systems. One proposed approach uses relativizing interactive proofs, in which a weak verifier checks the output of a complex oracle-aided computation by interacting with one or more powerful provers. A prominent example is debate, which is highly efficient but assumes that one of two powerful AI models, or provers, is truthful. For certain classes of oracle-aided computations, this assumption can be removed, but at substantially greater computational cost. In this work, we introduce \emph{rewindable interactive proofs} (RIPs), a new model of relativizing interactive proofs for scalable oversight. In an RIP, the verifier may rewind the prover to an earlier state of the interaction and continue from there. This is possible when the prover is an AI model, since the verifier can save a snapshot of the model's state and later restore it. We construct a relativizing RIP for computations whose outputs are robust to changing a small fraction of oracle answers. Our construction is more efficient than prior relativizing proofs that do not assume a truthful prover, and it uses no cryptography. In our construction the honest prover runs in time linear in that of the original computation, and the verifier, after a one-time preprocessing step, runs in time nearly linear in the input length (which can be much smaller than the computation itself). We implement our protocol, report a preliminary MNIST experiment, and show that an RIP can be faster than a state-of-the-art deployed proof system. RIPs may be of independent interest. Rewinding is possible whenever the verifier controls the prover's machine, for example when the prover runs on trusted hardware or in a virtual machine whose state can be checkpointed.
David P. Woodruff, Vincent Cohen-Addad, Lalit Jain, Jieming Mao, Song Zuo, MohammadHossein Bateni, Simina Branzei, Michael P. Brenner 等 36 位作者
Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.