让下一篇重要论文，不再错过。

In LLM-based recommendation, memory acts as a user-level agent in a memory-augmented backbone. Yet users and items remain asymmetric: only the user is given a structured profile; it enters a bandwidth-limited reranker prompt; and it is frozen after warmup. We recast LLM-based recommendation as an agentic-communication process in four stages: BUILD a self-description, TRANSMIT it along the collaborative graph, UNDERSTAND the other side, and SYNC it from the next interaction. This formulation reveals three unresolved communication challenges: the item side never produces a comparable self-description (one-sided BUILD); profile-level signals enter only the bandwidth-limited reranker prompt rather than retrieval, where they would not compete for context tokens (prompt-trapped UNDERSTAND); and the user's description is frozen after warmup with no principled update rule (absent SYNC). We instantiate the missing stages as HARP (Homophily-aware Agentic Recommendation via dual Profiles), a training-free, three-operator addition to a frozen LLM backbone: a rule-extracted symmetric item profile (zero extra LLM calls), a channel-decomposable profile-level homophily H(phi_u, phi_i) consumed at retrieval time rather than inside the reranker prompt, and a single-pass reflective update realising in-context profile evolution without any gradient step. On four public benchmarks (Yelp, Books, MovieTV, Goodreads), HARP lifts Hit@1 over the strongest published baseline by 6.9%-24.0%, with family-wise Holm-corrected p < 1e-9 on every dataset. Ablations and a per-case attribution study show that the operators contribute complementary gains, with the retrieval-side gate as the main source; we also report the trade-off introduced by the reflective pass. We formulate agentic communication and provide a training-free instantiation. Code is available at https://github.com/Jove-Zhen/HARP.

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.