Scientific weak signals are early, low-visibility research directions that later become central to mature scientific topics, yet existing resources such as trend tracking, citation forecasting, and foresight reports rarely provide validated reference sets that link concrete early precursors to later paradigms. We introduce BackTrend, a retrospective benchmark in which, given a mature target topic and a temporal evidence constraint, systems must recover two types of precursors: problem-space signals, underrecognized research problems, and solution-space signals, emerging methods for known problems. BackTrend contains 25 mature target topics in artificial intelligence and machine learning and 66 human-validated weak signals, reconstructed from large-scale literature by grounding each candidate in its 2019–2024 publication-frequency trajectory. We evaluate frontier LLMs, RAG systems, and agentic research systems via set-level and signal-level semantic matching. Current systems generate plausible but misaligned precursors, with topic drift, granularity mismatch, lexical near-miss, and coverage failure; no system exceeds single-digit LLM-judged F1, and additional retrieval or web search does not consistently help.