Learning Monotone Information Time for Fixed-Budget Intraday Representations

We study representations of intraday market and order-book data for predicting stocks' relative next-day close-to-close returns. Uniform tokenization partitions 240 one-minute records at a fixed temporal resolution, although trading activity varies across intervals, stocks, and trading dates. We introduce a tokenizer that learns sample-dependent temporal coverage under a fixed token budget. A local causal encoder assigns a positive information rate to each minute; normalized cumulative rates define a monotone time coordinate. Soft aggregation around a fixed number of equally spaced centers in this coordinate yields tokens with adaptive spans in natural time while preserving chronological order. The rates are learned jointly with the prediction objective, without supervision of discrete boundaries. A causal convolutional Mixer and a constrained pooling head integrate these representations to predict next-day stock-ranking scores. Historical validation results support the tested adaptive encoding configuration and its learned rate-based allocation. A system built on the proposed method achieved champion status in an external quantitative modeling competition. The organizers executed the submitted training code and evaluated the resulting model on hidden test data using the submitted inference code; test labels and scores were not used for training or model selection.