Kevin Song

Xiao Ye, Jacob Dineen, Evan Zhu et al.

Forecasters are evaluated by backtesting, which replays resolved questions and grades the probability the system would have assigned before the outcome was known. For LLMs, two channels leak the answer into this test. A model that retrieves can surface reports written after the event, turning forecasting into a lookup, and each new model is trained on data closer to the event, so a question that lay in the future for last year's models sits inside this year's training data. Either way, the test grades recall while claiming to grade foresight. We introduce Hindcast, which closes both leaks by grading a model as if it stood at a chosen past date $t_0$, before the outcome existed in either channel. Hindcast replays resolved Polymarket prediction markets against a frozen snapshot of public Reddit, lets the model read only posts written before $t_0$, and scores each forecast against both what happened and the market's own price at $t_0$, itself a human forecast made from the same past information. Because the cutoff is set per market and the snapshot never changes, the evaluation re-runs on new markets as models improve, without going stale. Once the leak is closed, retrieval still helps most models, but only where Reddit discussed the event beforehand. Where the archive carried only speculation, retrieval hurts.

Kevin Song, Evan Diewald, Ornob Siddiquee et al.

Defensive coverage schemes in the National Football League (NFL) represent complex tactical patterns requiring coordinated assignments among defenders who must react dynamically to the offense's passing concept. This paper presents a factorized attention-based transformer model applied to NFL multi-agent play tracking data to predict individual coverage assignments, receiver-defender matchups, and the targeted defender on every pass play. Unlike previous approaches that focus on post-hoc coverage classification at the team level, our model enables predictive modeling of individual player assignments and matchup dynamics throughout the play. The factorized attention mechanism separates temporal and agent dimensions, allowing independent modeling of player movement patterns and inter-player relationships. Trained on randomly truncated trajectories, the model generates frame-by-frame predictions that capture how defensive responsibilities evolve from pre-snap through pass arrival. Our models achieve approximately 89\%+ accuracy for all tasks, with true accuracy potentially higher given annotation ambiguity in the ground truth labels. These outputs also enable novel derivative metrics, including disguise rate and double coverage rate, which enable enhanced storytelling in TV broadcasts as well as provide actionable insights for team strategy development and player evaluation.

Kevin Song

Multi-agent trajectory generation in team sports requires models that capture both the diversity of possible plays and realistic spatial coordination between players on plays. Standard generative approaches such as Conditional Variational Autoencoders (CVAE) and diffusion models struggle with this task, exhibiting posterior collapse or convergence to the dataset mean. Moreover, most trajectory prediction methods operate in a forecasting regime that requires multiple frames of observed history, limiting their use for play design where only the initial formation is available. We present PlayGen-MoG, an extensible framework for formation-conditioned play generation that addresses these challenges through three design choices: 1/ a Mixture-of-Gaussians (MoG) output head with shared mixture weights across all agents, where a single set of weights selects a play scenario that couples all players' trajectories, 2/ relative spatial attention that encodes pairwise player positions and distances as learned attention biases, and 3/ non-autoregressive prediction of absolute displacements from the initial formation, eliminating cumulative error drift and removing the dependence on observed trajectory history, enabling realistic play generation from a single static formation alone. On American football tracking data, PlayGen-MoG achieves 1.68 yard ADE and 3.98 yard FDE while maintaining full utilization of all 8 mixture components with entropy of 2.06 out of 2.08, and qualitatively confirming diverse generation without mode collapse.

Kevin Song

Infinite-shoe casino blackjack provides a rigorous, exactly verifiable benchmark for discrete stochastic control under dynamically masked actions. Under a fixed Vegas-style ruleset (S17, 3:2 payout, dealer peek, double on any two, double after split, resplit to four), an exact dynamic programming (DP) oracle was derived over 4,600 canonical decision cells. This oracle yielded ground-truth action values, optimal policy labels, and a theoretical expected value (EV) of -0.00161 per hand. To evaluate sample-efficient policy recovery, three model-free optimizers were trained via simulated interaction: masked REINFORCE with a per-cell exponential moving average baseline, simultaneous perturbation stochastic approximation (SPSA), and the cross-entropy method (CEM). REINFORCE was the most sample-efficient, achieving a 46.37% action-match rate and an EV of -0.04688 after 10^6 hands, outperforming CEM (39.46%, 7.5x10^6 evaluations) and SPSA (38.63%, 4.8x10^6 evaluations). However, all methods exhibited substantial cell-conditional regret, indicating persistent policy-level errors despite smooth reward convergence. This gap shows that tabular environments with severe state-visitation sparsity and dynamic action masking remain challenging, while aggregate reward curves can obscure critical local failures. As a negative control, it was proven and empirically confirmed that under i.i.d. draws without counting, optimal bet sizing collapses to the table minimum. In addition, larger wagers strictly increased volatility and ruin without improving expectation. These results highlight the need for exact oracles and negative controls to avoid mistaking stochastic variability for genuine algorithmic performance.