arXiv subjects

Max Yu

Publications and source records attributed to Max Yu.

3 recordsLinked to original sources

arXiv2026

PokaiTrainer: Scaling Belief-State Search to Competitive Pok\'emon VGC

Decision-time equilibrium search carried poker to superhuman play, but it has so far relied on tractable subgames: a handful of actions per decision, chance confined to card deals, one player moving at a time. Competitive Pok\'emon in its official doubles format (VGC) breaks all three assumptions at once. Both players act simultaneously from joint menus in the hundreds, each joint action resolves to hundreds of stochastic outcomes, and the opponent's reserves and stat allocations are hidden. We set out to build a strong VGC agent and report what that took. PokaiEngine, our Rust battle engine, enumerates a joint action's full weighted outcome distribution in one pass, at ${\sim}99\%$ parity with Pok\'emon Showdown and a fraction of the cost of sampling it. On top of the engine, PokaiTrainer adapts Student of Games to this scale, solving every decision as a Bayesian matrix game over public belief states and growing subgames under an explicit compute budget. On the live Showdown best-of-three ladder, the agent wins 59% of 150 sets against a human field averaging ${\sim}1320$ Elo. It settles into a 1350-1400 Elo band, and at its peak briefly entered the format's top 500.

cs.LG↗

arXiv2026

SuperThoughts: Reasoning Tokens in Superposition

Long Chain-of-Thought (CoT) reasoning improves LLM problem-solving but is computationally expensive due to sequential token generation. While recent works explore reasoning in continuous latent spaces to bypass discrete token generation, they often struggle with training stability and fail to scale to complex, long-horizon tasks due to lack of supervision signal. We propose SuperThoughts, which compresses pairs of consecutive CoT tokens into single latent representations and decodes two tokens per step via a lightweight Multi-Token Prediction (MTP) module. This preserves discrete token supervision at training time while doubling throughput at inference time. We finetune Qwen2.5-Math-1.5B-Instruct, Qwen2.5-Math-7B-Instruct, Qwen2.5-Math-14B-Instruct, and evaluate on MATH500, AMC, OlympiadBench, and GPQA-Diamond. With a confidence-based adaptive mechanism that falls back to standard decoding when uncertain, SuperThoughts achieves $\sim$20--30\% CoT length reduction while maintaining accuracy with minimal degradation (1-2 points accuracy drop on most tasks).

cs.LG↗

arXiv2016

Generalized Algorithm for Wythoff's Game with Basis Vector $(2^b,2^b)$

Wythoff's Game is a variation of Nim in which players may take an equal number of stones from each pile or make valid Nim moves. W. A. Wythoff proved that the set of P-Positions (losing position), $C$, for Wythoff's Game is given by $C := \left\{ (\lfloor k\phi \rfloor, \lfloor k\phi^2 \rfloor), (\lfloor k\phi^2 \rfloor, \lfloor k\phi \rfloor) : k \in \mathbb Z_{\geq 0} \right\}$. An open Wythoff problem remains where players make the valid Nim moves or remove $kb$ stones from each pile, where $b$ is a fixed integer. We denote this as the $(b,b)$ game. For example, regular Wythoff's Game is just the $(1,1)$ game. In 2009, Duch${\^e}$ne and Gravier proved an algorithm to generate the set of P-Positions for the $(2,2)$ game by exploiting the periodic nature of the differences of stones between the two piles modulo $4$. We observe similar cyclic behaviour for any $b$, where $b$ is a power of $2$, modulo $b^2$, and construct an algorithm to generate the set of P-Positions for this game. Let $a$ be a power of $2$. We prove our algorithm works by first showing that it holds for the first $a^2$ terms in the $(a,a)$ game. Next, we construct an ordered multiset for the $(2a,2a)$ game from the $a^2$ terms, and an inductive proof follows. Moreover, we conjecture that all cyclic games require $a$ to be a power of $2$, suggesting that there is no similar structure in the generalised $(b,b)$ game where $b$ isn't a power of $2$. Future directions for generalising this result would likely utilise numeration systems, particularly the PV numbers.

math.CO↗