Related papers: Adaptive Multi-Head Finite-State Gamblers

We introduce multi-head finite-state dimension, a generalization of finite-state dimension in which a group of finite-state agents (the heads) with oblivious, one-way movement rules, each reporting only one symbol at a time, enable their…

The multi-armed bandit is a concise model for the problem of iterated decision-making under uncertainty. In each round, a gambler must pull one of $K$ arms of a slot machine, without any foreknowledge of their payouts, except that they are…

This paper develops the theory of pushdown dimension and explores its relationship with finite-state dimension. Pushdown dimension is trivially bounded above by finite-state dimension for all sequences, since a pushdown gambler can simulate…

We study a two-player Stackelberg game with incomplete information such that the follower's strategy belongs to a known family of parameterized functions with an unknown parameter vector. We design an adaptive learning approach to…

We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…

This study identifies the specific conditions under which large language models exhibit human-like gambling addiction patterns, providing critical insights into their decision-making mechanisms and AI safety. We analyze LLM decision-making…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable…

Attention is a powerful and ubiquitous mechanism for allowing neural models to focus on particular salient pieces of information by taking their weighted average when making predictions. In particular, multi-headed attention is a driving…

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means…

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention…

Attending to what is relevant is fundamental to both the mammalian brain and modern machine learning models such as Transformers. Yet, determining relevance remains a core challenge, traditionally offloaded to learning algorithms like…

The state of the art in learning meaningful semantic representations of words is the Transformer model and its attention mechanisms. Simply put, the attention mechanisms learn to attend to specific parts of the input dispensing recurrence…

Modern transformer attention is internally multi-agent -- heads compete and coordinate -- yet we train it as if it were a monolithic optimizer. We formalize this gap: cross-entropy training induces an implicit potential game among heads,…

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

Multi-head attention powers Transformer networks, the primary deep learning architecture behind the success of large language models (LLMs). Yet, the theoretical advantages of multi-head versus single-head attention, beyond mere parallel…

The neural attention mechanism plays an important role in many natural language processing applications. In particular, the use of multi-head attention extends single-head attention by allowing a model to jointly attend information from…

The multi-head attention layer is one of the key components of the transformer architecture that sets it apart from traditional feed-forward models. Given a sequence length $k$, attention matrices…

This work investigates the problem of multi-agents trajectory prediction. Prior approaches lack of capability of capturing fine-grained dependencies among coordinated agents. In this paper, we propose a spatial-temporal trajectory…

Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be…