Prior work suggests that human brain responses to language exhibit hierarchically organized "integration windows" that substantially constrain the

We consider the Continuum Bandit problem where the goal is to find the optimal action under an unknown reward function, with an additional monotonicity constraint (or, markdown constraint) that requires that the action sequence be non-increasing. This problem faithfully models a natural single-product dynamic pricing problem, called markdown pricing, where the objective is to adaptively reduce the price over a finite sales horizon to maximize expected revenues. Jia et al '21 and Chen '21 independently showed a tight $T^{3/4}$ regret bound over $T$ rounds under *minimal* assumptions of unimodality and Lipschitzness in the reward (or, revenue) function. This bound shows that the demand learning in markdown pricing is harder than unconstrained (i.e., without the monotonicity constraint) pricing under unknown demand which suffers regret only of the order of $T^{2/3}$ under the same assumptions (Kleinberg '04). However, in practice the demand functions are usually assumed to have certain functional forms (e.g.

Large Language Models (OpenAI et al., 2024; Team et al., 2025; DeepSeek-AI et al., 2025) based on the Transformer (Vaswani et al., 2023) architecture have achieved impressive results, approaching or exceeding human-level performance across multiple domains. Scaling laws (Hestness et al., 2017; Kaplan et al., 2020) are an established method for modeling the performance of these networks, enabling researchers to plan large-scale training runs based on curated sets of smaller experiments. Traditionally, these laws focus on predicting proxy metrics for model quality, such as pre-training log-perplexity. This has proven invaluable for optimizing training hyperparameters, like the optimal ratio of tokens to parameters. Another important direction in understanding the scaling of LLMs is tracking the behavior of more interpretable indicators of model capabilities, like accuracy on downstream benchmarks measuring the performance on general knowledge, reasoning, math and coding tasks. Despite early attempts to solve this problem (Grattafiori et al., 2024; Isik et al., 2025; Chen et al., 2025), scaling downstream metrics have been often referred to as noisy and unreliable (Schaeffer et al., 2025; Lourie et al., 2025). Current approaches to modeling the downstream performance performance of LLMs (Grattafiori et al., 2024; Chen et al., 2025; Bhagia et al., 2024) typically rely on a two-stage approach, where the training budget is first mapped to a proxy metric like mean log-probability of the correct answer, and then another dependence is established, mapping to benchmark accuracy. Work done as an intern at Apple.

It detects attention weights from input event sequence and returns the sequence representation.

We address the reviewer comments below. R1: More discussion about how this idea could be applied to other generative models. Belief Propagation messages, then the model would also be able to run on discrete variables. Currently, in the paper, we only show the plots for J=1 and J=2 expansion terms. Therefore, we don't see as a limitation the fact that the functional form is Given the functional form, our method has the advantage to combine it with deep learning. R2: Missing citation to related work: http://proceedings.mlr

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Developing learning methods which do not discriminate subgroups in the population is a central goal of algorithmic fairness.