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We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
Consider a model where $N$ equal agents possess `values', belonging to $\mathbb{N}_0$, that are subject to incremental growth over time. More precisely, the values of the agents are represented by $N$ independent, increasing $\mathbb{N}_0$…
We explore which linguistic factors -- at the sentence and token level -- play an important role in influencing language model predictions, and investigate whether these are reflective of results found in humans and human corpora (Gries and…
Self-improvement has emerged as a state-of-the-art paradigm in Neural Combinatorial Optimization (NCO), where models iteratively refine their policies by generating and imitating high-quality solutions. Despite strong empirical performance,…
Optimizing robotic action parameters is a significant challenge for manipulation tasks that demand high levels of precision and generalization. Using a model-based approach, the robot must quickly reason about the outcomes of different…
Self-play preference optimization has emerged as a prominent paradigm for aligning large language models (LLMs). It typically involves a language model to generate on-policy responses for prompts and a reward model (RM) to guide the…
The susceptible-infected-recovered (SIR) model and its variants form the foundation of our understanding of the spread of diseases. Here, each agent can be in one of three states (susceptible, infected, or recovered), and transitions…
Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is…
Large language models memorize parts of their training data. Memorizing short snippets and facts is required to answer questions about the world and to be fluent in any language. But models have also been shown to reproduce long verbatim…
As more machine learning agents interact with humans, it is increasingly a prospect that an agent trained to perform a task optimally, using only a measure of task performance as feedback, can violate societal norms for acceptable behavior…
Machine learning models can capture and amplify biases present in data, leading to disparate test performance across social groups. To better understand, evaluate, and mitigate these biases, a deeper theoretical understanding of how model…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
We tested whether and how biases in visual perception might influence motor actions. To do so, we designed an interception task in which subjects had to indicate the time when a moving object, whose trajectory was occluded, would reach a…
We study the problem of how to coordinate the actions of independent agents in a distributed system where message arrival times are unbounded, but are determined by an exponential probability distribution. Asynchronous protocols executed in…
The standard feedback model of reinforcement learning requires revealing the reward of every visited state-action pair. However, in practice, it is often the case that such frequent feedback is not available. In this work, we take a first…
The most general exclusion single species one dimensional reaction-diffusion models with nearest-neighbor interactions which are both autonomous and can be solved exactly through full interval method are introduced. Using a generating…
Randomized controlled trials are the gold standard for evaluating the efficacy of an intervention. However, there is often a trade-off between selecting the most scientifically relevant primary endpoint versus a less relevant, but more…
Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they…
Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…
We consider the problem of estimating a dose-response curve. Continuous treatments arise often in practice, e.g. in the form of time spent on an operation, distance traveled to a location or dosage of a drug. Letting $A$ denote a continuous…