Recently, deep learning-based pan-sharpening algorithms have achieved notable advancements over traditional methods. However, deep learning-based methods incur substantial computational overhead during inference, especially with large images. This excessive computational demand limits the applicability of these methods in real-world scenarios, particularly in the absence of dedicated computing devices such as GPUs and TPUs. To address these challenges, we propose Pan-LUT, a novel learnable look-up table (LUT) framework for pan-sharpening that strikes a balance between performance and computational efficiency for large remote sensing images. Our method makes it possible to process 15K 15K remote sensing images on a 24GBGPU. To finely control the spectral transformation, we devise the PAN-guided look-up table (PGLUT) for channel-wise spectral mapping. To effectively capture fine-grained spatial details, we introduce the spatial details look-up table (SDLUT).

Recently, deep learning-based pan-sharpening algorithms have achieved notable advancements over traditional methods. However, deep learning-based methods incur substantial computational overhead during inference, especially with large images. This excessive computational demand limits the applicability of these methods in real-world scenarios, particularly in the absence of dedicated computing devices such as GPUs and TPUs. To address these challenges, we propose Pan-LUT, a novel learnable look-up table (LUT) framework for pan-sharpening that strikes a balance between performance and computational efficiency for large remote sensing images. Our method makes it possible to process 15K$\times$15K remote sensing images on a 24GB GPU. To finely control the spectral transformation, we devise the PAN-guided look-up table (PGLUT) for channel-wise spectral mapping. To effectively capture fine-grained spatial details, we introduce the spatial details look-up table (SDLUT).

For many machine learning problems, there are some inputs that are known to be positively (or negatively) related to the output, and in such cases training the model to respect that monotonic relationship can provide regularization, and makes the model more interpretable. However, flexible monotonic functions are computationally challenging to learn beyond a few features. We break through this barrier by learning ensembles of monotonic calibrated interpolated look-up tables (lattices). A key contribution is an automated algorithm for selecting feature subsets for the ensemble base models. We demonstrate that compared to random forests, these ensembles produce similar or better accuracy, while providing guaranteed monotonicity consistent with prior knowledge, smaller model size and faster evaluation.

Similarly, a model that predicts the time it will take a customer to grocery shop should decrease in the number of cashiers, but each addedcashierreduces average wait time by less. In both cases, we would like to be able to incorporate this prior knowledge by constraining the machine learned model's output to have a diminishing returns response to the size of the apartment or number of cashiers.

We demonstrate on real-world examples that these shape constrained models can provide tuning-free regularization and improve model understandability.

LUT is not necessary within our framework for three reasons.

The most fundamental abstraction underlying all modern computers is the Turing Machine, that is if any modern computer can simulate a Turing Machine, an equivalence which is called Turing completeness, it is theoretically possible to achieve any task that can be algorithmically described by executing a series of discrete unit operations. In chemistry, the ability to program chemical processes is demanding because it is hard to ensure that the process can be understood at a high level of abstraction, and then reduced to practice. Herein we exploit the concept of Turing completeness applied to robotic platforms for chemistry that can be used to synthesise complex molecules through unit operations that execute chemical processes using a chemically-aware programming language, XDL. We leverage the concept of computability by computers to synthesizability of chemical compounds by automated synthesis machines. The results of an interactive demonstration of Turing completeness using the colour gamut and conditional logic are presented and examples of chemical use-cases are discussed. Over 16.7 million combinations of Red, Green, Blue (RGB) colour space were binned into 5 discrete values and measured over 10 regions of interest (ROIs), affording 78 million possible states per step and served as a proxy for conceptual, chemical space exploration. This formal description establishes a formal framework in future chemical programming languages to ensure complex logic operations are expressed and executed correctly, with the possibility of error correction, in the automated and autonomous pursuit of increasingly complex molecules.

The extraordinary success of recent Large Language Models (LLMs) on a diverse array of tasks has led to an explosion of scientific and philosophical theorizing aimed at explaining how they do what they do. Unfortunately, disagreement over fundamental theoretical issues has led to stalemate, with entrenched camps of LLM optimists and pessimists often committed to very different views of how these systems work. Overcoming stalemate requires agreement on fundamental questions, and the goal of this paper is to address one such question, namely: is LLM behavior driven partly by representation-based information processing of the sort implicated in biological cognition, or is it driven entirely by processes of memorization and stochastic table look-up? This is a question about what kind of algorithm LLMs implement, and the answer carries serious implications for higher level questions about whether these systems have beliefs, intentions, concepts, knowledge, and understanding. I argue that LLM behavior is partially driven by representation-based information processing, and then I describe and defend a series of practical techniques for investigating these representations and developing explanations on their basis. The resulting account provides a groundwork for future theorizing about language models and their successors.