Entropy, Thermodynamics and the Geometrization of the Language Model

In this paper, we discuss how pure mathematics and theoretical physics can be applied to the study of language models. Using set theory and analysis, we formulate mathematically rigorous definitions of language models, and introduce the concept of the moduli space of distributions for a language model. We formulate a generalized distributional hypothesis using functional analysis and topology. We define the entropy function associated with a language model and show how it allows us to understand many interesting phenomena in languages. We argue that the zero points of the entropy function and the points where the entropy is close to 0 are the key obstacles for an LLM to approximate an intelligent language model, which explains why good LLMs need billions of parameters. Using the entropy function, we formulate a conjecture about AGI. Then, we show how thermodynamics gives us an immediate interpretation to language models. In particular we will define the concepts of partition function, internal energy and free energy for a language model, which offer insights into how language models work. Based on these results, we introduce a general concept of the geometrization of language models and define what is called the Boltzmann manifold. While the current LLMs are the special cases of the Boltzmann manifold.

Feature-Fused SSD: Fast Detection for Small Objects

Small objects detection is a challenging task in computer vision due to its limited resolution and information. In order to solve this problem, the majority of existing methods sacrifice speed for improvement in accuracy. In this paper, we aim to detect small objects at a fast speed, using the best object detector Single Shot Multibox Detector (SSD) with respect to accuracy-vs-speed trade-off as base architecture. We propose a multi-level feature fusion method for introducing contextual information in SSD, in order to improve the accuracy for small objects. In detailed fusion operation, we design two feature fusion modules, concatenation module and element-sum module, different in the way of adding contextual information. Experimental results show that these two fusion modules obtain higher mAP on PASCALVOC2007 than baseline SSD by 1.6 and 1.7 points respectively, especially with 2-3 points improvement on some smallobjects categories. The testing speed of them is 43 and 40 FPS respectively, superior to the state of the art Deconvolutional single shot detector (DSSD) by 29.4 and 26.4 FPS. Keywords: small object detection, feature fusion, real-time, single shot multi-box detector