Generative Artificial Intelligence (AI) is revolutionizing educational technology by enabling highly personalized and adaptive learning environments within Intelligent Tutoring Systems (ITS). This report delves into the integration of Generative AI, particularly large language models (LLMs) like GPT-4, into ITS to enhance personalized education through dynamic content generation, real-time feedback, and adaptive learning pathways. We explore key applications such as automated question generation, customized feedback mechanisms, and interactive dialogue systems that respond to individual learner needs. The report also addresses significant challenges, including ensuring pedagogical accuracy, mitigating inherent biases in AI models, and maintaining learner engagement. Future directions highlight the potential advancements in multimodal AI integration, emotional intelligence in tutoring systems, and the ethical implications of AI-driven education. By synthesizing current research and practical implementations, this report underscores the transformative potential of Generative AI in creating more effective, equitable, and engaging educational experiences.

Accurate mathematical reasoning with Large Language Models (LLMs) is crucial in revolutionizing domains that heavily rely on such reasoning. However, LLMs often encounter difficulties in certain aspects of mathematical reasoning, leading to flawed reasoning and erroneous results. To mitigate these issues, we introduce a novel mechanism, the Chain of Self-Correction (CoSC), specifically designed to embed self-correction as an inherent ability in LLMs, enabling them to validate and rectify their own results. The CoSC mechanism operates through a sequence of self-correction stages. In each stage, the LLMs generate a program to address a given problem, execute this program using program-based tools to obtain an output, subsequently verify this output. Based on the verification, the LLMs either proceed to the next correction stage or finalize the answer. This iterative self-correction process allows the LLMs to refine their reasoning steps and improve the accuracy of their mathematical reasoning. To enable the CoSC mechanism at a low cost, we employ a two-phase finetuning approach. In the first phase, the LLMs are trained with a relatively small volume of seeding data generated from GPT-4, establishing an initial CoSC capability. In the second phase, the CoSC capability is further enhanced by training with a larger volume of self-generated data using the trained model in the first phase, without relying on the paid GPT-4. Our comprehensive experiments demonstrate that CoSC significantly improves performance on traditional mathematical datasets among existing open-source LLMs. Notably, our CoSC-Code-34B model achieved a 53.5% score on MATH, the most challenging mathematical reasoning dataset in the public domain, surpassing the performance of well-established models such as ChatGPT, GPT-4, and even multi-modal LLMs like GPT-4V, Gemini-1.0 Pro, and Gemini-1.0 Ultra.

This study proposes a novel artificial intelligence (AI) driven flight computer, integrating an online free-retraining-prediction model, a swarm control, and an obstacle avoidance strategy, to track dynamic targets using a distributed drone swarm for military applications. To enable dynamic target tracking the swarm requires a trajectory prediction capability to achieve intercept allowing for the tracking of rapid maneuvers and movements while maintaining efficient path planning. Traditional predicative methods such as curve fitting or Long ShortTerm Memory (LSTM) have low robustness and struggle with dynamic target tracking in the short term due to slow convergence of single agent-based trajectory prediction and often require extensive offline training or tuning to be effective. Consequently, this paper introduces a novel robust adaptive bidirectional fuzzy brain emotional learning prediction (BFBEL-P) methodology to address these challenges. The controller integrates a fuzzy interface, a neural network enabling rapid adaption, predictive capability and multi-agent solving enabling multiple solutions to be aggregated to achieve rapid convergence times and high accuracy in both the short and long term. This was verified through the use of numerical simulations seeing complex trajectory being predicted and tracked by a swarm of drones. These simulations show improved adaptability and accuracy to state of the art methods in the short term and strong results over long time domains, enabling accurate swarm target tracking and predictive capability.

The term "K-12" stands for "Kindergarten through 12th grade" and represents the full range of primary and secondary education. Within this system, a strong emphasis has been placed on STEM (Science, Technology, Engineering, and Mathematics) education as a means to prepare students for a technology-driven future. STEM education at the K-12 level focuses on building foundational knowledge in scientific inquiry, technological literacy, engineering principles, and mathematical reasoning [10, 29, 64]. The K-12 STEM education emphasizes interdisciplinary learning, where students apply concepts from multiple domains to solve real-world challenges, such as integrating mathematics with science to tackle engineering problems [29]. The importance of K-12 STEM education lies in its ability to prepare students for a rapidly evolving, technology-driven world by fostering critical thinking, creativity, and problem-solving skills from an early age [10]. Students who engage in well-structured STEM curricula are more likely to pursue further education and careers in high-demand fields like information technology and engineering which are essential for technological innovation. Additionally, K-12 STEM education equips students with competencies such as analytical thinking, which prepare them for a wide range of career paths while enabling them to tackle complex problems [64]. Recognizing the importance of STEM education at the K-12 level, it is essential to deliver K-12 STEM education at scale to ensure equitable access to individual students.

Large language models (LLMs) require alignment, such as instruction-tuning or reinforcement learning from human feedback, to effectively and safely follow user instructions. This process necessitates training aligned versions for every model size in each model family, resulting in significant computational overhead. In this work, we propose nudging, a simple, plug-and-play, and training-free algorithm that aligns any base model at inference time using a small aligned model. Nudging is motivated by recent findings that alignment primarily alters the model's behavior on a small subset of stylistic tokens, such as "Sure" or "Thank". We find that base models are significantly more uncertain when generating these tokens. Leveraging this observation, nudging employs a small aligned model to generate nudging tokens to steer the large base model's output toward desired directions when the base model's uncertainty is high. We evaluate the effectiveness of nudging across 3 model families and 13 tasks, covering reasoning, general knowledge, instruction following, and safety benchmarks. Without any additional training, nudging a large base model with a 7x - 14x smaller aligned model achieves zero-shot performance comparable to, and sometimes surpassing, that of large aligned models. For example, nudging OLMo-7b with OLMo-1b-instruct, affecting less than 9% of tokens, achieves a 10% absolute improvement on GSM8K over OLMo-7b-instruct. Unlike prior inference-time tuning methods, nudging enables off-the-shelf collaboration between model families. For instance, nudging Gemma-2-27b with Llama-2-7b-chat outperforms Llama-2-70b-chat on various tasks. Overall, this work introduces a simple yet powerful approach to token-level model collaboration, offering a modular solution to LLM alignment. Our project website: https://fywalter.github.io/nudging/ .

Empirical, benchmark-driven testing is a fundamental paradigm in the current RL community. While using off-the-shelf benchmarks in reinforcement learning (RL) research is a common practice, this choice is rarely discussed. Benchmark choices are often done based on intuitive ideas like "legged robots" or "visual observations". In this paper, we argue that benchmarking in RL needs to be treated as a scientific discipline itself. To illustrate our point, we present a case study on different variants of the Hopper environment to show that the selection of standard benchmarking suites can drastically change how we judge performance of algorithms. The field does not have a cohesive notion of what the different Hopper environments are representative - they do not even seem to be representative of each other. Our experimental results suggests a larger issue in the deep RL literature: benchmark choices are neither commonly justified, nor does there exist a language that could be used to justify the selection of certain environments. This paper concludes with a discussion of the requirements for proper discussion and evaluations of benchmarks and recommends steps to start a dialogue towards this goal.

Demographics and cultural background of annotators influence the labels they assign in text annotation -- for instance, an elderly woman might find it offensive to read a message addressed to a "bro", but a male teenager might find it appropriate. It is therefore important to acknowledge label variations to not under-represent members of a society. Two research directions developed out of this observation in the context of using large language models (LLM) for data annotations, namely (1) studying biases and inherent knowledge of LLMs and (2) injecting diversity in the output by manipulating the prompt with demographic information. We combine these two strands of research and ask the question to which demographics an LLM resorts to when no demographics is given. To answer this question, we evaluate which attributes of human annotators LLMs inherently mimic. Furthermore, we compare non-demographic conditioned prompts and placebo-conditioned prompts (e.g., "you are an annotator who lives in house number 5") to demographics-conditioned prompts ("You are a 45 year old man and an expert on politeness annotation. How do you rate {instance}"). We study these questions for politeness and offensiveness annotations on the POPQUORN data set, a corpus created in a controlled manner to investigate human label variations based on demographics which has not been used for LLM-based analyses so far. We observe notable influences related to gender, race, and age in demographic prompting, which contrasts with previous studies that found no such effects.

The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design choices which are hard to justify in principle and whose effectiveness often goes unexplained. Research debt is increasing and many papers are found not to be reproducible. This thesis is a survey that covers some recent work attempting to study machine learning categorically. Category theory is a branch of abstract mathematics that has found successful applications in many fields, both inside and outside mathematics. Acting as a lingua franca of mathematics and science, category theory might be able to give a unifying structure to the field of machine learning. This could solve some of the aforementioned problems. In this work, we mainly focus on the application of category theory to deep learning. Namely, we discuss the use of categorical optics to model gradient-based learning, the use of categorical algebras and integral transforms to link classical computer science to neural networks, the use of functors to link different layers of abstraction and preserve structure, and, finally, the use of string diagrams to provide detailed representations of neural network architectures.

Software engineers mainly write code by editing existing programs. In contrast, large language models (LLMs) autoregressively synthesize programs in a single pass. One explanation for this is the scarcity of open-sourced edit data. While high-quality instruction data for code synthesis is already scarce, high-quality edit data is even scarcer. To fill this gap, we develop a synthetic data generation algorithm called LintSeq. This algorithm refactors existing code into a sequence of code edits by using a linter to procedurally sample across the error-free insertions that can be used to sequentially write programs. It outputs edit sequences as text strings consisting of consecutive program diffs. To test LintSeq, we use it to refactor a dataset of instruction + program pairs into instruction + program-diff-sequence tuples. Then, we instruction finetune a series of smaller LLMs ranging from 2.6B to 14B parameters on both the re-factored and original versions of this dataset, comparing zero-shot performance on code synthesis benchmarks. We show that during repeated sampling, edit sequence finetuned models produce more diverse programs than baselines. This results in better inference-time scaling for benchmark coverage as a function of samples, i.e. the fraction of problems "pass@k" solved by any attempt given "k" tries. For example, on HumanEval pass@50, small LLMs finetuned on synthetic edit sequences are competitive with GPT-4 and outperform models finetuned on the baseline dataset by +20% (+/-3%) in absolute score. Finally, we also pretrain our own tiny LMs for code understanding. We show that finetuning tiny models on synthetic code edits results in state-of-the-art code synthesis for the on-device model class. Our 150M parameter edit sequence LM matches or outperforms code models with twice as many parameters, both with and without repeated sampling, including Codex and AlphaCode.

Deep learning methods - consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays key tools to solve data driven supervised learning problems. Despite the great success of SGD methods in the training of DNNs, it remains a fundamental open problem of research to explain the success and the limitations of such methods in rigorous theoretical terms. In particular, even in the standard setup of data driven supervised learning problems, it remained an open research problem to prove (or disprove) that SGD methods converge in the training of DNNs with the popular rectified linear unit (ReLU) activation function with high probability to global minimizers in the optimization landscape. In this work we answer this question negatively. Specifically, in this work we prove for a large class of SGD methods that the considered optimizer does with high probability not converge to global minimizers of the optimization problem. It turns out that the probability to not converge to a global minimizer converges at least exponentially quickly to one as the width of the first hidden layer of the ANN and the depth of the ANN, respectively, increase. The general non-convergence results of this work do not only apply to the plain vanilla standard SGD method but also to a large class of accelerated and adaptive SGD methods such as the momentum SGD, the Nesterov accelerated SGD, the Adagrad, the RMSProp, the Adam, the Adamax, the AMSGrad, and the Nadam optimizers.