We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After discretizations both inputs and outputs are high-dimensional. We aim to approximate not only the operators with improved accuracy but also their derivatives (Jacobians) with respect to the input function-valued parameter to empower derivative-based algorithms in many applications, e.g., Bayesian inverse problems, optimization under parameter uncertainty, and optimal experimental design. The major difficulties include the computational cost of generating derivative training data and the high dimensionality of the problem leading to large training cost. To address these challenges, we exploit the intrinsic low-dimensionality of the derivatives and develop algorithms for compressing derivative information and efficiently imposing it in neural operator training yielding derivative-informed neural operators. We demonstrate that these advances can significantly reduce the costs of both data generation and training for large classes of problems (e.g., nonlinear steady state parametric PDE maps), making the costs marginal or comparable to the costs without using derivatives, and in particular independent of the discretization dimension of the input and output functions. Moreover, we show that the proposed DINO achieves significantly higher accuracy than neural operators trained without derivative information, for both function approximation and derivative approximation (e.g., Gauss-Newton Hessian), especially when the training data are limited.

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose procedure for rigorously evaluating whether newly proposed models indeed successfully learn from data. We show that such a procedure cannot exist. For PAC binary classification, uniform and universal online learning, and exact learning through teacher-learner interactions, learnability is in general undecidable, both in the sense of independence of the axioms in a formal system and in the sense of uncomputability. Our proofs proceed via computable constructions that encode the consistency problem for formal systems and the halting problem for Turing machines into whether certain function classes are trivial/finite or highly complex, which we then relate to whether these classes are learnable via established characterizations of learnability through complexity measures. Our work shows that undecidability appears in the theoretical foundations of artificial intelligence: There is no one-size-fits-all algorithm for deciding whether a machine learning model can be successful. We cannot in general automatize the process of assessing new learning models.

Compared to Markov Decision Processes (MDPs), learning in Partially Observable Markov Decision Processes (POMDPs) can be significantly harder due to the difficulty of interpreting observations. In this paper, we consider episodic learning problems in POMDPs with unknown transition and observation models. We consider the Posterior Sampling-based Reinforcement Learning (PSRL) algorithm for POMDPs and show that its Bayesian regret scales as the square root of the number of episodes. In general, the regret scales exponentially with the horizon length $H$, and we show that this is inevitable by providing a lower bound. However, under the condition that the POMDP is undercomplete and weakly revealing, we establish a polynomial Bayesian regret bound that improves the regret bound by a factor of $\Omega(H^2\sqrt{SA})$ over the recent result by arXiv:2204.08967.

The Mixture of Experts (MoE) has emerged as a highly successful technique in deep learning, based on the principle of divide-and-conquer to maximize model capacity without significant additional computational cost. Even in the era of large-scale language models (LLMs), MoE continues to play a crucial role, as some researchers have indicated that GPT-4 adopts the MoE structure to ensure diverse inference results. However, MoE is susceptible to performance degeneracy, particularly evident in the issues of imbalance and homogeneous representation among experts. While previous studies have extensively addressed the problem of imbalance, the challenge of homogeneous representation remains unresolved. In this study, we shed light on the homogeneous representation problem, wherein experts in the MoE fail to specialize and lack diversity, leading to frustratingly high similarities in their representations (up to 99% in a well-performed MoE model). This problem restricts the expressive power of the MoE and, we argue, contradicts its original intention. To tackle this issue, we propose a straightforward yet highly effective solution: OMoE, an orthogonal expert optimizer. Additionally, we introduce an alternating training strategy that encourages each expert to update in a direction orthogonal to the subspace spanned by other experts. Our algorithm facilitates MoE training in two key ways: firstly, it explicitly enhances representation diversity, and secondly, it implicitly fosters interaction between experts during orthogonal weights computation. Through extensive experiments, we demonstrate that our proposed optimization algorithm significantly improves the performance of fine-tuning the MoE model on the GLUE benchmark, SuperGLUE benchmark, question-answering task, and name entity recognition tasks.

While machine learning (ML) has made significant contributions to the biopharmaceutical field, its applications are still in the early stages in terms of providing direct support for quality-by-design based development and manufacturing of biopharmaceuticals, hindering the enormous potential for bioprocesses automation from their development to manufacturing. However, the adoption of ML-based models instead of conventional multivariate data analysis methods is significantly increasing due to the accumulation of large-scale production data. This trend is primarily driven by the real-time monitoring of process variables and quality attributes of biopharmaceutical products through the implementation of advanced process analytical technologies. Given the complexity and multidimensionality of a bioproduct design, bioprocess development, and product manufacturing data, ML-based approaches are increasingly being employed to achieve accurate, flexible, and high-performing predictive models to address the problems of analytics, monitoring, and control within the biopharma field. This paper aims to provide a comprehensive review of the current applications of ML solutions in a bioproduct design, monitoring, control, and optimisation of upstream, downstream, and product formulation processes. Finally, this paper thoroughly discusses the main challenges related to the bioprocesses themselves, process data, and the use of machine learning models in biopharmaceutical process development and manufacturing. Moreover, it offers further insights into the adoption of innovative machine learning methods and novel trends in the development of new digital biopharma solutions.

In the challenging field of introductory programming, high enrollments and failure rates drive us to explore tools and systems to enhance student outcomes, especially automated tools that scale to large cohorts. This paper presents and evaluates the dcc --help tool, an integration of a Large Language Model (LLM) into the Debugging C Compiler (DCC) to generate unique, novice-focused explanations tailored to each error. dcc --help prompts an LLM with contextual information of compile- and run-time error occurrences, including the source code, error location and standard compiler error message. The LLM is instructed to generate novice-focused, actionable error explanations and guidance, designed to help students understand and resolve problems without providing solutions. dcc --help was deployed to our CS1 and CS2 courses, with 2,565 students using the tool over 64,000 times in ten weeks. We analysed a subset of these error/explanation pairs to evaluate their properties, including conceptual correctness, relevancy, and overall quality. We found that the LLM-generated explanations were conceptually accurate in 90% of compile-time and 75% of run-time cases, but often disregarded the instruction not to provide solutions in code. Our findings, observations and reflections following deployment indicate that dcc-help provides novel opportunities for scaffolding students' introduction to programming.

The principal goal of data science is to derive meaningful information from data. To do this, data scientists develop a space of analytic possibilities and from it reach their information goals by using their knowledge of the domain, the available data, the operations that can be performed on those data, the algorithms/models that are fed the data, and how all of these facets interweave. In this work, we take the first steps towards automating a key aspect of the data science pipeline: data analysis. We present an extensible taxonomy of data analytic operations that scopes across domains and data, as well as a method for codifying domain-specific knowledge that links this analytics taxonomy to actual data. We validate the functionality of our analytics taxonomy by implementing a system that leverages it, alongside domain labelings for 8 distinct domains, to automatically generate a space of answerable questions and associated analytic plans. In this way, we produce information spaces over data that enable complex analyses and search over this data and pave the way for fully automated data analysis.

Student modeling is central to many educational technologies as it enables the prediction of future learning outcomes and targeted instructional strategies. However, open-ended learning environments pose challenges for accurately modeling students due to the diverse behaviors exhibited by students and the absence of a well-defined set of learning skills. To approach these challenges, we explore the application of Large Language Models (LLMs) for in-context student modeling in open-ended learning environments. We introduce a novel framework, LLM-SS, that leverages LLMs for synthesizing student's behavior. More concretely, given a particular student's solving attempt on a reference task as observation, the goal is to synthesize the student's attempt on a target task. Our framework can be combined with different LLMs; moreover, we fine-tune LLMs using domain-specific expertise to boost their understanding of domain background and student behaviors. We evaluate several concrete methods based on LLM-SS using the StudentSyn benchmark, an existing student's attempt synthesis benchmark in visual programming. Experimental results show a significant improvement compared to baseline methods included in the StudentSyn benchmark. Furthermore, our method using the fine-tuned Llama2-70B model improves noticeably compared to using the base model and becomes on par with using the state-of-the-art GPT-4 model.

Reinforcement learning (RL) has shown an outstanding capability for solving complex computational problems. However, most RL algorithms lack an explicit method that would allow learning from contextual information. Humans use context to identify patterns and relations among elements in the environment, along with how to avoid making wrong actions. On the other hand, what may seem like an obviously wrong decision from a human perspective could take hundreds of steps for an RL agent to learn to avoid. This paper proposes a framework for discrete environments called Iota explicit context representation (IECR). The framework involves representing each state using contextual key frames (CKFs), which can then be used to extract a function that represents the affordances of the state; in addition, two loss functions are introduced with respect to the affordances of the state. The novelty of the IECR framework lies in its capacity to extract contextual information from the environment and learn from the CKFs' representation. We validate the framework by developing four new algorithms that learn using context: Iota deep Q-network (IDQN), Iota double deep Q-network (IDDQN), Iota dueling deep Q-network (IDuDQN), and Iota dueling double deep Q-network (IDDDQN). Furthermore, we evaluate the framework and the new algorithms in five discrete environments. We show that all the algorithms, which use contextual information, converge in around 40,000 training steps of the neural networks, significantly outperforming their state-of-the-art equivalents.

Most legal text in the Indian judiciary is written in complex English due to historical reasons. However, only about 10% of the Indian population is comfortable in reading English. Hence legal text needs to be made available in various Indian languages, possibly by translating the available legal text from English. Though there has been a lot of research on translation to and between Indian languages, to our knowledge, there has not been much prior work on such translation in the legal domain. In this work, we construct the first high-quality legal parallel corpus containing aligned text units in English and nine Indian languages, that includes several low-resource languages. We also benchmark the performance of a wide variety of Machine Translation (MT) systems over this corpus, including commercial MT systems, open-source MT systems and Large Language Models. Through a comprehensive survey by Law practitioners, we check how satisfied they are with the translations by some of these MT systems, and how well automatic MT evaluation metrics agree with the opinions of Law practitioners.