Quantum many-body systems are of great interest for many research areas, including physics, biology and chemistry. However, their simulation is extremely challenging, due to the exponential growth of the Hilbert space with the system size, making it exceedingly difficult to parameterize the wave functions of large systems by using exact methods. Neural networks and machine learning in general are a way to face this challenge. For instance, methods like Tensor networks and Neural Quantum States are being investigated as promising tools to obtain the wave function of a quantum mechanical system. In this tutorial, we focus on a particularly promising class of deep learning algorithms. We explain how to construct a Physics-Informed Neural Network (PINN) able to solve the Schr\"odinger equation for a given potential, by finding its eigenvalues and eigenfunctions. This technique is unsupervised, and utilizes a novel computational method in a manner that is barely explored. PINNs are a deep learning method that exploits Automatic Differentiation to solve Integro-Differential Equations in a mesh-free way. We show how to find both the ground and the excited states. The method discovers the states progressively by starting from the ground state. We explain how to introduce inductive biases in the loss to exploit further knowledge of the physical system. Such additional constraints allow for a faster and more accurate convergence. This technique can then be enhanced by a smart choice of collocation points in order to take advantage of the mesh-free nature of the PINN. The methods are made explicit by applying them to the infinite potential well and the particle in a ring, a challenging problem to be learned by an Artificial Intelligence agent due to the presence of complex-valued eigenfunctions and degenerate states.

Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual payoffs, it is however possible that aiming for highest levels of cooperation might be detrimental for social welfare -- the later broadly defined as the total population payoff, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparatively analysing the social welfare and cooperation levels obtained from stochastic evolutionary models of two well-established mechanisms of prosocial behaviour, namely, peer and institutional incentives, we demonstrate exactly that. We show that the objectives of maximising cooperation levels and the objectives of maximising social welfare are often misaligned. We argue for the need of adopting social welfare as the main optimisation objective when designing and implementing evolutionary mechanisms for social and collective goods.

Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) have demonstrated impressive language/vision reasoning abilities, igniting the recent trend of building agents for targeted applications such as shopping assistants or AI software engineers. Recently, many data science benchmarks have been proposed to investigate their performance in the data science domain. However, existing data science benchmarks still fall short when compared to real-world data science applications due to their simplified settings. To bridge this gap, we introduce DSBench, a comprehensive benchmark designed to evaluate data science agents with realistic tasks. This benchmark includes 466 data analysis tasks and 74 data modeling tasks, sourced from Eloquence and Kaggle competitions. DSBench offers a realistic setting by encompassing long contexts, multimodal task backgrounds, reasoning with large data files and multi-table structures, and performing end-to-end data modeling tasks. Our evaluation of state-of-the-art LLMs, LVLMs, and agents shows that they struggle with most tasks, with the best agent solving only 34.12% of data analysis tasks and achieving a 34.74% Relative Performance Gap (RPG). These findings underscore the need for further advancements in developing more practical, intelligent, and autonomous data science agents.

The rapid advancement of artificial intelligence systems has brought the challenge of AI alignment to the forefront of research, particularly in complex decision-making and task execution. As these systems surpass human-level performance in sophisticated problems, ensuring their alignment with human values, intentions, and ethical guidelines becomes crucial. Building on previous work in explanation generation for human-agent alignment, we address the more complex dynamics of multi-agent systems and human-AI teams. This paper introduces a novel approach to model alignment through weak-to-strong generalization in the context of language models. We present a framework where a strong model facilitates the improvement of a weaker model, bridging the gap between explanation generation and model alignment. Our method, formalized as a facilitation function, allows for the transfer of capabilities from advanced models to less capable ones without direct access to extensive training data. Our results suggest that this facilitation-based approach not only enhances model performance but also provides insights into the nature of model alignment and the potential for scalable oversight of AI systems.

Finding the optimal learning rate for language model pretraining is a challenging task. This is not only because there is a complicated correlation between learning rate, batch size, number of training tokens, model size, and other hyperparameters but also because it is prohibitively expensive to perform a hyperparameter search for large language models with Billions or Trillions of parameters. Recent studies propose using small proxy models and small corpus to perform hyperparameter searches and transposing the optimal parameters to large models and large corpus. While the zero-shot transferability is theoretically and empirically proven for model size related hyperparameters, like depth and width, the zero-shot transfer from small corpus to large corpus is underexplored. In this paper, we study the correlation between optimal learning rate, batch size, and number of training tokens for the recently proposed WSD scheduler. After thousands of small experiments, we found a power-law relationship between variables and demonstrated its transferability across model sizes. Based on the observation, we propose a new learning rate scheduler, Power scheduler, that is agnostic about the number of training tokens and batch size. The experiment shows that combining the Power scheduler with Maximum Update Parameterization (muP) can consistently achieve impressive performance with one set of hyperparameters regardless of the number of training tokens, batch size, model size, and even model architecture. Our 3B dense and MoE models trained with the Power scheduler achieve comparable performance as state-of-the-art small language models. We open-source these pretrained models at https://ibm.biz/BdKhLa.

Continual and interactive robot learning is a challenging problem as the robot is present with human users who expect the robot to learn novel skills to solve novel tasks perpetually with sample efficiency. In this work we present a framework for robots to query and learn visuo-motor robot skills and task relevant information via natural language dialog interactions with human users. Previous approaches either focus on improving the performance of instruction following agents, or passively learn novel skills or concepts. Instead, we used dialog combined with a language-skill grounding embedding to query or confirm skills and/or tasks requested by a user. To achieve this goal, we developed and integrated three different components for our agent. Firstly, we propose a novel visual-motor control policy ACT with Low Rank Adaptation (ACT-LoRA), which enables the existing SoTA ACT model to perform few-shot continual learning. Secondly, we develop an alignment model that projects demonstrations across skill embodiments into a shared embedding allowing us to know when to ask questions and/or demonstrations from users. Finally, we integrated an existing LLM to interact with a human user to perform grounded interactive continual skill learning to solve a task. Our ACT-LoRA model learns novel fine-tuned skills with a 100% accuracy when trained with only five demonstrations for a novel skill while still maintaining a 74.75% accuracy on pre-trained skills in the RLBench dataset where other models fall significantly short. We also performed a human-subjects study with 8 subjects to demonstrate the continual learning capabilities of our combined framework. We achieve a success rate of 75% in the task of sandwich making with the real robot learning from participant data demonstrating that robots can learn novel skills or task knowledge from dialogue with non-expert users using our approach.

We study a continuous-time approximation of the stochastic gradient descent process for minimizing the expected loss in learning problems. The main results establish general sufficient conditions for the convergence, extending the results of Chatterjee (2022) established for (nonstochastic) gradient descent. We show how the main result can be applied to the case of overparametrized linear neural network training.

In recent years, federated learning has garnered significant attention as an efficient and privacy-preserving distributed learning paradigm. In the Euclidean setting, Federated Averaging (FedAvg) and its variants are a class of efficient algorithms for expected (empirical) risk minimization. This paper develops and analyzes a Riemannian Federated Averaging Gradient Stream (RFedAGS) algorithm, which is a generalization of FedAvg, to problems defined on a Riemannian manifold. Under standard assumptions, the convergence rate of RFedAGS with fixed step sizes is proven to be sublinear for an approximate stationary solution. If decaying step sizes are used, the global convergence is established. Furthermore, assuming that the objective obeys the Riemannian Polyak-{\L}ojasiewicz property, the optimal gaps generated by RFedAGS with fixed step size are linearly decreasing up to a tiny upper bound, meanwhile, if decaying step sizes are used, then the gaps sublinearly vanish. Numerical simulations conducted on synthetic and real-world data demonstrate the performance of the proposed RFedAGS.

Modern listwise recommendation systems need to consider both long-term user perceptions and short-term interest shifts. Reinforcement learning can be applied on recommendation to study such a problem but is also subject to large search space, sparse user feedback and long interactive latency. Motivated by recent progress in hierarchical reinforcement learning, we propose a novel framework called mccHRL to provide different levels of temporal abstraction on listwise recommendation. Within the hierarchical framework, the high-level agent studies the evolution of user perception, while the low-level agent produces the item selection policy by modeling the process as a sequential decision-making problem. We argue that such framework has a well-defined decomposition of the outra-session context and the intra-session context, which are encoded by the high-level and low-level agents, respectively. To verify this argument, we implement both a simulator-based environment and an industrial dataset-based experiment. Results observe significant performance improvement by our method, compared with several well-known baselines. Data and codes have been made public.

Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow references to Wirtinger calculus. Unfortunately, the equivalence $\mathbb{C}^d \cong \mathbb{R}^{2d}$ becomes insufficient as soon as we need to derive custom gradient rules, e.g., to avoid differentiating "through" expensive linear algebra functions or differential equation simulators. To combat such a lack of documentation, this article surveys forward- and reverse-mode automatic differentiation with complex numbers, covering topics such as Wirtinger derivatives, a modified chain rule, and different gradient conventions while explicitly avoiding holomorphicity and the Cauchy--Riemann equations (which would be far too restrictive). To be precise, we will derive, explain, and implement a complex version of Jacobian-vector and vector-Jacobian products almost entirely with linear algebra without relying on complex analysis or differential geometry. This tutorial is a call to action, for users and developers alike, to take complex values seriously when implementing custom gradient propagation rules -- the manuscript explains how.