We develop a solvable model of neural scaling laws beyond the kernel limit. Theoretical analysis of this model shows how performance scales with model size, training time, and the total amount of available data. We identify three scaling regimes corresponding to varying task difficulties: hard, easy, and super easy tasks. For easy and super-easy target functions, which lie in the reproducing kernel Hilbert space (RKHS) defined by the initial infinite-width Neural Tangent Kernel (NTK), the scaling exponents remain unchanged between feature learning and kernel regime models. For hard tasks, defined as those outside the RKHS of the initial NTK, we demonstrate both analytically and empirically that feature learning can improve scaling with training time and compute, nearly doubling the exponent for hard tasks. This leads to a different compute optimal strategy to scale parameters and training time in the feature learning regime. We support our finding that feature learning improves the scaling law for hard tasks but not for easy and super-easy tasks with experiments of nonlinear MLPs fitting functions with power-law Fourier spectra on the circle and CNNs learning vision tasks. Deep learning models tend to improve in performance with model size, training time and total available data. The dependence of performance on the available statistical and computational resources are often regular and well-captured by a power-law (Hestness et al., 2017; Kaplan et al., 2020).

There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning approaches, for a given method it may be non-trivial to decide whether the obtained fairness-performance curve of the method is optimal, i.e., whether it is close to the true Pareto front for these quantities for the underlying data distribution. In this paper we propose a new method to compute the optimal Pareto front, which does not require the training of complex representation models. We show that optimal fair representations possess several useful structural properties, and that these properties enable a reduction of the computation of the Pareto Front to a compact discrete problem. We then also show that these compact approximating problems can be efficiently solved via off-the shelf concave-convex programming methods. Since our approach is independent of the specific model of representations, it may be used as the benchmark to which representation learning algorithms may be compared. We experimentally evaluate the approach on a number of real world benchmark datasets.

The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into how to build better algorithms to solve decision problems. Therefore, we focus on presenting the connection between the Banach fixed point theorem and the convergence of reinforcement learning algorithms, and we illustrate how the insights gained from this can practically help in designing more efficient algorithms. Before doing so, however, we first introduce relevant concepts such as metric spaces, normed spaces and Banach spaces for better understanding, before expressing the entire reinforcement learning problem in terms of Markov decision processes. This allows us to properly introduce the Banach contraction principle in a language suitable for reinforcement learning, and to write the Bellman equations in terms of operators on Banach spaces to show why reinforcement learning algorithms converge. Finally, we show how the insights gained from the mathematical study of convergence are helpful in reasoning about the best ways to make reinforcement learning algorithms more efficient.

Signal Processing (SP) and Machine Learning (ML) rely on good math and coding knowledge, in particular, linear algebra, probability, and complex numbers. A good grasp of these relies on scalar algebra learned in middle school. The ability to understand and use scalar algebra well, in turn, relies on a good foundation in basic arithmetic. Because of various systemic barriers, many students are not able to build a strong foundation in arithmetic in elementary school. This leads them to struggle with algebra and everything after that. Since math learning is cumulative, the gap between those without a strong early foundation and everyone else keeps increasing over the school years and becomes difficult to fill in college. In this article we discuss how SP faculty and graduate students can play an important role in starting, and participating in, university-run (or other) out-of-school math support programs to supplement students' learning. Two example programs run by the authors (CyMath at ISU and Ab7G at Purdue) are briefly described. The second goal of this article is to use our perspective as SP, and engineering, educators who have seen the long-term impact of elementary school math teaching policies, to provide some simple almost zero cost suggestions that elementary schools could adopt to improve math learning: (i) more math practice in school, (ii) send small amounts of homework (individual work is critical in math), and (iii) parent awareness (math resources, need for early math foundation, clear in-school test information and sharing of feedback from the tests). In summary, good early math support (in school and through out-of-school programs) can help make SP and ML more accessible.

Context-aware Human Activity Recognition (CHAR) is challenging due to the need to recognize the user's current activity from signals that vary significantly with contextual factors such as phone placements and the varied styles with which different users perform the same activity. In this paper, we argue that context-aware activity visit patterns in realistic in-the-wild data can equivocally be considered as a general graph representation learning task. We posit that exploiting underlying graphical patterns in CHAR data can improve CHAR task performance and representation learning. Building on the intuition that certain activities are frequently performed with the phone placed in certain positions, we focus on the context-aware human activity problem of recognizing the tuple. We demonstrate that CHAR data has an underlying graph structure that can be viewed as a heterogenous hypergraph that has multiple types of nodes and hyperedges (an edge connecting more than two nodes). Subsequently, learning representations becomes a graph node representation learning problem. After task transformation, we further propose a novel Heterogeneous HyperGraph Neural Network architecture for Context-aware Human Activity Recognition (HHGNN-CHAR), with three types of heterogeneous nodes (user, phone placement, and activity). Connections between all types of nodes are represented by hyperedges. Rigorous evaluation demonstrated that on an unscripted, in-the-wild CHAR dataset, our proposed framework significantly outperforms state-of-the-art (SOTA) baselines including CHAR models that do not exploit graphs, and GNN variants that do not incorporate heterogeneous nodes or hyperedges with overall improvements 14.04% on Matthews Correlation Coefficient (MCC) and 7.01% on Macro F1 scores.

Recent advances in automated essay scoring (AES) have shifted towards evaluating multiple traits to provide enriched feedback. Like typical AES systems, multi-trait AES employs the quadratic weighted kappa (QWK) to measure agreement with human raters, aligning closely with the rating schema; however, its non-differentiable nature prevents its direct use in neural network training. In this paper, we propose Scoring-aware Multi-reward Reinforcement Learning (SaMRL), which integrates actual evaluation schemes into the training process by designing QWK-based rewards with a mean-squared error penalty for multi-trait AES. Existing reinforcement learning (RL) applications in AES are limited to classification models despite associated performance degradation, as RL requires probability distributions; instead, we adopt an autoregressive score generation framework to leverage token generation probabilities for robust multi-trait score predictions. Empirical analyses demonstrate that SaMRL facilitates model training, notably enhancing scoring of previously inferior prompts.

Reinforcement Learning (RL) has the potential to enable extreme off-road mobility by circumventing complex kinodynamic modeling, planning, and control by simulated end-to-end trial-and-error learning experiences. However, most RL methods are sample-inefficient when training in a large amount of manually designed simulation environments and struggle at generalizing to the real world. To address these issues, we introduce Verti-Selector (VS), an automatic curriculum learning framework designed to enhance learning efficiency and generalization by selectively sampling training terrain. VS prioritizes vertically challenging terrain with higher Temporal Difference (TD) errors when revisited, thereby allowing robots to learn at the edge of their evolving capabilities. By dynamically adjusting the sampling focus, VS significantly boosts sample efficiency and generalization within the VW-Chrono simulator built on the Chrono multi-physics engine. Furthermore, we provide simulation and physical results using VS on a Verti-4-Wheeler platform. These results demonstrate that VS can achieve 23.08% improvement in terms of success rate by efficiently sampling during training and robustly generalizing to the real world.

ChatGPT has been used in several educational contexts,including learning, teaching and research. It also has potential to conduct the systematic literature review (SLR). However, there are limited empirical studies on how to use ChatGPT in conducting a SLR. Based on a SLR published,this study used ChatGPT to conduct a SLR of the same 33 papers in a design-based approach, to see what the differences are by comparing the reviews' results,and to answer: To what extent can ChatGPT conduct SLR? What strategies can human researchers utilize to structure prompts for ChatGPT that enhance the reliability and validity of a SLR? This study found that ChatGPT could conduct a SLR. It needs detailed and accurate prompts to analyze the literature. It also has limitations. Guiding principles are summarized from this study for researchers to follow when they need to conduct SLRs using ChatGPT.

We present BabyLlama-2, a 345 million parameter model distillation-pretrained from two teachers on a 10 million word corpus for the BabyLM competition. On BLiMP and SuperGLUE benchmarks, BabyLlama-2 outperforms baselines trained on both 10 and 100 million word datasets with the same data mix, as well as its teacher models. Through an extensive hyperparameter sweep, we demonstrate that the advantages of distillation cannot be attributed to suboptimal hyperparameter selection of the teachers. Our findings underscore the need for further investigation into distillation techniques, particularly in data-limited settings.

Humans possess innate collaborative capacities. However, effective teamwork often remains challenging. This study delves into the feasibility of collaboration within teams of rational, self-interested agents who engage in teamwork without the obligation to contribute. Drawing from psychological and game theoretical frameworks, we formalise teamwork as a one-shot aggregative game, integrating insights from Steiner's theory of group productivity. We characterise this novel game's Nash equilibria and propose a multiagent multi-armed bandit system that learns to converge to approximations of such equilibria. Our research contributes value to the areas of game theory and multiagent systems, paving the way for a better understanding of voluntary collaborative dynamics. We examine how team heterogeneity, task typology, and assessment difficulty influence agents' strategies and resulting teamwork outcomes. Finally, we empirically study the behaviour of work teams under incentive systems that defy analytical treatment. Our agents demonstrate human-like behaviour patterns, corroborating findings from social psychology research.