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).

Large Language Models (LLMs) show promising potential in Software Engineering, especially for code-related tasks like code completion and code generation. LLMs' evaluation is generally centred around general metrics computed over benchmarks. While painting a macroscopic view of the benchmarks and of the LLMs' capacity, it is unclear how each programming task in these benchmarks assesses the capabilities of the LLMs. In particular, the difficulty level of the tasks in the benchmarks is not reflected in the score used to report the performance of the model. Yet, a model achieving a 90% score on a benchmark of predominantly easy tasks is likely less capable than a model achieving a 90% score on a benchmark containing predominantly difficult tasks. This paper devises a framework, HardEval, for assessing task difficulty for LLMs and crafting new tasks based on identified hard tasks. The framework uses a diverse array of prompts for a single task across multiple LLMs to obtain a difficulty score for each task of a benchmark. Using two code generation benchmarks, HumanEval+ and ClassEval, we show that HardEval can reliably identify the hard tasks within those benchmarks, highlighting that only 21% of HumanEval+ and 27% of ClassEval tasks are hard for LLMs. Through our analysis of task difficulty, we also characterize 6 practical hard task topics which we used to generate new hard tasks. Orthogonal to current benchmarking evaluation efforts, HardEval can assist researchers and practitioners in fostering better assessments of LLMs. The difficulty score can be used to identify hard tasks within existing benchmarks. This, in turn, can be leveraged to generate more hard tasks centred around specific topics either for evaluation or improvement of LLMs. HardEval generalistic approach can be applied to other domains such as code completion or Q/A.

Meta-learning has emerged as an effective methodology to model several real-world tasks and problems due to its extraordinary effectiveness in the low-data regime. There are many scenarios ranging from the classification of rare diseases to language modelling of uncommon languages where the availability of large datasets is rare. Similarly, for more broader scenarios like self-driving, an autonomous vehicle needs to be trained to handle every situation well. This requires training the ML model on a variety of tasks with good quality data. But often times, we find that the data distribution across various tasks is skewed, i.e.the data follows a long-tail distribution. This leads to the model performing well on some tasks and not performing so well on others leading to model robustness issues. Meta-learning has recently emerged as a potential learning paradigm which can effectively learn from one task and generalize that learning to unseen tasks. In this study, we aim to exploit external knowledge of task relations to improve training stability via effective mini-batching of tasks. We hypothesize that selecting a diverse set of tasks in a mini-batch will lead to a better estimate of the full gradient and hence will lead to a reduction of noise in training.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Since its launch on the 30th of November, ChatGPT has taken the world by storm.

We introduce a new algorithm, Regression based Supervised Learning (RSL), for learning per instance Neural Network (NN) defined heuristic functions for classical planning problems. RSL uses regression to select relevant sets of states at a range of different distances from the goal. RSL then formulates a Supervised Learning problem to obtain the parameters that define the NN heuristic, using the selected states labeled with exact or estimated distances to goal states. Our experimental study shows that RSL outperforms, in terms of coverage, previous classical planning NN heuristics functions while requiring two orders of magnitude less training time.

The support/query (S/Q) training protocol is widely used in meta-learning. S/Q protocol trains a task-specific model on S and then evaluates it on Q to optimize the meta-model using query loss, which depends on size and quality of Q. In this paper, we study a new S/T protocol for meta-learning. Assuming that we have access to the theoretically optimal model T for a task, we can directly match the task-specific model trained on S to T. S/T protocol offers a more accurate evaluation since it does not rely on possibly biased and noisy query instances. There are two challenges in putting S/T protocol into practice. Firstly, we have to determine how to match the task-specific model to T. To this end, we minimize the discrepancy between them on a fictitious dataset generated by adversarial learning, and distill the prediction ability of T to the task-specific model. Secondly, we usually do not have ready-made optimal models. As an alternative, we construct surrogate target models by fine-tuning on local tasks the globally pre-trained meta-model, maintaining both efficiency and veracity.

Model-Agnostic Meta-Learning (MAML) has demonstrated widespread success in training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard Empirical Risk Minimization (ERM), and little is understood about how much MAML improves over ERM in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is determined by the number of gradient steps required to solve the task. Specifically, we prove that for $\Omega(d_{\text{eff}})$ labelled test samples (for gradient-based fine-tuning) where $d_{\text{eff}}$ is the effective dimension of the problem, in order for MAML to achieve substantial gain over ERM, the optimal solutions of the hard tasks must be closely packed together with the center far from the center of the easy task optimal solutions. We show that these insights also apply in a low-dimensional feature space when both MAML and ERM learn a representation of the tasks, which reduces the effective problem dimension. Further, our few-shot image classification experiments suggest that our results generalize beyond linear regression.

Deep neural networks are highly effective when a large number of labeled samples are available but fail with few-shot classification tasks. Recently, meta-learning methods have received much attention, which train a meta-learner on massive additional tasks to gain the knowledge to instruct the few-shot classification. Usually, the training tasks are randomly sampled and performed indiscriminately, often making the meta-learner stuck into a bad local optimum. Some works in the optimization of deep neural networks have shown that a better arrangement of training data can make the classifier converge faster and perform better. Inspired by this idea, we propose an easy-to-hard expert meta-training strategy to arrange the training tasks properly, where easy tasks are preferred in the first phase, then, hard tasks are emphasized in the second phase. A task hardness aware module is designed and integrated into the training procedure to estimate the hardness of a task based on the distinguishability of its categories. In addition, we explore multiple hardness measurements including the semantic relation, the pairwise Euclidean distance, the Hausdorff distance, and the Hilbert-Schmidt independence criterion. Experimental results on the miniImageNet and tieredImageNetSketch datasets show that the meta-learners can obtain better results with our expert training strategy.

In this paper, we investigate the combination of synthesis techniques and learning techniques to obtain safe and near optimal schedulers for a preemptible task scheduling problem. We study both model-based learning techniques with PAC guarantees and model-free learning techniques based on shielded deep Q-learning. The new learning algorithms have been implemented to conduct experimental evaluations.