Data-driven machine learning (ML) has demonstrated tremendous potential in material property predictions. However, the scarcity of materials data with costly property labels in the vast chemical space presents a significant challenge for ML in efficiently predicting properties and uncovering structure-property relationships. Here, we propose a novel hierarchy-boosted funnel learning (HiBoFL) framework, which is successfully applied to identify semiconductors with ultralow lattice thermal conductivity ($\kappa_\mathrm{L}$). By training on only a few hundred materials targeted by unsupervised learning from a pool of hundreds of thousands, we achieve efficient and interpretable supervised predictions of ultralow $\kappa_\mathrm{L}$, thereby circumventing large-scale brute-force calculations without clear objectives. As a result, we provide a list of candidates with ultralow $\kappa_\mathrm{L}$ for potential thermoelectric applications and discover a new factor that significantly influences structural anharmonicity. This study offers a novel practical pathway for accelerating the discovery of functional materials.

Animals learn to predict external contingencies from experience through a process of conditioning. A natural mechanism for conditioning is stimulus substitution, whereby the neuronal response to a stimulus with no prior behavioral significance becomes increasingly identical to that generated by a behaviorally significant stimulus it reliably predicts. We propose a recurrent neural network model of stimulus substitution which leverages two forms of inductive bias pervasive in the cortex: representational inductive bias in the form of mixed stimulus representations, and architectural inductive bias in the form of two-compartment pyramidal neurons that have been shown to serve as a fundamental unit of cortical associative learning. The properties of these neurons allow for a biologically plausible learning rule that implements stimulus substitution, utilizing only information available locally at the synapses. We show that the model generates a wide array of conditioning phenomena, and can learn large numbers of associations with an amount of training commensurate with animal experiments, without relying on parameter fine-tuning for each individual experimental task. In contrast, we show that commonly used Hebbian rules fail to learn generic stimulus-stimulus associations with mixed selectivity, and require task-specific parameter fine-tuning. Our framework highlights the importance of multi-compartment neuronal processing in the cortex, and showcases how it might confer cortical animals the evolutionary edge.

Linear temporal logic (LTL) is widely used in industrial verification. LTL formulae can be learned from traces. Scaling LTL formula learning is an open problem. We implement the first GPU-based LTL learner using a novel form of enumerative program synthesis. The learner is sound and complete. Our benchmarks indicate that it handles traces at least 2048 times more numerous, and on average at least 46 times faster than existing state-of-the-art learners. This is achieved with, among others, novel branch-free LTL semantics that has $O(\log n)$ time complexity, where $n$ is trace length, while previous implementations are $O(n^2)$ or worse (assuming bitwise boolean operations and shifts by powers of 2 have unit costs -- a realistic assumption on modern processors).

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies theoretical properties of orthogonal convolutional layers. We establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. The conditions prove that orthogonal convolutional transforms exist for almost all architectures used in practice for 'circular' padding.We also exhibit limitations with 'valid' boundary condition and 'same' boundary condition with zero padding. Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed, and impressive empirical results have been obtained in different applications (Wang et al. 2020).The second motivation of the present paper is to specify the theory behind this.We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and that, in the presence of small errors and when the size of the signal/image is large, the convolutional layers remain close to isometric.The theoretical results are confirmed with experiments, the landscape of the regularization term is studied and the regularization strategy is validated on real datasets. Altogether, the study guarantees that the regularization with L_{orth} (Wang et al. 2020) is an efficient, flexible and stable numerical strategy to learn orthogonal convolutional layers.