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We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) build an inverted-U relation. Leveraging the Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity out-perform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization. 

We report the results of thermodynamic measurements in external magnetic field of the cubic Ce-based cage compounds CeT₂Cd₂₀(T= Ni,Pd). Our analysis of the heat-capacity data shows that the Γ₇doublet is the ground state multiplet of the Ce³⁺ions. Consequently, for the Γ₇doublet it can be theoretically shown that the Ruderman–Kittel–Kasuya–Yosida interaction between the localized Ce moments mediated by the conduction electrons, must vanish at temperatures much lower than the energy separating the ground state doublet from the first excited Γ₈quartet. Our findings provide an insight as to why no long range order has been observed in these compounds down to temperatures in the milliKelvin range.

 

Inspired by humans’ exceptional ability to master arithmetic and generalize to new problems, we present a new dataset, Handwritten arithmetic with INTegers (HINT), to examine machines’ capability of learning generalizable concepts at three levels: perception, syntax, and semantics. In HINT, machines are tasked with learning how concepts are perceived from raw signals such as images (i.e., perception), how multiple concepts are structurally combined to form a valid expression (i.e., syntax), and how concepts are realized to afford various reasoning tasks (i.e., semantics), all in a weakly supervised manner. Focusing on systematic generalization, we carefully design a five-fold test set to evaluate both the interpolation and the extrapolation of learned concepts w.r.t. the three levels. Further, we design a few-shot learning split to determine whether or not models can rapidly learn new concepts and generalize them to more complex scenarios. To comprehend existing models’ limitations, we undertake extensive experiments with various sequence-to-sequence models, including RNNs, Transformers, and GPT-3 (with the chain of thought prompting). The results indicate that current models struggle to extrapolate to long-range syntactic dependency and semantics. Models exhibit a considerable gap toward human-level generalization when evaluated with new concepts in a few-shot setting. Moreover, we discover that it is infeasible to solve HINT by merely scaling up the dataset and the model size; this strategy contributes little to the extrapolation of syntax and semantics. Finally, in zero-shot GPT-3 experiments, the chain of thought prompting exhibits impressive results and significantly boosts the test accuracy. We believe the HINT dataset and the experimental findings are of great interest to the learning community on systematic generalization. 

We present bolometric luminosities, black hole masses, and Eddington ratios for 42 luminous quasars at z  ≳ 6 using high signal-to-noise ratio VLT/X-shooter spectra, acquired as part of the enlarged ESO Large Programme XQR-30 . In particular, we derived the bolometric luminosities from the rest-frame 3000 Å luminosities using a bolometric correction from the literature, as well as the black hole masses by modeling the spectral regions around the C  IV 1549 Å and the Mg  II 2798 Å emission lines, with scaling relations calibrated in the Local Universe. We find that the black hole masses derived from both emission lines are in the same range and the scatter of the measurements agrees with expectations from the scaling relations. The Mg  II -derived masses are between ∼(0.8−12) ×10 9   M ⊙ and the derived Eddington ratios are within ∼0.13−1.73, with a mean (median) of 0.84(0.72). By comparing the total sample of quasars at z  > 5.8, from this work and from the literature, to a bolometric luminosity distribution-matched sample at z  ∼ 1.5, we find that quasars at high redshift host slightly less massive black holes, which accrete slightly more rapidly than those at lower z , with a difference in the mean Eddington ratios of the two samples of ∼0.27. These findings are in agreement with the results of recent works in the literature.