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Most schools allow students to have cell phones for safety, which seems unlikely to change as long as school shootings remain a common occurrence. But phones aren't just tools for emergencies; they can also be valuable tools in the classroom. If there's a word or concept a student doesn't understand, the student can find information instantly. Phones have calculators as well as spelling and grammar checks. Most importantly, phones allow students to communicate with one another and with experts in fields of interest. The question remains, however, whether the use of cell phones in school outweighs the distraction they cause.

Students tend to be highly susceptible to the kinds of distractions smartphones provide. My colleague caught a student watching Grey's Anatomy during her class. Other students tweet, text, and listen to music when they should be on task. According to Jeffrey Kuznekoff, who conducted a study on phone use by college students, "You're putting yourself at a disadvantage when you are actively engaged with your mobile device in class and not engaged in what's going on." Saraswathi Bellur, a researcher at the University of Connecticut, found that multitasking in class "is likely to harm academic performance."

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The seven-level English Language Learning program, ranging from pre-literacy to advanced, provides instruction on life skills, college and career readiness, citizenship, employability skills, financial literacy, family literacy, and digital literacy. Our classes integrate all skills, including reading, writing, listening, speaking, pronunciation, and grammar.

We evaluate our BPL approach on 70 data sets spanning the morphophonology of 58 languages. These data sets come from phonology textbooks: they have high linguistic diversity, but are much simpler than full language learning, with tens to hundreds of words at most, and typically isolate just a handful of grammatical phenomena. We will then shift our focus from linguists to children, and show that the same approach for finding grammatical structure in natural language also captures classic findings in the infant artificial grammar learning literature. Finally, by performing hierarchical Bayesian inference across these linguistic data sets, we show that the model can distill universal cross-language patterns, and express those patterns in a compact, human understandable form. Collectively, these findings point the way toward more human-like AI systems for learning theories, and for systems that learn to learn those theories more effectively over time by refining their inductive biases.

These AGL stimuli contain very little data, and thus these few-shot learning problems admit a broad range of possible generalizations. Children select from this space of possible generalizations to select the linguistically plausible ones. Thus, rather than producing a single grammar, we use the model to search a massive space of possible grammars and then visualize all those grammars that are Pareto-optimal solutions41 to the trade-off between parsimony and fit to data. Here parsimony means size of rules and affixes (the prior in Eq. (10)); fit to data means average stem size (the likelihood in Eq. (10)); and a Pareto-optimal solution is one which is not worse than any other along both these competing axes. Figure 7 visualizes Pareto fronts for two classic artificial grammars while varying the number of example words provided to the learner, illustrating both the set of grammars entertained by the learner and how the learner weighs these grammars against each other. These figures show the exact contours of the Pareto frontier: these problems are small enough that exact SAT solving is tractable over the entire search space, so our heuristic incremental synthesizer is unneeded. With more examples the shape of the Pareto frontier develops a sharp kink around the correct generalization; with fewer examples, the frontier is smoother and more diffuse. By explaining both natural language data and AGL studies, we see our model as delivering on a basic hypothesis underpinning AGL research: that artificial grammar learning must engage some cognitive resource shared with first language acquisition. To the extent that this hypothesis holds, we should expect an overlap between models capable of learning real linguistic phenomena, like ours, and models of AGL phenomena.

Few-shot learning of language patterns can be highly ambiguous as to the correct grammar. Here we visualize the geometry of generalization for several natural and artificial grammar learning problems. These visualizations are Pareto frontiers: the set of solutions consistent with the data that optimally trade-off between parsimony and fit to data. We show Pareto fronts for ABB (ref. 39; top two) & AAX (Gerken53; bottom right, data drawn from isomorphic phenomena in Mandarin) AGL problems for either one example word (upper left) or three example words (right column). In the bottom left we show the Pareto frontier for a textbook Polish morpho-phonology problem. Rightward on x-axis corresponds to more parsimonious grammars (smaller rule size + affix size) and upward on y-axis corresponds to grammars that best fit the data (smaller stem size), so the best grammars live in the upper right corners of these graphs. N.B.: Because the grammars and lexica vary in size across panels, the x and y axes have different scales in each panel. Pink shade: correct grammar. As the number of examples increases, the Pareto fronts develop a sharp kink around the correct grammar, which indicates a stronger preference for the correct grammar. With one example the kinks can still exist but are less pronounced. The blue lines provably show the exact contour of the Pareto frontier, up to the bound on the number of rules. This precision is owed to our use of exact constraint solvers. We show the Polish problem because the textbook author accidentally chose data with an unintended extra pattern: all stems vowels are /o/ or /u/, which the upper left solution encodes via an insertion rule. Although the Polish MAP solution is correct, the Pareto frontier can reveal other possible analyses such as this one, thereby serving as a kind of linguistic debugging. Source data are provided as a Source data file.

where P(M) is a prior on fragment grammars over SPE-style rules. In practice, jointly optimizing over the space of Ms and grammars is intractable, and so we instead alternate between finding high-probability grammars under our current M, and then shifting our inductive bias, M, to more closely match the current grammars. We estimate M by applying this procedure to a training subset comprising 30 problems, chosen to exemplify a range of distinct phenomena, and then applied this M to all 70 problems. Critically this unsupervised procedure is not given access to any ground-truth solutions to the training subset.

a Re-solving the hardest textbook problems using the learned fragment grammar metatheory leads to an average of 31% more of the problem being solved. b illustrates a case where these discovered tendencies allow the model to find a set of six interacting rules solving the entirety of an unusually complex problem. c The metatheory comprises rule schemas that are human understandable and often correspond to motifs previously identified within linguistics. Left column shows four out of 21 induced rule schemas (Supplementary Fig. 6), which encode cross-language tendencies. These learned schemas include vowel harmony and spirantization (a process where stops become fricatives near vowels). The symbol FM means a slot that can hold any feature matrix, and trigger means a slot that can hold any rule triggering context. Middle column shows model output when solving each language in isolation: these solutions can be overly specific (Koasati, Bukusu), overly general (Kerewe, Turkish), or even essentially unrelated to the correct generalization (Tibetan). Right column shows model output when solving problems jointly with inferring a metatheory. Source data are provided as a Source Data file.

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