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"published": "2022-12-15T22:12:38Z",
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"content": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://fediscience.org/@matspike\" class=\"u-url mention\">@<span>matspike</span></a></span> Focusing on your final couple of points: linguistics needs structural representation & PDEs (continuous maths models) offer nothing for structure - You might want to take a look at Hyperdimensional Computing (HDC) / Vector Symbolic Architectures (VSA), which are all about how to represent and manipulate composite structures (trees, graphs, etc.) by simple arithmetic on high dimensional vector spaces (as a model of, say, the firing rates of a large group of neurons). Mostly it's algebraic, but PDEs are optional if you wanted to model the dynamics of a VSA/HDC system.</p><p>Early VSA paper referring to the Jackendoff example you use: <a href=\"https://arxiv.org/abs/cs/0412059\" target=\"_blank\" rel=\"nofollow noopener\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/cs/0412059</span><span class=\"invisible\"></span></a></p><p>Me droning on about VSA as analogue computing for discrete structures: <a href=\"https://archive.org/details/Redwood_Center_2013_06_14_Ross_Gayler\" target=\"_blank\" rel=\"nofollow noopener\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">archive.org/details/Redwood_Ce</span><span class=\"invisible\">nter_2013_06_14_Ross_Gayler</span></a></p><p>A recent survey of the topic: <a href=\"https://arxiv.org/abs/2111.06077\" target=\"_blank\" rel=\"nofollow noopener\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/2111.06077</span><span class=\"invisible\"></span></a></p><p><a href=\"https://aus.social/tags/VSA\" class=\"mention hashtag\" rel=\"tag\">#<span>VSA</span></a> <a href=\"https://aus.social/tags/HDC\" class=\"mention hashtag\" rel=\"tag\">#<span>HDC</span></a> <br /><a href=\"https://aus.social/tags/VectorSymbolicArchitecture\" class=\"mention hashtag\" rel=\"tag\">#<span>VectorSymbolicArchitecture</span></a><br /><a href=\"https://aus.social/tags/HyperdimensionalComputing\" class=\"mention hashtag\" rel=\"tag\">#<span>HyperdimensionalComputing</span></a></p>",
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"en": "<p><span class=\"h-card\" translate=\"no\"><a href=\"https://fediscience.org/@matspike\" class=\"u-url mention\">@<span>matspike</span></a></span> Focusing on your final couple of points: linguistics needs structural representation & PDEs (continuous maths models) offer nothing for structure - You might want to take a look at Hyperdimensional Computing (HDC) / Vector Symbolic Architectures (VSA), which are all about how to represent and manipulate composite structures (trees, graphs, etc.) by simple arithmetic on high dimensional vector spaces (as a model of, say, the firing rates of a large group of neurons). Mostly it's algebraic, but PDEs are optional if you wanted to model the dynamics of a VSA/HDC system.</p><p>Early VSA paper referring to the Jackendoff example you use: <a href=\"https://arxiv.org/abs/cs/0412059\" target=\"_blank\" rel=\"nofollow noopener\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/cs/0412059</span><span class=\"invisible\"></span></a></p><p>Me droning on about VSA as analogue computing for discrete structures: <a href=\"https://archive.org/details/Redwood_Center_2013_06_14_Ross_Gayler\" target=\"_blank\" rel=\"nofollow noopener\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"ellipsis\">archive.org/details/Redwood_Ce</span><span class=\"invisible\">nter_2013_06_14_Ross_Gayler</span></a></p><p>A recent survey of the topic: <a href=\"https://arxiv.org/abs/2111.06077\" target=\"_blank\" rel=\"nofollow noopener\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/2111.06077</span><span class=\"invisible\"></span></a></p><p><a href=\"https://aus.social/tags/VSA\" class=\"mention hashtag\" rel=\"tag\">#<span>VSA</span></a> <a href=\"https://aus.social/tags/HDC\" class=\"mention hashtag\" rel=\"tag\">#<span>HDC</span></a> <br /><a href=\"https://aus.social/tags/VectorSymbolicArchitecture\" class=\"mention hashtag\" rel=\"tag\">#<span>VectorSymbolicArchitecture</span></a><br /><a href=\"https://aus.social/tags/HyperdimensionalComputing\" class=\"mention hashtag\" rel=\"tag\">#<span>HyperdimensionalComputing</span></a></p>"
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