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{
    "pk": 23985,
    "title": "Symbolic Variables in Distributed Networks that Count",
    "subtitle": null,
    "abstract": "The discrete entities and explicit relations of symbolic systems make them transparent and easy to communicate. This contrasts with distributed systems, which tend to be opaque. This can lead us to pursue symbolic characterizations of human cognition. Symbolic interpretations can, however, oversimplify distributed systems. This is demonstrated in the developmental number cognition literature, where recent findings suggest a gradience of counting ability in children's learning. We take inspiration from these findings to explore the meaning of symbols in Recurrent Neural Networks (RNNs). We align recurrent neural representations with number symbols by causally intervening on the neural representations. We find that symbol-like representations of numbers do emerge in RNNs. We use this to inform the discussion on how neural systems represent quantity. We also show that the symbol-like representations evolve with learning, and continue to vary after the RNNs solve the task, demonstrating the graded nature of symbols in distributed systems.",
    "language": "eng",
    "license": {
        "name": "",
        "short_name": "",
        "text": null,
        "url": ""
    },
    "keywords": [
        {
            "word": "Concepts and categories; Reasoning; Computational Modeling; Knowledge representation; Neural Networks"
        }
    ],
    "section": "Papers with Poster Presentation",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7gm9d3hp",
    "frozenauthors": [
        {
            "first_name": "Satchel",
            "middle_name": "",
            "last_name": "Grant",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        },
        {
            "first_name": "Zhengxuan",
            "middle_name": "",
            "last_name": "Wu",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        },
        {
            "first_name": "Jay",
            "middle_name": "",
            "last_name": "McClelland",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        },
        {
            "first_name": "Noah",
            "middle_name": "",
            "last_name": "Goodman",
            "name_suffix": "",
            "institution": "Stanford University",
            "department": ""
        }
    ],
    "date_submitted": null,
    "date_accepted": null,
    "date_published": "2024-01-01T18:00:00Z",
    "render_galley": null,
    "galleys": [
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            "label": "PDF",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cognitivesciencesociety/article/23985/galley/13579/download/"
        },
        {
            "label": "PDF",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cognitivesciencesociety/article/23985/galley/21582/download/"
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    ]
}