{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"536e0332796500af20797007040cb37d8e0b4372360db636cc7594aea2d629ab","created":"2026-10-03T07:17:57Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"29cee38d003669b2c11be9c361891afd925832134ec6096ecb6c5b1c534fc4f0","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"bio.neural-criticality.power-law-spectrum","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"When thousands of visual-cortex neurons respond to natural images, the variance carried by the n-th strongest activity pattern falls roughly as 1/n. This is close to the slowest decay, meaning the most high-dimensional code, that still keeps the response a smooth function of the image, and which circuit mechanism sets it is unknown.","posed_since":"2019","precise":"In mouse primary visual cortex, principal-component variances of responses to natural images follow $\\lambda_n \\sim n^{-\\alpha}$ with $\\alpha \\sim 1$ (Stringer and co-workers, 2019), near the bound $\\alpha > 1 + 2/d$ required for a smooth representation of d-dimensional inputs. Identify the circuit mechanism (recurrent dynamics, plasticity, input statistics) that yields $\\alpha \\sim 1$, and explain why alpha stays near the bound $1 + 2/d$ for low-dimensional stimulus sets, as measured.","problem_ref":null,"references":"","settled_by":"A circuit model with measured connectivity statistics that predicts $\\alpha$ for several stimulus ensembles, confirmed by recordings.","status_note":"","title":"Origin of the 1/n spectrum of cortical population responses","topic_ref":"b8c0dcb1fa176a19eb52e966985f2d4e4b691e14755231f7ecf414ce1a70712a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"e3e12629c0871b50b49146981f34159c27fc5b76e8933664e4ab6bbb69caf953","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"8056201ac7bf8a117e1a51ca0a6eee231dd18febcce1fc4bf9805157ca1695d9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"YaiGRXHcJd_tDHGAkhmTYczvOxvkazXU_3u1P410Xzi1H_BUoU_tCfbkyVdiBUdfLeucvL0ufh59ufeD-5oBBw"},"schema":"pubphys.envelope/1"},"record_hash":"e3e12629c0871b50b49146981f34159c27fc5b76e8933664e4ab6bbb69caf953","leaf_index":807}