{
  "schema_version": 1,
  "title": "Reproduction: Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory",
  "emoji": "🧲",
  "space_id": "snaykey/repro-assoc-memory-phase",
  "paper": {
    "openreview_id": "P0eayHlqb7"
  },
  "tags": [
    "icml2026-repro",
    "paper-P0eayHlqb7"
  ],
  "updated_at": "2026-08-01T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "claim-1-zeroT-capacity",
        "title": "For continuous Dense Associative Memory with exponential pattern capacity p=e^(αN) on the N-sphere, the maximum retrieval capacity at zero temperature is α_c(0) = 0.5 for both LSE and LSR kernels (Section 4.3, Figure 1).",
        "file": "pages/claim-1-zeroT-capacity/page.md",
        "children": []
      },
      {
        "slug": "claim-2-geometric-entropy",
        "title": "The geometric entropy density depends only on the alignment φ via s(φ) = (1/2)ln(1-φ²), independent of the choice of energy kernel (Section 3.2, Equation 19).",
        "file": "pages/claim-2-geometric-entropy/page.md",
        "children": []
      },
      {
        "slug": "claim-3-phase-boundaries",
        "title": "The LSE and LSR kernels have distinct finite-temperature phase boundaries, given respectively by α_c^LSE(T) = (1/2)[1-f_ret^LSE(T)]² (Equation 35) and α_c^LSR(T) = (1/2)[1-f_ret^LSR(T)]² (Equation 39) (Section 4.3).",
        "file": "pages/claim-3-phase-boundaries/page.md",
        "children": []
      },
      {
        "slug": "claim-4-lsr-threshold",
        "title": "For the LSR kernel with shape parameter b=3.41, there exists a support threshold α_th = (1/2)(1-1/b)² ≈ 0.25 below which retrieval is perfect at any temperature, a behavior absent for the LSE kernel (Section 4.2-4.3).",
        "file": "pages/claim-4-lsr-threshold/page.md",
        "children": []
      },
      {
        "slug": "claim-5-monte-carlo",
        "title": "Monte Carlo simulations at N=50, α=0.1 confirm the theoretical predictions, showing the LSE kernel undergoes a retrieval-to-disorder transition around T≈0.7-0.8, while the LSR kernel below its threshold maintains retrieval across all tested temperatures (Figure 2).",
        "file": "pages/claim-5-monte-carlo/page.md",
        "children": []
      },
      {
        "slug": "executive-summary",
        "title": "executive-summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}