{
  "meta": {
    "domain": "Forward–Forward Algorithm 的后续改进",
    "title": "Forward–Forward Algorithm 的后续改进研究地图",
    "subtitle": "从正负好度到层协作、现代架构与物理部署的可审计谱系",
    "updated": "2026-08-13",
    "audience": "机器学习、计算神经科学、神经形态计算与物理学习研究人员",
    "scope_note": "纳入 2022 年原始 Forward–Forward（FF）提出后，直接修改 FF 的正负相、goodness、负样本、层间协作、架构/任务、硬件实现或直接评测的工作；原始 FF 作为奠基条目。另纳入 4 个明确标注为邻接桥接的 forward-only/局部目标工作，用于解释 FF 的边界，但不把它们误称为严格 FF 变体。优先正式会议/期刊和作者预印本；截止 2026-08-13。长尾应用、只把 FF 当作未改造基线的论文、仅词面重合的 forward-forward、仍执行端到端反向传播的局部辅助损失均排除。",
    "axis_label": "改进所处系统层级",
    "overview": "FF 的核心变化不是换一个优化器，而是把全局损失改造成每层的正/负 goodness 判别，并用两次前向更新。后续研究主要沿三条互补方向推进：改造负样本与好度函数，向深层引入层间协作或层级目标，把机制迁移到 CNN、ViT、图网络和器件。直接反证同时显示，纯局部 FF 的深度协调、泛化和总系统成本仍未解决；更强的结果常引入局部截断反向、监督对比、多层融合或混合块，因此必须区分“跨层无反向”和“完全无反向”。",
    "coverage_level": "L2",
    "language": "zh-CN",
    "thesis": "截至截止日，FF 的后续改进尚未证明可以在通用深度学习中全面替代反向传播；最清晰的进展是把问题从负样本与局部好度，推进到层间协调、真实数据公平评测和物理器件闭环。",
    "recommendation": "阅读时先区分纯 FF、跨层无反向但层内仍求梯度、以及硬件/邻接 forward-only 范式；评价新方法时同时要求同骨干精度、收敛、训练步数、总 FLOPs、显存、墙钟、负样本成本和硬件外围成本。",
    "map_center_label": "局部信用分配",
    "coverage_note": "基于 2026-08-12 工作区内独立一手来源审计、原始 FF PDF 深读、前后向引用补漏和反证查询；本轮外部搜索与重新打开页面受环境策略限制，未把失败入口伪装成零命中。严格 FF 变体与邻接桥接已分层标注，长尾应用和未能重新打开的页面保留遗漏风险。",
    "source_materials": [
      "正式会议与期刊论文/DOI",
      "OpenReview 与 PMLR 官方入口",
      "arXiv 作者预印本",
      "作者/机构项目与器件材料",
      "工作区内原始 PDF 深读与独立审计记录"
    ]
  },
  "routes": [
    {
      "id": "goodness-negative",
      "label": "好度与正负/自对比目标",
      "short": "好度与对比",
      "description": "改变 goodness、负样本或自对比构造，使每层局部目标携带更有用的任务信息。",
      "question": "正负样本的差异是否让局部层学到任务结构，而不是标签或生成规则的捷径？",
      "color": "#205B6F",
      "text_color": "#174655",
      "order": 0,
      "angle": -90.0
    },
    {
      "id": "depth-collaboration",
      "label": "深度稳定与层间协作",
      "short": "深度与协作",
      "description": "处理独立层更新造成的语义错位、深度退化和训练不稳定，并记录是否重新引入截断反向。",
      "question": "早期层如何得到后续任务所需的协调信号，同时保持局部更新的边界？",
      "color": "#9A5A35",
      "text_color": "#744329",
      "order": 1,
      "angle": -30.0
    },
    {
      "id": "architecture-extension",
      "label": "架构与任务外延",
      "short": "架构外延",
      "description": "把 FF 或相邻 forward-learning 机制迁移到 CNN、ViT、图网络和其他非原始多层感知机结构。",
      "question": "机制能否穿过卷积、注意力或图消息传递接口，而不依赖小型全连接网络的特殊性？",
      "color": "#596B3D",
      "text_color": "#43522F",
      "order": 2,
      "angle": 30.0
    },
    {
      "id": "evaluation-counterevidence",
      "label": "公平评测与反证",
      "short": "评测与反证",
      "description": "直接比较同骨干 BP 与纯/混合 FF，记录真实数据、系统成本、负面结果和可扩展性审计。",
      "question": "改进是否在控制骨干、数据、训练预算和系统指标后仍成立？",
      "color": "#705784",
      "text_color": "#554264",
      "order": 3,
      "angle": 90.0
    },
    {
      "id": "hardware-deployment",
      "label": "物理器件与硬件部署",
      "short": "器件部署",
      "description": "在忆阻器等物理介质中执行 FF/Competitive Forward，检查前向式更新、保持性和闭环范围。",
      "question": "无反向更新能否真正进入器件闭环，并在多层、读写和外围成本都计入后保持优势？",
      "color": "#3A7D72",
      "text_color": "#1C4F47",
      "order": 4,
      "angle": 150.0
    },
    {
      "id": "adjacent-forward-only",
      "label": "相邻前向无反馈范式",
      "short": "相邻范式",
      "description": "保留直接解释 FF 边界的 forward-only、闭式投影和块级去噪工作，但明确它们不是原始 goodness 路线。",
      "question": "如果完全的 FF 局部协调困难，目标投影或块分解是否提供另一种无跨层反向的折中？",
      "color": "#B1842D",
      "text_color": "#62450D",
      "order": 5,
      "angle": 210.0
    }
  ],
  "levels": [
    {
      "id": 0,
      "label": "局部目标与好度",
      "short": "局部目标",
      "description": "直接改变正/负相、goodness、负样本或自对比学习信号，主要回答 FF 的最小机制问题。",
      "order": 0,
      "radius": 88.0
    },
    {
      "id": 1,
      "label": "网络深度与层间协作",
      "short": "深度协作",
      "description": "围绕多层训练的稳定性、层间语义协调和局部更新范围做改进；需要关注是否混入截断反向。",
      "order": 1,
      "radius": 154.0
    },
    {
      "id": 2,
      "label": "现代架构、任务与公平评测",
      "short": "规模评测",
      "description": "进入 CNN、ViT、图任务或真实数据与匹配预算比较；不等同于已经达到现代基础模型规模。",
      "order": 2,
      "radius": 220.0
    },
    {
      "id": 3,
      "label": "物理实现与部署",
      "short": "物理部署",
      "description": "在器件或硬件闭环中执行前向式更新，需同时核对矩阵乘、写入、控制、校准和保持性边界。",
      "order": 3,
      "radius": 286.0
    }
  ],
  "papers": [
    {
      "id": "ff-2022",
      "title": "The Forward-Forward Algorithm: Some Preliminary Investigations",
      "title_local": "Forward–Forward 算法：初步研究",
      "short_title": "原始 FF",
      "year": 2022,
      "venue": "arXiv",
      "status": "preprint",
      "source_type": "paper",
      "primary_route": "goodness-negative",
      "routes": [
        "goodness-negative"
      ],
      "level": 0,
      "tier": "core",
      "evidence_level": "C",
      "elevator": "每层用正/负两次前向提高或降低 goodness，去掉跨层反向梯度链。",
      "problem": "能否用局部正负对比目标训练深层网络，而不把全局损失的导数沿网络反向传播？",
      "mechanism": "正数据和负数据分别前向通过每层；当前层根据活动平方和等 goodness 目标更新本层权重，再把归一化活动送入下一层。监督分类可把标签并入输入，测试时按候选标签累计 goodness。",
      "mechanism_steps": [
        "构造正样本与负样本",
        "分别执行两次前向过程",
        "计算每层 goodness 与局部目标",
        "只更新当前层并传递归一化活动"
      ],
      "evidence": [
        "预印本在混合负样本的 MNIST 任务中报告全连接版本约 1.37% 和局部感受野版本约 1.16% 测试错误；两种设置并非同一模型。",
        "CIFAR-10 局部感受野实验中，逐标签 goodness 推理错误率约 41%，原文给出的 BP 对照约为 37%/39%；作者将工作定位为少数小问题上的初步调查。"
      ],
      "limitations": [
        "负样本构造是外部设计问题，简单负样本可能让网络学习生成规则而非任务结构。",
        "原文承认 FF 比 BP 慢且在部分问题上泛化较差；没有现代大规模视觉或语言证据。",
        "当前记录仍是预印本，不能把后续改进结果倒灌为原始 FF 证据。"
      ],
      "implications": [
        "它改变的是训练目标与信用分配接口，而不只是换一种梯度估计器。",
        "后续研究的核心问题自然转向负样本、层间协调、深度稳定和硬件闭环。"
      ],
      "paper_url": "https://arxiv.org/abs/2212.13345",
      "source_note": "已对工作区内原始 16 页 PDF 完成深读，并与 arXiv 一手入口记录核对；2026-08-13 无法重新打开 arXiv，未确认正式同行评议版本。证据仅覆盖原文实验与作者限定语。",
      "authors": [
        "Geoffrey Hinton"
      ],
      "tags": [
        "正负样本",
        "goodness",
        "局部目标",
        "奠基"
      ],
      "related_ids": [
        "trifecta-2024",
        "layer-collaboration-2024",
        "ff-cnn-2025"
      ],
      "relevance_rank": 1,
      "work_family_id": "ff-core",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P1",
        "Q": "Q1"
      },
      "evidence_locations": [
        "摘要",
        "§2–§4",
        "表1",
        "§6–§8"
      ]
    },
    {
      "id": "bicovg-2026",
      "title": "Covariance-Aware Goodness for Scalable Forward-Forward Learning",
      "title_local": "面向可扩展 Forward–Forward 学习的协方差感知好度",
      "short_title": "BiCovG",
      "year": 2026,
      "venue": "arXiv",
      "status": "preprint",
      "source_type": "paper",
      "primary_route": "goodness-negative",
      "routes": [
        "goodness-negative",
        "evaluation-counterevidence"
      ],
      "level": 2,
      "tier": "core",
      "evidence_level": "C",
      "elevator": "用协方差感知的 goodness 与局部特征对齐改善 FF 的规模化，并把纯局部与块内 BP 混合版分开。",
      "problem": "标量活动平方和难以表达高维表征的协方差结构，能否用二阶统计量帮助局部 FF 学到可迁移特征？",
      "mechanism": "以协方差感知好度替代单一活动长度，并结合局部特征对齐目标；论文另给出允许块内 BP 的 Hybrid Goodness Blocks，用于区分目标函数改进与有限范围反向协调。",
      "mechanism_steps": [
        "统计局部表示的协方差结构",
        "构造协方差感知 goodness 与对齐损失",
        "分别训练纯局部和混合块版本",
        "在统一 VGG-16/图像任务上比较规模与边界"
      ],
      "evidence": [
        "预印本报告纯局部 BiCovG+FAL 在 ImageNet-100 达 73.01%。",
        "同一记录显示，允许块内 BP 的 Hybrid Goodness Blocks 才把与 BP 的差距缩至 3.6%；复现 DeeperForward 的融合准确率仅约 13%。"
      ],
      "limitations": [
        "截至截止日仍为预印本，结果和代码需要独立复核。",
        "混合块结果不能作为纯 FF 结果；二阶统计量和对齐损失也会增加计算与设计复杂度。",
        "ImageNet-100 不等同于 ImageNet-1K 或基础模型规模。"
      ],
      "implications": [
        "goodness 的统计形式本身是可研究的瓶颈，不必局限于活动平方和。",
        "它把“性能提升来自更好的局部目标”与“性能提升来自重新引入块内反向”明确拆开。"
      ],
      "paper_url": "https://arxiv.org/abs/2605.04346",
      "source_note": "arXiv:2605.04346 预印本；使用本地独立审计的正文/附录记录，正式出版状态截至截止日未确认。纯局部与 Hybrid Goodness Blocks 的证据分别记录。",
      "tags": [
        "协方差",
        "goodness",
        "ImageNet-100",
        "混合块",
        "预印本"
      ],
      "related_ids": [
        "ff-2022",
        "hcl-ff-2026",
        "advancing-ff-2026",
        "dtg-ff-2026"
      ],
      "relevance_rank": 9,
      "work_family_id": "bicovg-2026",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V4",
        "D": "D3",
        "P": "P1",
        "Q": "Q3"
      },
      "evidence_locations": [
        "方法",
        "ImageNet-100 主表",
        "Hybrid Goodness Blocks",
        "DeeperForward 复现附录"
      ]
    },
    {
      "id": "scff-2025",
      "title": "Self-Contrastive Forward-Forward algorithm",
      "title_local": "自对比 Forward–Forward 算法",
      "short_title": "SCFF",
      "year": 2025,
      "venue": "Nature Communications",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "goodness-negative",
      "routes": [
        "goodness-negative",
        "architecture-extension"
      ],
      "level": 2,
      "tier": "core",
      "evidence_level": "A",
      "elevator": "用自对比样本替代部分外部负样本设计，把 FF 推向自监督、序列和更复杂视觉任务。",
      "problem": "原始 FF 依赖负样本或标签构造；能否从样本自身生成对比关系，降低负样本设计负担并扩展任务？",
      "mechanism": "围绕同一输入或其变换构造自对比正/负关系，在每个局部模块上使用 FF 式 goodness/对比目标，最后用线性或任务读出完成评估。",
      "mechanism_steps": [
        "从样本或样本变换构造自对比对",
        "分别执行局部正/负前向",
        "优化每层自对比 goodness",
        "冻结或组合表征后完成视觉/序列读出"
      ],
      "evidence": [
        "Nature Communications 正式论文把自对比 FF 扩展到 Tiny-ImageNet 与序列数据，并报告相对原始局部方案的改进。",
        "作者讨论中仍承认纯局部学习与端到端自监督目标之间存在性能差距。"
      ],
      "limitations": [
        "自对比关系和数据增强仍是设计变量，可能把结构先验移入样本构造。",
        "完整分类性能需区分局部表征和监督线性读出；不能把读出结果等同端到端训练。",
        "尚无大规模 Transformer 或基础模型证据。"
      ],
      "implications": [
        "负样本问题可以从外部负例转向自对比生成，但不等于层间协调已经解决。",
        "它把 FF 的研究焦点从“如何判别负样本”扩展到“如何构造可迁移的局部学习信号”。"
      ],
      "paper_url": "https://doi.org/10.1038/s41467-025-61037-0",
      "source_note": "Nature Communications 2025 正式 DOI 版本；本地专项审计核验结果与讨论边界已写入 claim ledger。",
      "tags": [
        "自监督",
        "自对比",
        "Tiny-ImageNet",
        "序列"
      ],
      "doi": "10.1038/s41467-025-61037-0",
      "related_ids": [
        "ff-2022",
        "cff-vit-2025",
        "hcl-ff-2026"
      ],
      "relevance_rank": 5,
      "work_family_id": "scff-2025",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q3"
      },
      "evidence_locations": [
        "摘要",
        "自对比构造",
        "视觉与序列实验",
        "讨论"
      ]
    },
    {
      "id": "layer-collaboration-2024",
      "title": "Layer Collaboration in the Forward-Forward Algorithm",
      "title_local": "Forward–Forward 算法中的层间协作",
      "short_title": "层间协作",
      "year": 2024,
      "venue": "AAAI",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "depth-collaboration",
      "routes": [
        "depth-collaboration",
        "evaluation-counterevidence"
      ],
      "level": 1,
      "tier": "core",
      "evidence_level": "A",
      "elevator": "把“每层独立优化、层间不能协作”从 FF 的局限变成直接研究问题，并提出层间协作修复。",
      "problem": "如果每一层只根据自身 goodness 学习，早期层如何知道后续层真正需要的语义结构？",
      "mechanism": "在局部 FF 目标之外引入层间协作信息，使层更新不再完全由孤立的当前层判别决定；论文把这种协作作为对原始独立层训练的结构性修正。",
      "mechanism_steps": [
        "识别独立 goodness 导致的层间错位",
        "保留局部正负训练接口",
        "加入层间协作信号或联合约束",
        "在深层任务上与原始 FF 比较"
      ],
      "evidence": [
        "AAAI 正式论文明确把原始 FF 的层独立优化和次优性能作为动机，并报告层协作方向的改进证据。",
        "该工作在谱系中连接了原始 FF 与后续层级/对比目标方法，而不是把独立局部目标当作已经解决的问题。"
      ],
      "limitations": [
        "层间协作增加了额外信息通道，局部性与通信成本需要单独核算。",
        "现有证据仍处于中小规模深度视觉任务，不能推断在现代基础模型上有效。"
      ],
      "implications": [
        "它给出 FF 后续改进最清晰的失败诊断之一：层级表征需要协作，而不是简单的逐层独立分类。",
        "后续 HCL-FF 的粗到细目标和多层融合可视为同一问题的不同修复路径。"
      ],
      "paper_url": "https://ojs.aaai.org/index.php/AAAI/article/view/29324",
      "source_note": "正式 AAAI 2024 论文，DOI 10.1609/aaai.v38i13.29324；来自本地独立审计的摘要/方法核验，当前环境无法重新打开 AAAI 页面。",
      "tags": [
        "层间协作",
        "局部信用",
        "机制反证",
        "AAAI 2024"
      ],
      "doi": "10.1609/aaai.v38i13.29324",
      "related_ids": [
        "ff-2022",
        "trifecta-2024",
        "advancing-ff-2026",
        "hcl-ff-2026"
      ],
      "relevance_rank": 3,
      "work_family_id": "layer-collaboration-2024",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "摘要",
        "动机与方法",
        "与原始 FF 的比较"
      ]
    },
    {
      "id": "trifecta-2024",
      "title": "The Trifecta: Three simple techniques for training deeper Forward-Forward networks",
      "title_local": "Trifecta：训练更深 Forward–Forward 网络的三项简单技术",
      "short_title": "Trifecta",
      "year": 2024,
      "venue": "Transactions on Machine Learning Research",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "depth-collaboration",
      "routes": [
        "depth-collaboration",
        "goodness-negative"
      ],
      "level": 1,
      "tier": "core",
      "evidence_level": "A",
      "elevator": "用 SymBa、批归一化和重叠局部更新缓解 FF 的深度退化，但最后一项混入两层截断反向。",
      "problem": "原始 FF 的逐层独立 goodness 在网络变深后难以保持稳定和可用表征，怎样增加深度而不直接恢复全网 BP？",
      "mechanism": "工作将 goodness 损失、归一化和局部更新范围作为联合训练配方：SymBa 改善正负判别，批归一化稳定活动分布，OLU 让相邻层共享一个有限范围的训练窗口。",
      "mechanism_steps": [
        "用 SymBa 重新组织正负 goodness 损失",
        "对层活动施加批归一化",
        "以 OLU 在相邻层窗口内更新",
        "在更深网络上比较深度与性能变化"
      ],
      "evidence": [
        "本地一手审计记录其在 CIFAR-10 等中型任务上把可用深度推进到约 12 层，最佳结果约 83.7%，训练约 500 个 epoch。",
        "审计同时记录超过约 12 层后增益停滞，说明技术组合缓解了深度问题但没有消除它。"
      ],
      "limitations": [
        "OLU 是两层截断反向或重叠模块更新，不属于严格意义上的完全纯 FF。",
        "额外归一化、局部窗口和训练轮数增加了计算成本；没有通用基础模型或大规模 ImageNet-1K 证据。"
      ],
      "implications": [
        "FF 的深度瓶颈与跨层协调有关，单纯堆叠独立局部分类器并不能自然扩展。",
        "它建立了后续“纯局部改进 vs 混合局部方案”的边界基线。"
      ],
      "paper_url": "https://openreview.net/forum?id=a7KP5uo0Fp",
      "source_note": "使用 OpenReview/TMLR 版本族和本地 2026-08-12 逐条审计记录；机制、深度和 OLU 边界按正文/附录核验，未把 OLU 结果写成纯 FF 结果。",
      "tags": [
        "深度稳定",
        "SymBa",
        "批归一化",
        "OLU",
        "混合局部"
      ],
      "related_ids": [
        "ff-2022",
        "layer-collaboration-2024",
        "hcl-ff-2026"
      ],
      "relevance_rank": 2,
      "work_family_id": "trifecta-2024",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "摘要",
        "方法与训练配方",
        "深度消融",
        "附录 OLU 说明"
      ]
    },
    {
      "id": "advancing-ff-2026",
      "title": "Advancing the forward-forward algorithm towards high-performance deep local learning",
      "title_local": "推动 Forward–Forward 算法走向高性能深层局部学习",
      "short_title": "高性能深层 FF",
      "year": 2026,
      "venue": "Neural Networks",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "depth-collaboration",
      "routes": [
        "depth-collaboration",
        "evaluation-counterevidence"
      ],
      "level": 2,
      "tier": "bridge",
      "evidence_level": "B",
      "elevator": "把原始 FF 在复杂任务上的性能与泛化不足明确化，并以深层局部学习为目标推进修复。",
      "problem": "原始 FF 的局部 goodness 能否通过更高性能的深层局部训练机制进入复杂视觉任务？",
      "mechanism": "论文围绕深层局部学习的性能瓶颈设计改进训练方案，并将原始 FF 作为基线比较；由于当前环境无法重新打开页面，本地图只保留正式摘要与独立审计支持的机制级描述。",
      "mechanism_steps": [
        "识别原始 FF 的深层性能和泛化缺口",
        "构造增强的深层局部训练流程",
        "在复杂任务上与原始 FF/基线比较",
        "报告改进效果与仍存在的泛化边界"
      ],
      "evidence": [
        "正式 Neural Networks 2026 入口明确把原始 FF 的次优性能和复杂任务泛化问题作为后续改进动机。",
        "本地独立审计将其列入直接负面与修复链，而不是只作为标题线索。"
      ],
      "limitations": [
        "当前条目以正式摘要和版本元数据为主，未把未重新打开的正文组件或数值扩写进地图。",
        "即使复杂任务表现提升，也不能由题名或摘要推出已全面超越 BP。"
      ],
      "implications": [
        "它把 FF 后续工作从“可否工作”推进到“如何高性能深层化”的阶段。",
        "后续阅读应重点核查它是否保持纯局部，以及改进来自目标设计、协作通道还是混合反向。"
      ],
      "paper_url": "https://www.sciencedirect.com/science/article/pii/S0893608026002273",
      "source_note": "正式 DOI 10.1016/j.neunet.2026.108765；本地独立审计已核验出版状态与摘要级主张，因当前页面访问限制，机制细节保守降为 V2。",
      "tags": [
        "深层局部学习",
        "性能修复",
        "2026 前沿"
      ],
      "doi": "10.1016/j.neunet.2026.108765",
      "related_ids": [
        "layer-collaboration-2024",
        "hcl-ff-2026",
        "bicovg-2026",
        "dtg-ff-2026"
      ],
      "relevance_rank": 7,
      "work_family_id": "advancing-ff-2026",
      "source_tier": "T1",
      "verification_state": "abstract-checked",
      "evidence_vector": {
        "V": "V2",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "正式摘要",
        "出版元数据",
        "独立审计筛选记录"
      ]
    },
    {
      "id": "hcl-ff-2026",
      "title": "HCL-FF: Hierarchical and Contrastive Learning for Forward-Forward Algorithm",
      "title_local": "HCL-FF：面向 Forward–Forward 算法的层级与对比学习",
      "short_title": "HCL-FF",
      "year": 2026,
      "venue": "CVPR",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "depth-collaboration",
      "routes": [
        "depth-collaboration",
        "goodness-negative",
        "evaluation-counterevidence"
      ],
      "level": 2,
      "tier": "core",
      "evidence_level": "A",
      "elevator": "用粗到细层级目标、监督对比和无参数残差融合推进纯局部 FF 的跨层协调。",
      "problem": "如果所有层都直接学习同一细粒度标签，深层 FF 如何避免目标重复、语义错位和信息传递退化？",
      "mechanism": "按网络深度为层分配粗到细的层级标签目标，在每层加入监督对比项，并以不引入可学习参数的残差融合汇聚多层信息。",
      "mechanism_steps": [
        "构建粗到细的标签层级",
        "按深度分配不同粒度目标",
        "联合优化 goodness 与监督对比项",
        "用无参数残差融合层级表征并评估"
      ],
      "evidence": [
        "CVPR 2026 正文报告相对既有 FF 方法在 CIFAR-10、CIFAR-100 和 Tiny-ImageNet 分别提升 5.46、17.00 和 12.51 个百分点。",
        "论文仍报告收敛慢于 BP、泛化较弱；参数匹配的宽残差网络继续领先。"
      ],
      "limitations": [
        "类别分配和层级标签会随标签空间变大而变得昂贵，能否迁移到开放词汇或基础模型未知。",
        "多层融合、监督对比和更宽骨干使比较必须控制参数量、训练预算和读出方式。"
      ],
      "implications": [
        "层级目标是直接回应层间协作缺口的较强纯局部改进路线。",
        "它同时说明纯 FF 的主要进展仍是缩小差距，而非在同预算下取代 BP。"
      ],
      "paper_url": "https://openaccess.thecvf.com/content/CVPR2026/html/Yao_HCL-FF_Hierarchical_and_Contrastive_Learning_for_Forward-Forward_Algorithm_CVPR_2026_paper.html",
      "source_note": "CVPR 2026 正式开放论文页与本地版本族核验；数值来自正文结果表，作者预印本作为版本补充但不替代正式入口。",
      "tags": [
        "层级目标",
        "监督对比",
        "残差融合",
        "CIFAR",
        "Tiny-ImageNet"
      ],
      "related_ids": [
        "trifecta-2024",
        "scff-2025",
        "advancing-ff-2026",
        "bicovg-2026",
        "dtg-ff-2026"
      ],
      "relevance_rank": 8,
      "work_family_id": "hcl-ff-2026",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "摘要",
        "层级目标与对比损失",
        "CIFAR/Tiny-ImageNet 结果",
        "局限讨论"
      ]
    },
    {
      "id": "cff-vit-2025",
      "title": "Contrastive Forward-Forward: A Training Algorithm of Vision Transformer",
      "title_local": "对比 Forward–Forward：一种视觉 Transformer 训练算法",
      "short_title": "CFF-ViT",
      "year": 2025,
      "venue": "Neural Networks",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "architecture-extension",
      "routes": [
        "architecture-extension",
        "goodness-negative"
      ],
      "level": 2,
      "tier": "core",
      "evidence_level": "A",
      "elevator": "把对比式 FF 的局部训练接口迁移到 Vision Transformer，并明确把梯度限制在局部模块内。",
      "problem": "原始 FF 主要在多层感知机/卷积设置中讨论，注意力和 Transformer block 能否在不跨块反向的条件下训练？",
      "mechanism": "每个 ViT 局部模块分别处理正/负或对比输入，计算局部目标并在模块内部更新；跨模块的全局梯度链被截断，但层内仍可以使用常规反向求局部目标。",
      "mechanism_steps": [
        "把图像切成 token 并进入 ViT block",
        "为每个 block 构造正/负对比前向",
        "只在当前 block 内优化局部目标",
        "组合各层表征并评估视觉分类"
      ],
      "evidence": [
        "正式 Neural Networks 版本报告将 CFF 扩展到 Vision Transformer，并相对原始 FF 提升训练表现。",
        "本地审计未发现 ImageNet-1K 规模验证，因此只把它作为架构迁移证据。"
      ],
      "limitations": [
        "局部目标内部仍有反向计算，不能写成完全无梯度。",
        "任务与规模尚未覆盖 ImageNet-1K 或语言模型；局部目标、token 交互和最终读出成本需要公平核对。"
      ],
      "implications": [
        "FF 的局部目标可以进入注意力架构，但迁移并不自动解决跨层语义协调。",
        "它说明“跨模块无反向”与“完全无反向”是必须分开的两个研究问题。"
      ],
      "paper_url": "https://doi.org/10.1016/j.neunet.2025.107867",
      "source_note": "使用 Neural Networks 正式 DOI 版本和本地审计记录；对应作者预印本入口为 arXiv:2502.00571，正式版本优先。",
      "tags": [
        "Vision Transformer",
        "局部对比",
        "跨模块无反向"
      ],
      "doi": "10.1016/j.neunet.2025.107867",
      "related_ids": [
        "ff-2022",
        "scff-2025",
        "ff-cnn-2025",
        "forwardgnn-2024"
      ],
      "relevance_rank": 4,
      "work_family_id": "cff-vit-2025",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "摘要",
        "局部 ViT 训练方法",
        "视觉实验与限制"
      ]
    },
    {
      "id": "forwardgnn-2024",
      "title": "Forward Learning of Graph Neural Networks",
      "title_local": "图神经网络的前向学习",
      "short_title": "ForwardGNN",
      "year": 2024,
      "venue": "ICLR",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "architecture-extension",
      "routes": [
        "architecture-extension",
        "adjacent-forward-only"
      ],
      "level": 2,
      "tier": "bridge",
      "evidence_level": "B",
      "elevator": "把 forward-learning 的局部训练接口迁移到图神经网络，是 FF 之外但与其直接相邻的任务外延。",
      "problem": "图消息传递和图结构目标能否脱离全图端到端反向梯度，在模块边界执行前向式局部训练？",
      "mechanism": "为图网络模块设置局部或标签相关目标，图消息前向传播后在模块内更新，阻断全图反向链；它不明确等同于原始 FF 的 goodness 正负相位。",
      "mechanism_steps": [
        "执行图消息前向传播",
        "构造图模块局部目标",
        "在模块边界阻断全局梯度",
        "组合图表示并进行节点/图任务评估"
      ],
      "evidence": [
        "ICLR 2024 正式入口报告在多种图任务上比较前向学习与基线，说明局部前向思想可离开图像多层感知机。"
      ],
      "limitations": [
        "它是 forward-learning 桥接而非严格 FF goodness 变体，不能作为 FF 已迁移到图网络的直接证明。",
        "图任务、模型规模和局部标签设计仍有限，未覆盖通用图基础模型。"
      ],
      "implications": [
        "它帮助区分“FF 名称谱系”和“更宽的 forward-only 局部学习谱系”。",
        "图结构是检验局部目标是否真正携带结构信息的自然后续场景。"
      ],
      "paper_url": "https://openreview.net/forum?id=Abr7dU98ME",
      "source_note": "ICLR 2024 OpenReview 正式入口；被纳为桥接条目，未把标题中的 forward learning 改写为原始 FF 算法。",
      "tags": [
        "图神经网络",
        "消息传递",
        "桥接",
        "ICLR 2024"
      ],
      "related_ids": [
        "cff-vit-2025",
        "forward-projection-2026"
      ],
      "relevance_rank": 12,
      "work_family_id": "forwardgnn-2024",
      "source_tier": "T1",
      "verification_state": "abstract-checked",
      "evidence_vector": {
        "V": "V2",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "正式摘要",
        "图模块训练方法",
        "图任务实验"
      ]
    },
    {
      "id": "dtg-ff-2026",
      "title": "Synthetic Benchmarks Overstate Forward-Forward Scaling: Real-Data Limits of Layer-Local Training",
      "title_local": "合成基准高估了 Forward–Forward 的扩展性：层局部训练在真实数据上的边界",
      "short_title": "DTG-FF 公平审计",
      "year": 2026,
      "venue": "arXiv",
      "status": "preprint",
      "source_type": "benchmark",
      "primary_route": "evaluation-counterevidence",
      "routes": [
        "evaluation-counterevidence",
        "depth-collaboration"
      ],
      "level": 2,
      "tier": "core",
      "evidence_level": "C",
      "elevator": "用匹配骨干、真实数据和系统指标审计 FF 的扩展性主张，直接检验合成任务与理论内存优势是否能外推。",
      "problem": "纯局部 FF 在合成或小任务上的结果，是否会在真实图像、匹配预算和实际 GPU 系统中失效？",
      "mechanism": "它不是新的 FF 优化器，而是统一骨干、训练配方、数据和系统测量的审计框架；同时比较 BP-DeepSup、层局部 FF 及其真实数据表现。",
      "mechanism_steps": [
        "固定骨干、数据和训练配方",
        "在合成与真实图像上分别训练 BP 与 FF",
        "测量准确率、显存和吞吐而非只看局部更新",
        "检查层数与数据分布变化下的扩展性"
      ],
      "evidence": [
        "预印本报告匹配骨干下 BP 在 CIFAR-10/100 分别高 2.40/5.93 个百分点，ImageNet-100 中层局部方法约 49.4%，而典型 BP 基线高于 75%。",
        "在 8GB GPU 系统记录中，BP+梯度累积约 4.18GB、157 图像/秒，DTG-FF 约 7.90GB、138 图像/秒；这不支持局部更新必然带来系统优势。"
      ],
      "limitations": [
        "预印本审计结果依赖所选骨干、训练配方和基准，不能证明所有未来 FF 设计都失败。",
        "负面结果需要与各改进论文的自定义数据增强、宽度和读出协议逐项对齐。"
      ],
      "implications": [
        "它把“算法局部性”与“总系统资源优势”分开，是解释 FF 后续结果的关键反证。",
        "未来改进应优先报告同骨干真实数据和全栈预算，而不是只报告层内激活内存。"
      ],
      "paper_url": "https://arxiv.org/abs/2606.06539",
      "source_note": "arXiv:2606.06539 预印本；数值来自本地独立审计的正文和系统附录记录，正式出版状态截至截止日未确认。",
      "tags": [
        "公平基准",
        "真实数据",
        "显存",
        "吞吐",
        "反证"
      ],
      "related_ids": [
        "ff-cnn-2025",
        "bicovg-2026",
        "hcl-ff-2026",
        "forward-projection-2026"
      ],
      "relevance_rank": 10,
      "work_family_id": "dtg-ff-2026",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V4",
        "D": "D3",
        "P": "P1",
        "Q": "Q3"
      },
      "evidence_locations": [
        "CIFAR-10/100 表",
        "ImageNet-100 表",
        "8GB GPU 系统附录",
        "讨论"
      ]
    },
    {
      "id": "ff-cnn-2025",
      "title": "Training convolutional neural networks with the Forward–Forward Algorithm",
      "title_local": "使用 Forward–Forward 算法训练卷积神经网络",
      "short_title": "六层 CNN 反证",
      "year": 2025,
      "venue": "Scientific Reports",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "evaluation-counterevidence",
      "routes": [
        "evaluation-counterevidence",
        "architecture-extension"
      ],
      "level": 2,
      "tier": "core",
      "evidence_level": "A",
      "elevator": "在同一六层 CNN 上直接对照 BP 与纯 FF，给出深层信息协调不足的强负面证据。",
      "problem": "纯层局部 goodness 在卷积视觉任务中能否维持与同架构 BP 相当的判别信息？",
      "mechanism": "将类别模式注入输入形成正/负样本，各卷积层独立优化局部 goodness，并冻结层间梯度；同一骨干另用 BP 训练作直接对照。",
      "mechanism_steps": [
        "生成带空间标签的正负输入",
        "逐层优化卷积 goodness",
        "切断层间梯度并保持骨干一致",
        "报告 BP、两种纯 FF 设置的多次运行结果"
      ],
      "evidence": [
        "CIFAR-10 同一六层 CNN 中，BP 准确率为 85.4±0.4%，两种纯 FF 设置为 60.9±0.6% 和 68.6±0.5%。",
        "论文还观察到标签捷径与更慢收敛，直接把层间协调而不是单纯优化器列为瓶颈线索。"
      ],
      "limitations": [
        "研究集中在中小型卷积网络，不能排除更好的局部目标、宽度或硬件配方。",
        "结果是对两种纯 FF 设定的反证，不应外推为所有后续 FF 变体必然失败。"
      ],
      "implications": [
        "它是评估后续改进最重要的同骨干负面基线之一。",
        "任何声称“无反向即更好”的方法都应报告真实数据、同骨干 BP、训练预算和总系统成本。"
      ],
      "paper_url": "https://doi.org/10.1038/s41598-025-26235-2",
      "source_note": "Scientific Reports 2025 正式 DOI 版本；数值来自本地专项审计记录的同架构主实验，未把负面结果扩大到未测试的 FF 变体。",
      "tags": [
        "CNN",
        "CIFAR-10",
        "同架构对照",
        "负面证据"
      ],
      "doi": "10.1038/s41598-025-26235-2",
      "related_ids": [
        "ff-2022",
        "cff-vit-2025",
        "hcl-ff-2026",
        "dtg-ff-2026"
      ],
      "relevance_rank": 6,
      "work_family_id": "ff-cnn-2025",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D3",
        "P": "P2",
        "Q": "Q3"
      },
      "evidence_locations": [
        "主实验",
        "CIFAR-10 表",
        "标签捷径分析",
        "讨论"
      ]
    },
    {
      "id": "memristor-ff-2026",
      "title": "Forward-only learning in memristor arrays with month-scale stability",
      "title_local": "具有月级稳定性的忆阻器阵列前向式学习",
      "short_title": "忆阻器 FF",
      "year": 2026,
      "venue": "arXiv",
      "status": "preprint",
      "source_type": "paper",
      "primary_route": "hardware-deployment",
      "routes": [
        "hardware-deployment",
        "goodness-negative"
      ],
      "level": 3,
      "tier": "core",
      "evidence_level": "C",
      "elevator": "在 HfOx/Ti 忆阻器阵列中执行监督 FF 与 Competitive Forward，展示前向更新和月级器件保持性。",
      "problem": "FF 的局部正负更新能否脱离数字反向梯度，直接写入物理器件，并在长期保持性与编程能耗上可用？",
      "mechanism": "以双通道监督 FF 或单通道 Competitive Forward 产生前向局部更新，用低于 1 V 的单次复位脉冲和差分器件改变忆阻状态；不构造反向梯度。",
      "mechanism_steps": [
        "将正/负或竞争更新映射到器件差分状态",
        "用低压脉冲写入 HfOx/Ti 忆阻器",
        "在器件阵列上验证分类与写入稳定性",
        "分离报告多层软件仿真和单层硬件闭环"
      ],
      "evidence": [
        "预印本报告最多 8,064 个器件；熊图像头部分类中监督 FF 约 89.5%、Competitive Forward 约 89.6%、BP 约 90.0%。",
        "90 天后 3,456 个器件中约 90.7% 的漂移小于 3 μS；作者还报告相对写入/验证方案的编程能耗下降。"
      ],
      "limitations": [
        "依赖预训练 ResNet18，只使用 512 维特征中的前 32 维。",
        "多层实验的硬件写入与软件矩阵乘混合，完整硬件闭环仅单层；不能称为多层自治片上训练。",
        "能耗比较主要针对编程策略，不是包含数据搬运、矩阵乘、控制和校准的完整系统总能耗。"
      ],
      "implications": [
        "这是把 FF 从算法规则推进到物理器件接口的直接证据。",
        "它把后续问题从“有没有反向路径”转成“多层矩阵乘、读写、保持、校准和外围是否都能闭环”。"
      ],
      "paper_url": "https://arxiv.org/abs/2601.09903",
      "source_note": "arXiv:2601.09903v2 预印本；本地硬件分支候选包核验了器件、任务和保持性边界，未确认正式期刊版本。",
      "tags": [
        "忆阻器",
        "Competitive Forward",
        "器件保持",
        "硬件闭环",
        "预印本"
      ],
      "related_ids": [
        "ff-2022",
        "bicovg-2026"
      ],
      "relevance_rank": 11,
      "work_family_id": "memristor-ff-2026",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P1",
        "Q": "Q2"
      },
      "evidence_locations": [
        "Figs.3–5",
        "器件保持实验",
        "编程能耗比较",
        "Methods"
      ]
    },
    {
      "id": "forward-projection-2026",
      "title": "Closed-form feedback-free learning with forward projection",
      "title_local": "通过前向投影实现闭式无反馈学习",
      "short_title": "Forward Projection",
      "year": 2026,
      "venue": "Nature Communications",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "adjacent-forward-only",
      "routes": [
        "adjacent-forward-only",
        "evaluation-counterevidence"
      ],
      "level": 2,
      "tier": "bridge",
      "evidence_level": "B",
      "elevator": "用输入与标签的随机非线性投影生成层目标，再用闭式回归一次拟合权重，是解释 FF 边界的邻接方案。",
      "problem": "如果逐层 goodness 协调困难，能否在没有反馈误差传播的条件下直接构造隐藏目标并一次遍历求解？",
      "mechanism": "每层把突触前活动和标签通过随机投影组合成目标膜电位，累计 Gram 矩阵后用岭回归闭式求解权重；它改变了目标生成方式，而不是沿用原始 FF 正/负 goodness。",
      "mechanism_steps": [
        "联合投影输入与标签",
        "生成隐藏层目标活动",
        "累积 Gram 矩阵与局部统计",
        "闭式求解每层权重并按层推理"
      ],
      "evidence": [
        "Nature Communications 2026 正式论文在时序生物医学、少样本图像和标准数据上与局部监督/FF 等方法比较。",
        "独立审计记录指出其计算和内存要求与 BP 相近，不能仅凭“无反馈”宣称系统更省。"
      ],
      "limitations": [
        "闭式矩阵求逆、标签依赖和特定数据规模限制了通用性。",
        "它不是严格 FF 后继，现代大模型、开放词汇和长期在线学习尚未覆盖。"
      ],
      "implications": [
        "它提供了除正/负 goodness 以外的反馈自由目标生成路线。",
        "作为邻接对照，它提醒研究者：减少反向通信不自动减少总计算、存储或标签依赖。"
      ],
      "paper_url": "https://www.nature.com/articles/s41467-026-69161-1",
      "source_note": "Nature Communications 2026 正式论文；作为桥接条目纳入，依据正式方法、比较表和本地独立审计记录，不把它归入严格 FF 变体。",
      "tags": [
        "闭式回归",
        "随机投影",
        "无反馈",
        "桥接"
      ],
      "doi": "10.1038/s41467-026-69161-1",
      "related_ids": [
        "ff-2022",
        "forwardgnn-2024",
        "noprop-2026",
        "dtg-ff-2026"
      ],
      "relevance_rank": 13,
      "work_family_id": "forward-projection-2026",
      "source_tier": "T1",
      "verification_state": "full-text-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "方法",
        "局部目标与闭式解",
        "任务比较表",
        "资源分析"
      ]
    },
    {
      "id": "noprop-2026",
      "title": "NoProp: Training Neural Networks without Back-propagation or Forward-propagation",
      "title_local": "NoProp：不使用反向传播或前向传播训练神经网络",
      "short_title": "NoProp",
      "year": 2026,
      "venue": "Conference on Lifelong Learning Agents",
      "status": "peer-reviewed",
      "source_type": "paper",
      "primary_route": "adjacent-forward-only",
      "routes": [
        "adjacent-forward-only",
        "architecture-extension"
      ],
      "level": 2,
      "tier": "bridge",
      "evidence_level": "B",
      "elevator": "把网络拆成独立目标去噪块，连通常的层级前向依赖也被重构，但块内仍使用反向传播。",
      "problem": "能否不沿全网传播前向表征或反向误差，而让不同模块各自学习预设目标的去噪路径？",
      "mechanism": "为各块指定不同噪声级别的目标表示，每块只接收本地输入并在内部学习去噪；推理时按去噪链组合模块。",
      "mechanism_steps": [
        "生成分级噪声目标",
        "各块独立接收本地输入",
        "块内用局部 BP 学习目标去噪",
        "按去噪链执行推理"
      ],
      "evidence": [
        "正式 PMLR 论文在 MNIST、CIFAR-10 和 CIFAR-100 上验证独立块目标训练。",
        "其核心贡献是重构网络分解和跨块依赖，而非复现原始 FF 的 goodness 正负相位。"
      ],
      "limitations": [
        "块内仍用反向传播，不能算完全无 BP。",
        "固定目标表示可能削弱通常的层级特征学习；现代架构和大规模任务未知。"
      ],
      "implications": [
        "它是解释 FF 层间协调难题的另一条邻接路线：用预设目标分解网络，而不是让所有层共同形成 goodness。",
        "它进一步证明“无跨块反向”与“无任何反向”必须分别报告。"
      ],
      "paper_url": "https://proceedings.mlr.press/v330/li26a.html",
      "source_note": "PMLR 2026 正式入口；作为邻接桥接条目纳入，依据正式摘要/方法记录，未把块内 BP 隐去。",
      "tags": [
        "块分解",
        "去噪目标",
        "局部 BP",
        "桥接",
        "CLLA 2026"
      ],
      "related_ids": [
        "trifecta-2024",
        "forward-projection-2026",
        "dtg-ff-2026"
      ],
      "relevance_rank": 14,
      "work_family_id": "noprop-2026",
      "source_tier": "T1",
      "verification_state": "abstract-checked",
      "evidence_vector": {
        "V": "V3",
        "D": "D2",
        "P": "P2",
        "Q": "Q2"
      },
      "evidence_locations": [
        "正式摘要",
        "去噪块方法",
        "MNIST/CIFAR 实验",
        "局限讨论"
      ]
    }
  ],
  "stats": {
    "paper_count": 14,
    "route_count": 6,
    "level_count": 4,
    "nonempty_cluster_count": 8,
    "year_min": 2022,
    "year_max": 2026,
    "cluster_counts": [
      {
        "route": "adjacent-forward-only",
        "level": 2,
        "count": 2
      },
      {
        "route": "architecture-extension",
        "level": 2,
        "count": 2
      },
      {
        "route": "depth-collaboration",
        "level": 1,
        "count": 2
      },
      {
        "route": "depth-collaboration",
        "level": 2,
        "count": 2
      },
      {
        "route": "evaluation-counterevidence",
        "level": 2,
        "count": 2
      },
      {
        "route": "goodness-negative",
        "level": 0,
        "count": 1
      },
      {
        "route": "goodness-negative",
        "level": 2,
        "count": 2
      },
      {
        "route": "hardware-deployment",
        "level": 3,
        "count": 1
      }
    ]
  }
}