The ANM framework

Pipelines are usually judged by one final score. A wrong answer tells you something failed, not where: which input caused it, whether the information was lost in the carried state or ignored at the output, and whether the system is degraded or broken.

只看最终分数，只知道错了，不知道错在哪：是哪个输入，信息丢在中间状态还是读出没用上，是变差了还是已经坏了。

Forward: if the state moves but the output stays flat, the information arrived and the readout does not use it, or cancels it. Inverse: if two inputs reach the same state but give different outputs, the state is missing something the output depends on. For a declared observer the same test also selects: within a candidate set declared in advance, keep the candidates with no such violation and take the one with the fewest states (4.3).

正向：状态动了、输出不动，说明信息到了，但读出没用上（或被抵消）。逆向：两个输入到了同一个状态却给出不同输出，说明状态漏了输出所依赖的东西。声明观测者之后，同一检验还能做选择：在事先声明的候选集合里，保留没有这种违例的候选，取状态数最少的那个（见 4.3）。

Linearity is checked, not assumed: the slope measured with a push ε must match the slope with ε/2. The readouts are nested: ‘exactly right’ can only happen inside ‘still works’, so losing the first while keeping the second separates degraded from broken.

线性是检验出来的，不是假设的：用 ε 和 ε/2 测得的斜率必须一致。读出是嵌套的：“完全正确”只能发生在“还能用”之内，所以前者丢了而后者还在，就能区分“变差”和“坏了”。

64 sites on a ring, each coupled to four neighbours with delay τ, are driven by a sine. The retained state must include the history. Over 13 delays, measured amplitude and phase stayed within 2.51×10⁻³ (relative) and 0.74° of theory: a calibration of the measurement.

64 个位点的环，每个与 4 个邻居以延迟 τ 耦合，受正弦驱动，保留状态必须包含历史。13 个延迟上，测得的幅度和相位与解析解相差不超过 2.51×10⁻³（相对）和 0.74°。这是对测量本身的校准。

First declare the observer: what is read, which answers are allowed, and the boundary. ‘Still works’ = an allowed answer cleared the bar; ‘exactly right’ = it matches the key. The key grades only after the readout and never enters the evidence.

先写下观察者：读什么、允许哪些答案、边界在哪里。“还能用”是有答案过了门槛，“完全正确”是答案与答案标准一致。答案标准只在读出之后打分，从不进入证据。

The retained state is a candidate declared before the run; its choice is an experimental hypothesis, not established sufficiency. It is enough only if equal states always give equal readouts. With delay, two histories with the same present value but different pasts evolve differently, so the present value is not enough. A same-state violation shows what the state must separate.

For a declared observer the responses also select the state. Fix the readout, the pushes and the window. A candidate is rejected when identical states give resolved differences in output distributions. Then, within a candidate set declared in advance, the candidates with no observed same-state violation are kept, the one with the fewest states is selected, and it is fixed and validated on new comparisons. In the paper’s exact construction this gives the coarsest sufficient representation, 2 states. Limits: the candidate set is given, so this selects rather than discovers new variables, and such tests “constrain adequacy without uniquely identifying a missing variable”.

A model-based instance. The v2 draft has one model-based instance of this test, with the downstream model and its interface fixed. On recipient A only, 768 new calls (512 base + 256 control) reject a snapshot description: histories with the same snapshot but opposite routing differ by at least 0.8358 (largest probability difference). An association description chosen from declared candidates gets bounded support on four new histories and two continuation combinations: at most 0.0821, below the fixed margin 0.15. The broader development screen selected none, and the recipient-A scope was chosen after it. All 768 answers matched the reference, so support there coincides with the model answering correctly (our observation). The model is unchanged: this supports the analyst’s description, not a repair of the model.

The inverse loop, in the paper’s words. “Exactly equal retained states give a readout difference beyond measurement error” → “Reject sufficiency for these histories under the declared conditions” → “Separate the violating histories in a revised representation; test it with system and interface unchanged”. “Selection is within a supplied library, not discovery of a unique hidden variable”. In its broader development comparison “No candidate qualifies”; the restricted follow-up then gives each candidate its own outcome: the snapshot descriptions have rejected comparisons, every association-matched comparison has an upper bound below the margin, and “Full history has no matched-history comparison and remains uninformative”.

On TEDDY: E7 (registered, final). We registered the same three steps at TEDDY’s layer-11 cut, with the downstream component fixed (TEDDY’s layer 12, gene-mean pooling and our frozen head) and the same kind of rule (keep a candidate whose development differences stay within the tolerance; take the smallest); the third was not reached. The histories are exact mean-preserving state interventions. The declared library holds the layer-11 gene-mean, the gene-mean plus the six marker genes’ token states, and all token states. In the paper’s terms, the outcome is a rejection, as for its snapshot descriptions, together with a development comparison in which no candidate qualifies. Histories with the same layer-11 gene-mean gave readouts that differ beyond the tolerance on fresh site4 comparisons (median 0.125 [0.090, 0.161] of the measured NK–T gap, tolerance 0.05), and the marker-token augmentation was rejected too (0.122). No candidate passed in development, so no revised representation was validated. E7 →

保留状态是运行前声明的候选坐标，声明本身是实验假设，不等于充分。候选状态只有在“同一状态必给同一读出”时才够用。有延迟时，当前值相同但过去不同的两段历史会走向不同结果，所以只看当前值不够。一旦出现“同状态、不同读出”，就知道状态必须区分什么。

声明观测者之后，同样的响应还能选择保留状态：固定读出、推动和时间窗；同一状态下输出分布有可分辨差异的候选被否决；在事先声明的候选集合里，保留没有违例的候选，选出状态数最少的那个，固定后用新的比较验证。论文的精确构造由此得到最粗的充分表示，2 个状态。局限：候选集合是给定的，所以这是选择而不是发现新变量；这些检验“只约束充分性，不唯一确定缺失的变量”。

基于模型的实例：v2 草稿中有一项基于模型的此类检验，下游模型及其接口固定。仅针对接收者 A，768 次新调用（512 次基础 + 256 次对照）否决了快照描述：快照相同、路由相反的历史，最大概率差至少 0.8358。从声明候选中选出的关联描述，在四个新历史和两个后续组合上获得有界支持：至多 0.0821，低于固定容差 0.15。较广的开发筛选未选出任何候选，“仅接收者 A” 的范围在那之后确定。768 个回答全部答对，所以那里的“支持”与模型答对重合（我们的观察）。模型不变，支持的是分析者的描述，不是对模型的修复。

论文对逆向闭环的表述：若“完全相同的保留状态给出超出测量误差的读出差异”，就“在声明条件下否决这些历史的充分性”，再“用修订后的表示区分违反的历史，并在系统与接口不变的情况下检验”；选择只在给定的候选库内进行，不是发现唯一的隐藏变量；较广的开发比较中“没有候选合格”，限定后的后续比较再对每个候选分别给出结果：快照类描述有被否决的比较，每个关联匹配比较的上界都低于容差，全历史没有匹配历史的比较、无信息。TEDDY 上的 E7（预注册，已完成）在第 11 层切点、下游组件固定时按这三步、用同类规则（开发阶段差异不超过容差的候选保留，取最小者）预注册（第三步未进行）：历史是精确的保均值状态干预；gene-mean 在新的 site4 比较上被否决（中位差异 0.125 [0.090, 0.161]，容差 0.05），加六个标记基因 token 状态的候选也被否决（0.122）；开发阶段没有候选通过，因此没有验证任何修订后的表示。

Swapping two requests’ warehouses should move the answer 14→9; the model stayed 9→9. A request–return join, fixed in advance, restored 14→9; three controls stayed 9→9. Exploratory, one known case; calibration missed (21/24 vs 22/24); ordinary diagnosis picks the same join.

交换两个请求的仓库，答案应从 14 变成 9，模型却一直是 9→9。按事先固定的规则把每个请求与它的返回结果连接起来后，恢复为 14→9；三个对照仍是 9→9。这是探索性结果：一个已知案例，校准未达标（21/24 对 22/24），普通诊断也会选同一个连接。

Question

a written lineage question (soft, strict or B/T-priority in v2; Q1, Q2, Q3 on five classes in v3).

Sources

the head-predicted panel proteins (9 in v2, 12 in v3), all entering at t = 0.

Retained state

a declared candidate: TEDDY’s gene-mean embedding, tested rather than assumed sufficient (v3 E5-M: inconclusive for the one observer tested; E7 ran the reject → select → validate test at the layer-11 cut and selected nothing). Mode B works on the head’s outputs; Mode A steps through TEDDY’s layers (v3 E5).

Readout

call or no call, graded by measured protein.

问题：写下的谱系问题（v2 为宽松、严格、B/T 优先；v3 为五类上的 Q1、Q2、Q3）。源：head 预测的面板蛋白（v2 为 9 个，v3 为 12 个），都在 t = 0 进入。保留状态：声明的候选状态，即 TEDDY 的基因均值嵌入，需要检验而非假定充分（v3 E5-M：对所测的一个观察者判定为不确定；E7 在第 11 层切点运行了“否决 → 选择 → 验证”检验，什么也没选出）；Mode B 作用在 head 的输出上，Mode A 以 TEDDY 的层为步（v3 E5）。读出：判或不判，由实测蛋白打分。

v2 prototype of a sufficiency test, with TEDDY’s embedding as the declared candidate state: for 453 NK–T pairs that TEDDY’s embedding nearly merges, our head’s predicted gaps are a quarter to a third of the measured ones (CD335 0.88), right in direction. Random NK–T pairs: 0.8–1.5. Lost in the embedding, or unused by our head? Mode A probes on the frozen embedding: a linear probe keeps about as much as our head, but an MLP probe keeps about twice as much for CD56, CD94 and CD3, and gene-token states keep more than the gene-mean. v2 read this as: part of the loss is in our head’s readout and in mean pooling; part may not be in the detected RNA.

Superseded by v3 E3The registered test rejected “the NK–T loss is in the readout or pooling and is repairable on frozen TEDDY”: a layer-mean MLP (R1) and attention pooling over layer-12 gene tokens (R2) both told NK from T less accurately than our head (−0.0409 and −0.1925 at coverage 0.9, losses). On 253 within-donor pairs the head’s gap ratio is 0.1169 on flagged vs 0.3985 on unflagged pairs, with overlapping intervals and mostly from gdT CD158b+ pairs in the donor with the weak answer key; without them 0.4729 vs 0.5137. E5-M then tested the gene-mean against a token observer: inconclusive, for that one observer. E3 →

充分性检验：在 TEDDY 嵌入里几乎重合的 453 对 NK–T 细胞中，我们的 head 预测的差距方向正确，但只有实测差距的四分之一到三分之一（CD335 为 0.88）；随机 NK–T 对为 0.8–1.5。是嵌入丢了差别，还是 head 没用上？冻结嵌入上的 Mode A 探针：线性探针保留的与 head 相当，但 MLP 探针对 CD56、CD94、CD3 约保留两倍，基因 token 状态又比基因平均保留更多。v2 的解读是：一部分损失在 head 的读出和平均池化，一部分可能不在检出的 RNA 里。v3 E3（预注册）拒绝了“损失位于读出/池化并可在冻结 TEDDY 上修复”：两种读出的 NK/T 准确率均不如 head；头部在近邻配对上压缩更甚只是描述性结果。

TEDDY’s layers are a real processing order, so a push can be followed layer by layer (Mode A). E5 pushed each panel or NK/T gene’s input token along its own embedding on 478 unseen-donor cells (7,862 cases), carried the exact first-order change through each of the 12 post-norm layers with Jacobian-vector products, and projected it on the training NK-minus-T direction. The registered question: in which layer does the NK–T component shrink most, and is it the layer where a linear NK–T probe’s gap ratio drops most?

The registered gate failed in float32; float64 passes. Before any layer is read, finite differences must agree with the JVP in at least 95% of cases. In float32 at ε = 1e-3 they agreed in 0.854; the float64 version of the same check passes in all 79 cases, so the registered verdict attributes the failure to float32 rounding. No amendment adopting the float64 path was committed before site4, so the verdict stands: no layer is localised.

Descriptive only: for a push along the training NK − T input direction, the largest single-layer drop of its NK–T component is at layer 2 (median step −0.217 [−0.229, −0.197]); look-alike cells do not damp it more than random NK/T cells, and the head does not pass less of it than the layer-12 state.

E5（预注册）：沿基因输入 token 推动，用 Jacobian-向量积跟着 TEDDY 的 12 层走，看 NK–T 分量在哪一层收缩最多。注册的有限差分检验在 float32、ε = 1e-3 下通过率 0.854 < 0.95（float64 全部通过），按规则停止，未定位任何层；次要分析仅为描述性。

The ANM paper’s inverse loop (4.3), run on TEDDY. The downstream component is fixed and never trained: the token states leaving TEDDY’s layer 11 → TEDDY’s own layer 12 → the mean over real tokens → our frozen head, read on CD56, CD94, CD335 and CD3. Layer 12 has no positional input, so it sees only the set of token states. The histories are exact mean-preserving state interventions: disjoint pairs of tokens other than the six marker genes (G: NCAM1, KLRD1, NCR1, CD3E, CD3D, CD3G) have their states replaced by their average, for 1/32, 1/8 or 1/2 of those tokens, plus a fresh 1/4 in confirmation. Addendum E7.json version 2 (sha256 c35e91c5…) was pushed at 22:25:53 UTC, before any development run. The selection records were pushed at 22:40:19, and the site4 confirmation started at 22:40:20 by the local clock.

Step 1, reject: done. On fresh site4 cells, fresh pairs and a fresh size, histories with exactly the same layer-11 gene-mean give readouts that differ beyond the tolerance. The median is 0.125, and in both donors the interval lies above 0.05. Holding the six marker genes’ token states fixed as well does not remove the difference (0.122). Changing only the marker states, at a fixed gene-mean, moves the readout by a median 0.013. So for this downstream component and these interventions, what layer 12 and the head use is spread over the other tokens’ states: it is not held by the gene-mean, nor by the marker tokens. The controls show the comparisons could see a change. Clamping the gene-mean by the training NK − T difference moves the readout by 0.261, and delivering that shift through the patched tokens alone moves it by 0.260.

Step 2, select: no revision. On the validation donor, a candidate is kept if the 95th percentile of D is at most 0.05. The gene-mean scored 0.276 and the marker-token augmentation 0.256. The declared follow-up, with the NK–T score as readout, scored 0.236 for both. None was selected. In the paper’s terms this parallels its broader development comparison, in which “No candidate qualifies”; in the paper, a recipient-A scope chosen afterwards then led to a supported description, which E7 did not attempt. Step 3, validate: not reached. No revised representation is validated.

Secondary. The difference grows with the patch size: the site4 median is 0.022 at 1/32 (below the tolerance), 0.046 at 1/8, 0.073 at 1/4 and 0.125 at 1/2. It is larger in NK cells (0.141) than in T cells (0.091). Limits. The patches are exact state interventions at one cut, off the data manifold, not biological variation. The test covers one downstream component, a small declared library and 2 primary donors. It does not explain the NK–T loss or say what the RNA contains. The design was revised twice after code tests on training cells and once after a val smoke-pool check, all disclosed in the addendum.

E7（预注册，判定 REJECTED_NO_REVISION）：在 TEDDY 第 11 层切点运行论文的逆向闭环，下游组件固定（第 12 层 + gene-mean 池化 + 冻结 head），历史是精确的保均值状态干预。第一步（否决）完成：gene-mean 相同的历史在新的 site4 比较上读出差异超过容差（中位数 0.125 [0.090, 0.161]），固定六个标记基因的 token 状态也不能消除差异（0.122）；只改变标记基因状态时读出几乎不动（0.013）。第二步（选择）没有得到修订：开发阶段 95 分位数为 0.276、0.256，事先声明的后续为 0.236、0.236。第三步（验证）没有进行，没有验证任何修订后的表示。差异随补丁幅度增大，NK 大于 T。局限：切点上的状态干预（偏离数据流形），不是生物学变异；一个下游组件、一个小的候选库、2 个主要供体；不解释 NK–T 损失。

Mode A treats TEDDY’s transformer layers as the steps. The per-gene residual stream (and its gene-mean, which our head reads) is a candidate retained state, to be tested against a declared readout (and, within a declared candidate set, selected), not assumed sufficient; attention couples genes. v2 probes, on the frozen embedding: a linear NK-vs-T probe separates NK from T at every layer (held-out AUC 0.991–0.997). On the 453 look-alike pairs our head keeps 0.24 / 0.31 / 0.88 / 0.27 of the measured CD56 / CD94 / CD335 / CD3 gap and a linear probe on z about the same (0.28 / 0.40 / 0.40 / 0.28), but an MLP probe on the same z keeps about twice as much (0.47 / 0.59 / 0.74 / 0.61; MLP − head interval above 0 for CD56, CD94 and CD3 at every depth). At token level (probes fit on 990 other site4 NK/T cells, scored on the 483 pair cells), the states of 13 NK/T gene tokens keep more than the gene-mean of the same forward pass (layer 12, MLP, tokens + gene-mean 0.58 / 0.62 / 0.72 / 0.56 vs gene-mean 0.41 / 0.43 / 0.49 / 0.45), and about as much already at the input layer: the information is mostly which genes are detected and at what rank; the gene-mean keeps less of it, and TEDDY’s layers neither add nor remove much of it. Even the best probe keeps only about half to three-quarters, and key genes are often not detected (CD3E among the tokens in 45% of the NK and 60% of the T pair cells). v2 read this as: part of the loss is in our head’s readout and in mean pooling, and part may not be in the detected RNA (caveats: one site; probes are not the head’s objective; within-site protocol for the token probes; some intervals overlap; the pairs were chosen for closeness in z).

v3 · registeredE3 tested the repair reading and rejected it: a layer-mean MLP and attention pooling over layer-12 gene tokens both told NK from T less accurately than our head. E5 followed a push through the layers with Jacobian-vector products and stopped at its derivative check (float32; float64 passes). E5-M, the sufficiency test of the gene-mean, was inconclusive for the one observer tested. E7 ran the paper’s inverse loop at the layer-11 cut with the downstream component fixed: the layer-11 gene-mean was rejected, and no revision was selected. Gene perturbations beyond E2’s are not done.

Mode A 把 TEDDY 的 transformer 层当作步：按基因的残差流（及 head 读取的基因均值）是候选保留状态，需要用声明的读出检验（并在声明的候选集合内选择），而非假定充分；注意力让基因之间相互耦合。目前冻结嵌入上的探针：线性 NK/T 探针在每一层都能区分 NK 与 T（留出 AUC 0.991–0.997）。在 453 对相似细胞上，我们的 head 保留实测 CD56 / CD94 / CD335 / CD3 差距的 0.24 / 0.31 / 0.88 / 0.27，z 上的线性探针大致相同（0.28 / 0.40 / 0.40 / 0.28），而同一 z 上的 MLP 探针约为两倍（0.47 / 0.59 / 0.74 / 0.61；CD56、CD94、CD3 的 MLP − head 区间在每一层都大于 0）。在 token 层面（探针在另外 990 个 site4 NK/T 细胞上拟合，在 483 个配对细胞上打分），13 个 NK/T 基因 token 的状态比同一次前向的基因平均保留更多（第 12 层 MLP，token + 基因平均 0.58 / 0.62 / 0.72 / 0.56，基因平均 0.41 / 0.43 / 0.49 / 0.45），在输入层就已相当：信息主要是检出了哪些基因、排在第几；基因平均保留得更少，TEDDY 的各层既不明显增加也不明显减少。最好的探针也只保留约一半到四分之三，关键基因常常没有检出（CD3E 只出现在 45% 的 NK 和 60% 的 T 配对细胞的 token 中）。v2 的解读是：一部分损失在 head 的读出和平均池化，一部分可能不在检出的 RNA 里（单一 site；探针不是 head 的训练目标；token 探针在 site4 内部拟合；部分区间重叠；这些对按 z 中的接近程度选出）。v3：E3 拒绝了“可在冻结 TEDDY 上修复”；E5 用 Jacobian-向量积跟踪各层，停在导数检验；E5-M（基因均值的充分性检验）对所测的一个观察者判定为不确定；E7 在第 11 层切点、下游组件固定时运行了论文的逆向闭环，否决了第 11 层 gene-mean，且未选出修订。