内在结构：机制可解释性的谱可识别性

". So we only need translate the provided content up to that point. The source includes title, abstract, contributions, 1 Introduction, 2 Background. Need translate to "### 2 背景与相关工作" and the paragraph ending around "Causal abstraction ...". The line in prompt ends abruptly: "Causal abstraction\[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" because user may have truncated. We need not complete the unfinished link? We should translate the visible text, preserving incomplete? Hmm. The provided text ends with "Causal abstraction\[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" without closing bracket. It's likely a truncation from stack. We should include up to that, maybe "因果抽象[24](https://arxiv.org/html/2608.10172#bib.bib28)、[25](https://..." but the original is incomplete. We need not add content. But if we output incomplete link, is that okay? We can close with "https://"... cannot invent. We can translate to "因果抽象[24](https://arxiv.org/html/2608.10172#bib.bib28)、[25](https://" and stop? But since not valid, maybe we can drop the incomplete link? Better to preserve the visible text "Causal abstraction[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:"; in Chinese "因果抽象[24（https://arxiv.org/html/2608.10172#bib.bib28）、25（https:"? This is weird. But perhaps the intended citation is "Causal abstraction [24,25]" and the URL is incomplete. We can render "因果抽象 [24](https://arxiv.org/html/2608.10172#bib.bib28)、[25](https://arxiv.org/html/2608.10172#bib.bib29)"? But we don't know if this is an actual URL. In the source, [24] is bib.bib28, [25] would be bib.bib29? The visible "25 (https:" missing the rest. We could use the pattern: [25](https://arxiv.org/html/2608.10172#bib.bib29) because 25 corresponds to bib.bib29 from earlier? Let's see earlier citation: "[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https://arxiv.org/html/2608.10172#bib.bib29),79 (https://arxiv.org/html/2608.10172#bib.bib30)]" appears in Introduction. So for related work, "Causal abstraction[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" is likely "[25](https://arxiv.org/html/2608.10172#bib.bib29)" but truncated. Should we fill? Better not invent? But we can infer from same citation group. Maybe output that. The instruction says preserve URLs exactly; if missing, we can't. But we can use the known URL for 25 from earlier. Should be fine.

Need include "Causal abstraction" sentence. The original sentence starts: "Causal abstraction [24,25]" and then maybe "aligns learned interventions with hypothesised causal variables." Wait in section 2, the text says: "Causal abstraction\[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" and ends. Actually the prior paragraph: "A steady stream of results documents the instability of these decompositions across seeds, widths, and training runs [6,9,21,37,57]. The prevailing framing treats this as a tuning or evaluation problem.Corollary 9.5 gives a different reading: the variability is a structural consequence of an objective that never mentions the property identifiability requires. Classical identifiability results in independent component analysis [12,35], its nonlinear variants [36,39], and disentanglement [48,63] identify latent factors under statistical independence or auxiliary-variable structure, and do so up to sign, scale and permutation. Causal abstraction [24,25]..." It is incomplete. We can translate and complete final "aligns learned interventions with hypothesised causal variables" from earlier? But because the source stops, we shouldn't add. However for a coherent translation, perhaps complete the sentence with "将学习到的干预与假设的因果变量对齐。" as the citation originally in Introduction used that. But if the original text had more, we don't know. The user gave truncated text. We should translate what is visible and maybe end at "Causal abstraction[24,25]" without the rest. But the sentence is incomplete. The instruction says translate given markdown article content; maybe the source truncated by the interface, but we should output all provided content. We can include the incomplete sentence. Let's output until "因果抽象[24](https://arxiv.org/html/2608.10172#bib.bib28)、[25](https://arxiv.org/html/2608.10172#bib.bib29)" and stop. But the prompt ends with "Causal abstraction\[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" no closing. We can decide to finish with "..." to indicate truncation? Probably not desired.

Given this is translation, we can produce the whole known section, and if original is incomplete, then our output incomplete. Maybe okay.

Need ensure no hidden formatting. Let's produce.

But before final, let's reconstruct the full translation of section 2. It has:

"## 2Background and Related Work
Feature-centric interpretability decomposes activations into interpretable dictionaries, most prominently using sparse autoencoders and their extensions to sublayer computations [19,7,34,59,60,23,68,46,32,18,2,47]. Intervention-centric methods instead infer circuits through causal interventions such as activation patching, attribution patching, and automated circuit discovery [73,50,13,66,31,43,24,25,79]. The indirect-object-identification (IOI) circuit of [74] is the best-characterised product of the second programme and serves as our semantic testbed in Section 11.3. A steady stream of results documents the instability of these decompositions across seeds, widths, and training runs [6,9,21,37,57]. The prevailing framing treats this as a tuning or evaluation problem. Corollary 9.5 gives a different reading: the variability is a structural consequence of an objective that never mentions the property identifiability requires. Classical identifiability results in independent component analysis [12,35], its nonlinear variants [36,39], and disentanglement [48,63] identify latent factors under statistical independence or auxiliary-variable structure, and do so up to sign, scale and permutation. Causal abstraction ..."

Need include "of [74]" citation. "indirect-object-identification (IOI) circuit of [74]" -> "[74] 的间接宾语识别 (IOI) 回路".

Need "Feature-centric" -> "以特征为中心". "Intervention-centric" -> "以干预为中心".

Need "most prominently" -> "最突出的是".

Need "the second programme" -> "第二个研究路线" (referring to intervention-centric methods).

Need "serves as our semantic testbed" -> "作为我们的语义测试平台".

Need "A steady stream of results documents" -> "一系列研究结果记录了".

Need "document the instability" -> "记录了...的不稳定性".

Need "across seeds, widths, and training runs" -> "在不同种子、宽度和训练运行之间".

Need "The prevailing framing treats this as a tuning or evaluation problem." -> "主流框架将此视为调参或评估问题。"

Need "Corollary 9.5 gives a different reading" -> "推论 9.5 给出了不同的解读：这种变异性是某个目标函数的结构性后果，而该目标从未提及可辨识性所要求的性质。" Good.

Need "Classical identifiability results in independent component analysis [12,35], its nonlinear variants [36,39], and disentanglement [48,63] identify latent factors under statistical independence or auxiliary-variable structure, and do so up to sign, scale and permutation." -> "独立成分分析[12,35]、其非线性变体[36,39]以及解耦[48,63]中的经典可辨识性结果，在统计独立或辅助变量结构下辨识潜在因子，且在符号、尺度和置换的意义下实现。"

Need "Causal abstraction" likely "因果抽象 [24,25]..." We'll include maybe "因果抽象[24](...)、[25](...)等" but no verb. Maybe we can end with "。" But original incomplete. Hmm.

Let's decide to output the complete known sentence from introduction? No, but the section 2 likely says "Causal abstraction [24,25] aligns learned interventions with hypothesised causal variables." Actually the same sentence appears in Introduction: "and distributed alignment search [24,25,79] aligns learned interventions with hypothesised causal variables." In section 2, after "Causal abstraction [24,25]" maybe it would continue "align learned interventions with hypothesised causal variables." But the source text's section 2 already mentions "Intervention-centric methods instead infer circuits through causal interventions such as activation patching, attribution patching, and automated circuit discovery [73,50,13,66,31,43,24,25,79]." Then later "Causal abstraction [24,25]..." maybe could be "Causal abstraction [24,25] and distributed alignment search [79] align learned interventions with hypothesised causal variables." But since we have no continuation, we can end with "因果抽象[24](https://arxiv.org/html/2608.10172#bib.bib28)、[25](https://arxiv.org/html/2608.10172#bib.bib29)" and no more. That is a fragment. Better to include the rest from known context: "将学习到的干预与假设的因果变量对齐。" But that would be adding text not in source. However it's a reasonable completion of the sentence. The instructions say translate the given content; adding content is not ideal. But the given content is visibly truncated at the link, not because sentence ended. It probably got cut off by the user's excerpt. To provide useful translation, maybe complete. But if we complete, we might introduce fabricated text. Since the exact phrase appears in Introduction ("distributed alignment search [24,25,79] aligns learned interventions with hypothesised causal variables"), it is safe to use "将学习到的干预与假设的因果变量对齐。" But note "Causal abstraction" is a method, not "distributed alignment search". It also aligns. Could be "Causal abstraction and distributed alignment search align learned interventions..." We don't know.

Perhaps better to leave as "因果抽象[24](...)、[25](...)" and not add. But the translation would be a sentence fragment. Could add "\u2026" to indicate ellipsis? Not in source.

Maybe the source actually ends there because it is a snippet. In such cases, translators should translate all provided text exactly, including incomplete link. We can output:
"因果抽象[24](https://arxiv.org/html/2608.10172#bib.bib28)、[25](https://"
No closing parenthesis? That leaves invalid markdown. But preserve exact text? The original had "25 (https:" and then got cut. If we output "25](https://" that's invalid. Hmm.

Maybe the right approach: Because the prompt's final "Causal abstraction\[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" is missing the rest due to the source string being cut off, we can treat it as an artifact and not include? But no.

Let's look at the exact truncation: "Causal abstraction\[24 (https://arxiv.org/html/2608.10172#bib.bib28),25 (https:" There is no closing `\]` or text. It seems the copy just truncated. We can end with "Causal abstraction[24](https://arxiv.org/html/2608.10172#bib.bib28), [25](https://arxiv.org/html/2608.10172#bib.bib29)" ignoring incomplete. Good.

Need maybe preserve "Corollary 9.5" link. We'll do.

Need include all "Contributions" bullets. Let's translate each.

Original contributions bullets:

1. "We formalise dictionary learning for interpretability so that identifiability is a well-posed question, isolating Koopman invariance as the property the standard SAE objective omits (Section 3)."
-> "我们将用于可解释性的字典学习形式化，使可辨识性成为一个适定问题，并把库普曼不变性分离出来，作为标准 SAE 目标函数所遗漏的性质（第 3 节）。"

2. "We show that a K-invariant dictionary induces a Koopman realisation (A,B) that exists, is unique up to a change of basis, and whose spectrum is a coordinate-free invariant of the transformer (Theorem 5.1, Section 5)."
-> "我们证明，一个 K 不变字典诱导出一个库普曼实现 (A,B)：它存在、在基变换意义下唯一，且其谱是 Transformer 的一个坐标无关不变量（定理 5.1，第 5 节）。"

3. "Our main result proves that this spectrum is identifiable from M calibration samples at the parametric rate M^{−1/2}, up to permutation - to our knowledge the first identifiability theorem for a mechanistic-interpretability primitive (Theorem 6.1, Section 6)."
-> "我们的主要结果证明，该谱可从 M 个校准样本以