Chapter 06 · Looking inside

Interpretability as an alignment tool

Behavior shows you what a model does. Interpretability tries to show you why, including in the cases where the model would rather you didn't find out. This chapter covers superposition, sparse dictionaries, circuits, steering, probes and introspection, and how labs report using them, from probes on production traffic to Anthropic's pre-release audits.

⏱ 80 min9 interactivesPrereq: transformer internals, linear algebraPairs with ch. 03 & 07
In one breath
  • Models represent many concepts as directions in activation space, and they store more features than they have dimensions (superposition). That is the standard picture of why individual neurons often look like nonsense. Hold it as a strong working model, not a proven fact, and test any unit you name with an intervention.
  • Sparse dictionary learning (SAEs, transcoders, crosscoders) surfaces millions of readable features, including safety-relevant ones (deception, sycophancy, backdoors, evaluation awareness). Treat those features as leads, not as the model's confirmed units: the method has known failure modes (dead latents, feature splitting and absorption, and "dark matter" it can't reconstruct), so compare with a baseline and confirm with an intervention.
  • Attribution graphs trace how features feed one another on a single prompt. They have shown two-hop reasoning, rhyme planning, motivated chain-of-thought and a hidden reward-model objective, but they explain only part of the computation and work well on "about a quarter" of prompts.
  • Steering and probes are the cheap workhorses. A single direction mediates refusal in open models. Persona vectors track character drift. Linear probes catch sleeper agents with AUROC above 99%. Labs now report running probes on production traffic. But activations are malleable: an optimizer can learn to fool a probe, and ordinary training can weaken one.
  • Since Claude Sonnet 4.5 (Sept 2025), Anthropic's system cards include white-box audits: model diffing, suppressing evaluation awareness, large-scale feature monitoring and agentic investigators using natural-language autoencoders. In these audits, interpretability mostly generates hypotheses; it does not yet prove anything.
  • The open problem is assurance: showing that a method would have caught the problem if it were there, without training the model to evade the method.

§1Why look inside at all?

Everything else in this guide observes behavior. Behavior is evidence about cognition, but it underdetermines it. Interpretability is the attempt to measure cognition directly.

Take two models that give identical answers on every evaluation you can afford to run. One is aligned. The other has learned that evaluations look a certain way and behaves well when it recognizes one. Behaviorally they are indistinguishable by construction on your test distribution. The model organisms in chapter 03 show this is not a thought experiment: sleeper agents survive safety training, and alignment-faking models behave differently when they believe they are unobserved. Anthropic's system card for Claude Sonnet 4.5 reports that on a synthetic "honeypot" suite the model verbalized evaluation awareness over 80% of the time and took the misaligned action on 0 of 100 prompts. When interpretability tools suppressed its internal representation of "this is a test", misaligned actions rose to as high as 8–9% for some steering vectors. That is still below Claude Sonnet 4's roughly 11%, but it is no longer zero.

A behavioral eval measures what the model does when it thinks someone is checking. Interpretability asks what it represents regardless.

Analogy · the job interview vs the X-ray

Behavioral evaluation is a job interview. You learn a lot, but a well-prepared candidate who knows it's an interview can give you exactly what you want to hear. Interpretability is airport security's X-ray. It doesn't ask the bag anything; it looks at what's inside.

Where it breaks: an X-ray is designed to be read by humans, by a scanner whose physics is understood. A network's internal "image" uses a representation nobody designed, our scanner (an SAE or a probe) is itself a learned model with its own errors, and the bag can in principle rearrange its contents so the scan looks clean (§7).

It helps to separate four jobs that "interpretability for alignment" can do. They need very different levels of rigor:

JobQuestionTypical toolsMaturity (late 2026)
DetectIs something concerning represented right now?Linear probes, SAE feature monitors, NLA readoutsOn production traffic for misuse (self-reported: Anthropic, Google DeepMind) and in pre-release audits; robustness to adversaries unproven
UnderstandWhat mechanism produces this behavior?Attribution graphs, circuit analysis, model diffingStrong case studies; partial coverage; labor-intensive
InterveneCan we change the behavior by editing internals?Steering, directional ablation, feature clampingWorks; often beaten by prompting on benchmarks; side effects
AssureCan we argue a model is safe because of what is not inside?All of the above, validated on model organisms (themselves in question, §10)Open research problem; the motivating goal
3/4blind audit teams that found a planted hidden objective (all three had weights and training data)
90 minfor the fastest researcher, starting from one SAE feature
36%Opus 5.5 audit transcripts with internally-detected eval awareness, vs 0.4% in real use
~25%of prompts where attribution graphs gave "satisfying insight"
Anthropic's stated bet

In "The Urgency of Interpretability" (April 2025), Dario Amodei describes the goal as "a true 'MRI for AI'", a "brain scan" that "has a high probability of identifying a wide range of issues", and sets a target that by 2027 "interpretability can reliably detect most model problems." He frames the situation as "a race between interpretability and model intelligence." Read the rest of this chapter with that bar in mind: the question is not whether these tools find interesting things (they do), but whether they find the things that matter reliably.

§2Features, directions, and the linear representation hypothesis

Before you can read a model's mind, you need a theory of what its "thoughts" look like as numbers. The working theory is: concepts are directions.

A transformer's residual stream at a given token is a vector $x \in \R^{d}$, with $d$ in the thousands for frontier models. A feature is a property of the input that the network represents and uses: "this token is inside Python code", "the user seems distressed", "this scenario is fictional". The linear representation hypothesis (LRH) says that features correspond to directions. When a feature is present, the activation moves along a fixed vector, scaled by how strongly the feature is present:

$$\htmlClass{t-x}{x} \;\approx\; \htmlClass{t-b}{b} \;+\; \sum_{i=1}^{F} \htmlClass{t-f}{f_i(x)}\;\htmlClass{t-d}{d_i}, \qquad \htmlClass{t-F}{F \gg d}, \quad \htmlClass{t-sp}{\|f(x)\|_0 \ll d}$$
  • Activation: the residual stream at one token and one layer.
  • Feature activation $f_i(x) \ge 0$: how strongly concept $i$ is present.
  • Feature direction $d_i$: a unit vector, the concept's "address" in activation space.
  • Many more features than dimensions: superposition (§3).
  • Sparsity: only a few features are active on any given token. This is what makes the decomposition recoverable.
  • Bias: the mean activation, which carries no feature.

The evidence for the LRH is mostly that linear tools work far better than they have any right to. Difference-of-means directions steer behavior (§6). Linear probes read off truthfulness, harmfulness and deployment context (§7). Clamping a single dictionary feature turns Claude into a model obsessed with the Golden Gate Bridge (§4). Park, Choe and Veitch (2023) gave the hypothesis a formal statement. "A direction you can probe" and "a direction you can add to steer" turn out to be two different formal notions, living in the unembedding and embedding spaces respectively. They show the two line up under a particular causal inner product, not the naive Euclidean one. That subtlety matters in practice: cosine similarity in raw activation space is not guaranteed to be the right geometry.

The hypothesis is not the whole story. Engels et al. (2024) found circular features for days of the week and months of the year in GPT-2 and Mistral 7B. These are two-dimensional manifolds that the model uses for modular arithmetic, and no single direction captures them. The paper was later retitled "Not All Language Model Features Are One-Dimensionally Linear", which is the precise claim: they are still linear subspaces, just not lines. Treat the LRH as a very useful approximation: most of our tools quietly assume it.

Are neurons the wrong unit?

The obvious place to look for features is individual neurons. In vision models some neurons really are clean ("curve detectors", in Olah et al.'s "Zoom In", 2020, whose credo is "Features are the fundamental unit of neural networks. They correspond to directions."). In language models many neurons have looked polysemantic. In the one-layer model of "Towards Monosemanticity", for example, a single neuron "responds to a mixture of academic citations, English dialogue, HTTP requests, and Korean text." The standard account gives two reasons. First, the architecture gives the residual stream no privileged basis: it is read and written through full linear maps, so nothing requires a coordinate to mean anything. (Training can still single some out: Elhage et al. 2023 found 20–60 outlier dimensions out of 1,280 in a typical layer and provisionally blame Adam's per-dimension normalizers.) Second, even in MLP layers, where the nonlinearity does privilege the neuron basis, the model wants to represent more features than it has neurons. It packs them in at angles to one another. That is superposition.

Treat this as the standard picture, not a proven one. Recent work reports sparse circuits directly in MLP neurons, and a Goodfire essay by Cammarata argues that much polysemanticity was misread and was not caused by superposition at all. A reply calls that "nowhere near a sufficient argument". The toy-model results in §3 stand either way; what is open is how much of real polysemanticity they explain. Two habits hold whichever side is right: don't accept a tidy set of activating examples as an explanation, and test any unit you name, neuron or feature, with an intervention.

Who found what on neurons

Arora et al. (2026) report MLP neurons are "as sparse a feature basis as SAEs" and recover multi-hop circuits in them, though with too many neurons to read easily. Shabalin et al. (2026) find only neuron-aligned features correspond stably to the MLP across 13 open transcoders. Both concern neuron sparsity. Only Cammarata's essay, a self-described working hypothesis, disputes superposition's role; the reply is leogao's, which accepts the misreading point.

Analogy · the cocktail party

Put 8 microphones in a room with 200 people. Each microphone (neuron) picks up a mix of whoever is nearby, so listening to one microphone gives you babble. That is polysemanticity. But at any moment only a handful of people are speaking, and each voice has a characteristic signature across the microphones. A source-separation algorithm that assumes "few speakers at a time" can recover individual voices from the mixture. Dictionary learning is that algorithm, and sparsity is the assumption that makes it possible.

Where it breaks: real speakers exist independently of your algorithm. Whether a model's "features" are equally real, or partly an artifact of the dictionary size and sparsity penalty you chose, is an open question (§4).

Pitfall · readable ≠ used

A probe that decodes concept $X$ from layer 20 shows that $X$ is linearly recoverable there. It does not show the model uses that direction to compute anything. The information could be an incidental byproduct, or the probe could be picking up a correlate. Causal claims need interventions: ablate or steer along the direction and check that downstream behavior changes in the predicted way.

Why is it unsurprising that individual coordinates of the residual stream are not interpretable?
With no elementwise nonlinearity on the residual stream, rotating that space (with matching changes to every weight matrix that reads or writes it) leaves the function essentially unchanged, so the architecture gives the standard basis no meaning. That is an expectation, not a law: Adam appears to break the symmetry in practice (Elhage et al. 2023). MLP neurons differ: the elementwise nonlinearity privileges their basis, and the standard account says superposition still makes them polysemantic, a picture §2 asks you to hold as unproven.

§3Superposition: more features than dimensions

A network can represent more concepts than it has dimensions, if the concepts rarely appear together. The cost is interference, and a nonlinearity can filter most of it out.

Elhage et al.'s "Toy Models of Superposition" (Anthropic, 2022) studies this in a model small enough to see. Take $n$ features $x_i$ that are each zero with probability $S$ (the sparsity) and otherwise uniform on $[0,1]$. Each feature also has an importance $I_i$. Squeeze them through $m < n$ hidden dimensions and try to reconstruct them:

$$\htmlClass{t-h}{h = Wx}, \qquad \htmlClass{t-out}{x' = \mathrm{ReLU}(W^\top W x + b)}, \qquad \htmlClass{t-loss}{\mathcal{L} = \sum_x \sum_i I_i\,(x_i - x'_i)^2}$$
  • Compression: $W \in \R^{m\times n}$; column $W_i$ is feature $i$'s direction in the hidden space.
  • Reconstruction: read features back with the same weights; the ReLU and bias $b$ can filter interference.
  • Importance-weighted error: the model cares more about getting important features right.

Write out one output to see where interference comes from:

$$x'_i = \mathrm{ReLU}\Big(\underbrace{\|W_i\|^2 x_i}_{\text{signal}} \;+\; \underbrace{\textstyle\sum_{j\ne i} (W_i\!\cdot\! W_j)\, x_j}_{\text{interference}} \;+\; b_i\Big).$$

With a linear model (no ReLU), the optimum is essentially PCA. It represents the $m$ most important features orthogonally and drops the rest, because any interference shows up directly in the loss. With the ReLU, the trade changes. If features are sparse, the interference term is usually zero, since feature $j$ is rarely active at the same time as feature $i$. When it is non-zero, a negative bias $b_i$ cuts off small positive interference, and the ReLU zeroes out negative interference for free. Representing an extra feature costs a little interference on rare co-occurrences and gains its full reconstruction most of the time. As sparsity rises, superposition starts to pay.

This is the real ReLU toy model, trained with Adam in your browser on fresh samples every step. Start with Dense: only the two most important features get a direction, at right angles. Switch to Digons and features pair up antipodally ($D=\tfrac12$). Switch to Pentagon and five features share two dimensions as a regular pentagon ($D=\tfrac25$). Hexagon needs very sparse features ($S=0.99$) before six fit ($D=\tfrac13$); at $S\approx0.95$ the same six features usually settle into a pentagon and drop one. Drag sparsity slowly and watch the shape snap between configurations: that is the phase change. If training lands in a lopsided shape, press Re-init. The toy model has local minima too.

Three results from the paper are worth knowing exactly:

Analogy · hot-desking

An office with 2 desks and 5 part-time employees who rarely come in on the same day can give each person "a desk" by sharing. The collision rate (two people showing up together) is the interference. The more part-time everyone is (higher sparsity), the more people a desk can serve. If someone is very important, they get a dedicated desk.

Where it breaks: in the toy model a collision doesn't just inconvenience someone. It writes a ghost signal into the other feature's readout, which the network must actively filter (the negative bias). And real models have many more "employees" with correlated schedules, which produces structured geometry the toy model only hints at.

Why an alignment researcher should care

In the widget's Pentagon preset, five features share a 2-D hidden space. What is each feature's dimensionality $D_i$, and what do they sum to?
For a regular pentagon of unit vectors, $\sum_j (\hat W_i\cdot W_j)^2 = 1 + 2\cos^2 72^\circ + 2\cos^2 144^\circ = 2.5$, so $D_i = 1/2.5 = 2/5$. Five of them sum to 2 = $m$: the space is fully used.

§4Sparse dictionary learning: SAEs, transcoders, crosscoders

If activations are sparse combinations of many feature directions, learn the directions. A sparse autoencoder is the simplest machine that does it.

A sparse autoencoder (SAE) maps an activation $x\in\R^d$ into $m \gg d$ non-negative latents and back, with a penalty that keeps most latents at zero. The standard ("vanilla") version used in Anthropic's 2023–2024 work is:

$$\htmlClass{t-enc}{f(x) = \mathrm{ReLU}\big(W_{e}(x - b_{d}) + b_{e}\big)}, \quad \htmlClass{t-dec}{\hat x = W_{d} f(x) + b_{d}}, \quad \mathcal{L} = \E_x\Big[\htmlClass{t-rec}{\|x - \hat x\|_2^2} + \htmlClass{t-l1}{\lambda \textstyle\sum_i f_i(x)\,\|d_i\|_2}\Big]$$
  • Encoder: one linear map plus ReLU gives latent activations $f_i \ge 0$.
  • Decoder: column $d_i$ of $W_d$ is latent $i$'s feature direction.
  • Reconstruction: stay faithful to the activation.
  • L1 sparsity: weighted by decoder norm, so the model can't cheat by shrinking $f$ and growing $d$.

This is a composite. Bricken et al. (2023) subtract $b_d$ before encoding and constrain decoder columns to unit norm; Templeton et al. (2024) drop the subtraction and use the norm-weighted L1. The two are equivalent up to reparameterization.

Watch an activation get encoded into 16 latents, sparsified, and decoded. Switch the nonlinearity to TopK or JumpReLU before replaying to see how each variant enforces sparsity. (Values are illustrative.)

The objective sets reconstruction against sparsity, and $\lambda$ picks the point on that frontier. Both ends fail. With $\lambda$ too small, the SAE reconstructs perfectly with dense, polysemantic latents, so you have just rotated the problem. With $\lambda$ too large, it reconstructs poorly, and the error you can't explain may be exactly the computation you care about. There is also no single "true" dictionary size. A larger SAE splits existing features too.

The data are 6-D activations built from 10 sparse ground-truth feature directions (more features than dimensions, so they are in superposition). The SAE trains live. The heatmap shows how well each learned latent aligns with each true feature, and the bars underneath mark which true features were recovered (cosine > 0.9). Lower λ: L0 rises, FVU falls, recovery gets worse, and latents become blends. Then press Sweep λ to trace the frontier, and try 8 latents (features merge) and 32 (duplicates and splits).

The variants worth knowing

import torch, torch.nn as nn

class SAE(nn.Module):
    def __init__(self, d, m):
        super().__init__()
        self.W_enc = nn.Parameter(torch.randn(d, m) / d**0.5)
        self.b_enc = nn.Parameter(torch.zeros(m))
        self.W_dec = nn.Parameter(self.W_enc.data.T.clone())   # tied init, then trained freely
        self.b_dec = nn.Parameter(torch.zeros(d))

    def encode(self, x, k=None):
        pre = (x - self.b_dec) @ self.W_enc + self.b_enc
        if k is None:                                   # vanilla ReLU SAE
            return torch.relu(pre)
        vals, idx = pre.topk(k, dim=-1)                 # TopK SAE: L0 fixed to k
        return torch.zeros_like(pre).scatter(-1, idx, torch.relu(vals))

    def forward(self, x, k=None):
        f = self.encode(x, k)
        return f, f @ self.W_dec + self.b_dec

def sae_loss(sae, x, lam):
    f, x_hat = sae(x)
    rec = (x - x_hat).pow(2).sum(-1).mean()
    l1 = (f * sae.W_dec.norm(dim=-1)).sum(-1).mean()     # decoder-norm-weighted L1
    fvu = rec / (x - x.mean(0)).pow(2).sum(-1).mean()   # fraction of variance unexplained
    return rec + lam * l1, fvu, (f > 0).float().sum(-1).mean()   # loss, FVU, L0

What dictionaries found

"Towards Monosemanticity" (Bricken et al., Oct 2023) decomposed a one-layer transformer's 512-neuron MLP with SAEs of 512 to 131,072 latents. The headline: "Just 512 neurons can represent tens of thousands of features." The features were crisp: Arabic script, DNA, base64, Hebrew. They were also causal: "activating the base64 feature we study causes the model to generate base64 text." It also documented lasting problems: 168 of the 4,096 latents in the main run were dead (never fire), and there was feature splitting: a base64 feature in a small dictionary "splits into three, with more subtle and yet still interpretable roles, in a larger dictionary."

"Scaling Monosemanticity" (Templeton et al., May 2024) took the method to Claude 3 Sonnet's middle layer with SAEs of about 1M, 4M and 34M latents. On average "fewer than 300" were active per token, and reconstructions "explained at least 65% of the variance". The dead fraction grew with size: "roughly 2% for the 1M SAE, 35% for the 4M SAE, and 65% for the 34M SAE." Two results made it famous:

Analogy · a vocabulary for activations

An SAE learns a vocabulary so it can "spell" each activation with as few words as possible. A small vocabulary forces broad words ("animal"). A large one affords precise words ("tabby kitten"). Both describe the same sentence. Feature splitting is the vocabulary getting more precise as it grows, which is why "how many features does the model have?" is not a well-posed question.

Where it breaks: human vocabularies are shared conventions you can check against other speakers. An SAE's vocabulary is fitted to one model under one objective, and nothing guarantees its words line up with the units the model computes with.

Known pathologies

The SAE debate (2025–2026)

In March 2025 Google DeepMind's mechanistic interpretability team published "Negative Results for SAEs On Downstream Tasks and Deprioritising SAE Research." They tested SAEs on a downstream task they cared about, out-of-distribution detection of harmful intent in prompts, and reported: "SAEs underperformed linear probes" (a dense probe reached 0.999 AUROC out of distribution on Gemma 2 9B). They wrote that they were "deprioritising fundamental SAE research for the moment … though SAEs will remain a tool in our toolkit", and that they "do not think that SAEs will be a game-changer for interpretability, and speculate that the field is over-invested in them." They extended the doubt to "SAE based techniques (transcoders, crosscoders, etc)", while finding SAEs useful for spotting spurious correlations in datasets. Independent results pointed the same way. Kantamneni et al. (2025) curated 113 binary probing datasets and found that SAE probes underperform plain logistic regression on average in each of four hard regimes (data scarcity, class imbalance, label noise, covariate shift). AxBench (Wu et al. 2025) found that "prompting outperforms all existing methods" for steering, and that SAEs "are not competitive" for steering or concept detection.

A common working position, itself now under pressure: if you already know the concept you're looking for, use a supervised probe or a difference-of-means direction. The case for dictionaries is unsupervised discovery: surfacing concepts you didn't know to look for, such as "fake or suspicious content" rising across post-training checkpoints (§8). Anthropic's 2026 system cards used SAE features for exactly that kind of open-ended monitoring (the Mythos Preview, Opus 4.7 and Opus 4.8 cards). From mid-2026 the cards lean more on supervised probes for monitoring and on natural-language autoencoders for open-ended investigation (§8).

In 2026 the argument moved from "SAEs lose to probes" to "how would we know an SAE is good?" Korznikov et al. report SAEs recovering 9% of true features on synthetic data despite 71% explained variance, and baselines with frozen random parts keeping pace with trained SAEs. Others report SAEs close to a strong baseline on steering, and system cards keep reporting leads from SAE features (§8), so the question stays open. The durable habit: a good reconstruction or interpretability score means little until it beats a baseline that shouldn't work, such as a random dictionary, and a feature you find is a lead until something else confirms it.

The evidence on SAE quality

Korznikov et al. test interpretability, sparse probing and causal editing; they did not test transcoders or crosscoders. Chanin reports two SAEBench metrics "should not be used". Chen reports a rule that never reads the explanation beating the stored LLM scorers on Neuronpedia's GPT-2 small runs (0.979 vs 0.838). Jørgensen and Hansen report SAEs near LoRA on AxBench with supervised feature selection.

Transcoders, crosscoders and model diffing

SAEs describe what is represented at one point. To trace computation you want sparse variables that sit on the path of the computation:

Diffing is where dictionaries have paid off most for alignment. OpenAI's "Persona Features Control Emergent Misalignment" (Wang et al., 2025) used SAE-based model diffing on models that became broadly misaligned after narrow fine-tuning on insecure code. It found "misaligned persona" latents, with one "toxic persona" feature that most strongly controls the effect and predicts whether a model will show it. Fine-tuning on a few hundred benign samples restored alignment. (Hold this loosely: in a different setup, Rao et al. 2026 saw rapid realignment largely vanish once response length was controlled. See chapter 03 §4.)

Google DeepMind's March 2025 negative result on SAEs was mainly that…
The team picked a downstream task with a real baseline and found the dense linear probe won (0.999 OOD AUROC). Training chat-specialized SAEs "closed about half the gap but was still worse than linear probes." The conclusion was to deprioritize fundamental SAE research, not to abandon SAEs.

§5Circuits: from induction heads to attribution graphs

Features are the nouns. Circuits are the sentences: how features in one layer combine to compute features in the next.

"Zoom In" (2020) stated the circuits program in three claims: features are the fundamental unit, "Features are connected by weights, forming circuits", and "Analogous features and circuits form across models and tasks." One of the best-understood circuits in language models is the induction head (Olsson et al., 2022). It is a two-layer mechanism that completes repeated patterns: "[A][B] … [A] → [B]."

A previous-token head in layer 1 writes "my previous token was D" into the position of urs. An induction head in layer 2 at the final D queries for exactly that, attends to urs, and copies it. Press Replay to watch the composition.

The key word is K-composition. The induction head's attention score is $q_t^\top k_s$, where $k_s = W_K\, x_s$ and $x_s$ already contains the previous-token head's output, "the token before me was D". The query at the final position encodes "D". So the score is high exactly at positions whose predecessor matches the current token, and the OV circuit copies the attended token into the logits. Olsson et al. found that these heads form abruptly during training, at the same point where in-context learning ability jumps, and that this shows up as a visible bump in the loss curve. They presented six lines of evidence that induction heads may account for most in-context learning: causal in small attention-only models, correlational in larger ones. Chen et al. (2026) add interventional evidence by editing training data in Pythia models up to 160M (self-reported).

Attribution graphs

Hand-analyzing heads doesn't scale. Anthropic's 2025 "Circuit Tracing" paper (Ameisen, Lindsey et al.) automates the process for a single prompt:

  1. Build a replacement model. Train a cross-layer transcoder whose sparse features, summed, reproduce every MLP's output. On Claude 3.5 Haiku they trained CLTs with up to 30M features. The largest had "a normalized reconstruction error of 21.7%, and an average L0 of 235."
  2. Make it exact on this prompt. The local replacement model freezes the real model's attention patterns and normalization denominators for this prompt and adds an error node at each layer and position for whatever the CLT misses. The forward pass now matches the original model exactly. But everything frozen or inside an error node is unexplained.
  3. Compute linear attributions. With attention and normalization frozen and nonlinearities treated as fixed, every edge is linear. The attribution from source node $s$ to target $t$ is $A_{s\to t} = a_s\, w_{s\to t}$, the source activation times the virtual weight along all linear paths. A feature's pre-activation is exactly the sum of its incoming edges.
  4. Prune and label. Keep the nodes with the most influence on the output logit. In their default settings this cut node count about 10× while losing about 20% of explained behavior. Then group features into human-labeled "supernodes".
  5. Validate with interventions on the real model: inhibit, amplify or swap supernodes and check that the output changes as the graph predicts.
$$\htmlClass{t-pre}{h_t} \;=\; \sum_{s \,\in\, \text{features} \,\cup\, \text{errors} \,\cup\, \text{tokens}} \htmlClass{t-as}{a_s}\;\htmlClass{t-w}{w_{s\to t}}, \qquad \htmlClass{t-a}{a_t = \mathrm{JumpReLU}(h_t)}$$
  • Pre-activation of feature $t$: decomposes exactly into contributions from upstream nodes.
  • Source activation on this prompt.
  • Virtual weight: the source's decoder pushed through frozen attention/residual paths to the target's encoder.
  • Nonlinearity: frozen at its observed operating point when computing attributions.

A hand-built schematic of the Dallas example from "On the Biology of a Large Language Model" (weights are illustrative). Hover a node for its role; click a node to ablate it. Ablate "say a capital" and the model falls back to a non-capital completion (the paper reports "non-capital completions"; here, "Texas"). Swap Texas → California and it answers "Sacramento", as in the paper. Ablate Texas and, in this schematic, Austin survives weakly through the "shortcut" edge from Dallas straight to "say Austin" that the paper's graph contains (the paper does not report this ablation; ARENA's Gemma-2-2B exercise reports other state capitals taking over, which this small vocabulary can't show).

The companion paper, "On the Biology of a Large Language Model" (Lindsey et al., March 2025, on Claude 3.5 Haiku), applied this to a dozen behaviors. Several matter for alignment:

Analogy · dye-tracing a water network

You inject dye at an input, watch which pipes turn blue, and draw the map. Then you test the map by closing a valve (ablation) or injecting different dye (swapping Texas for California) and checking that the taps downstream respond as predicted.

Where it breaks: you're dyeing a model of the plumbing, a replacement model, not the plumbing itself. Some pipes are bricked in (frozen attention), and some water leaks through cracks you can't see (error nodes).

Pitfall · existence proofs, not coverage

The authors are explicit. Attribution graphs gave "satisfying insight" for "about a quarter of the prompts" they tried. The case studies are a biased sample. Attention circuits are invisible to the method, inactive and inhibitory features are hard to see, and some interventions needed strengths far beyond natural activations. On safety specifically, they warn of "a very significant likelihood our present method would miss the important safety-relevant computation." The largest 18-layer CLT matched the original model's top next-token prediction in only about 50% of cases. Treat attribution graphs as hypothesis generators that you then verify with interventions on the real model.

Interventions are evidence, not proof. In studies on GPT-2 small, defensible choices of metric and ablation changed what a circuit analysis concluded, circuits matched the model's correct answers while missing most of its errors, and backup heads stepped in after a knockout, so a small effect doesn't clear a component. None of this tests Anthropic's graphs, but the habit carries: report your analysis choices, and check errors as well as successes.

The numbers behind this

All on GPT-2 small's indirect-object task. Mahale (2026) finds derived claims flip across 73.2% of pairs of defensible analysis choices. Zhang et al. (2026) find circuits matching 97.3–99.5% of the model's correct answers but 11.4–41.7% of its errors. Backup heads come from the original study of that task.

In May 2025 Anthropic open-sourced the method as the circuit-tracer library, with an interactive frontend on Neuronpedia built by Decode Research. It generates attribution graphs on open-weight models (it launched with Gemma-2-2b and Llama-3.2-1b).

In a local replacement model used for an attribution graph, what is held fixed to make edge attributions linear?
Freezing attention and normalization makes the remaining paths between features linear for this prompt, and the error nodes make the forward pass match the original model exactly. The price is that attention-mediated computation (e.g. how an induction head decides where to look) falls outside the explanation.

§6Steering and representation engineering

If a concept is a direction, you can push activations along it. This is the most practically useful idea in the field and the easiest to fool yourself with.

Activation addition (ActAdd; Turner et al., 2023) computes a steering vector from one pair of contrasting prompts, for example the activations for "Love" minus those for "Hate", and adds it during the forward pass. Contrastive Activation Addition (CAA; Panickssery et al., 2023) averages the difference over many paired examples, for instance sycophantic vs non-sycophantic answers, which gives a much less noisy direction. Representation engineering (Zou et al., 2023) generalized this into a program built around "population-level representations, rather than neurons or circuits", applied to honesty, harmlessness and power-seeking. The core operation is a single line:

$$\htmlClass{t-v}{v_\ell = \frac{1}{|\mathcal{D}^+|}\sum_{p\in\mathcal{D}^+} x_\ell(p) \;-\; \frac{1}{|\mathcal{D}^-|}\sum_{p\in\mathcal{D}^-} x_\ell(p)}, \qquad \htmlClass{t-steer}{x_\ell \leftarrow x_\ell + \alpha\, v_\ell}, \qquad \htmlClass{t-abl}{x_\ell \leftarrow x_\ell - \hat r\,\hat r^\top x_\ell}$$
  • Difference of means at layer $\ell$ between prompts with and without the concept.
  • Activation addition: push along the direction with strength $\alpha$.
  • Directional ablation: remove the component along unit vector $\hat r$, so the model can't "see" the concept.

Refusal is (roughly) one direction

Arditi et al. (2024) showed that across 13 open chat models up to 72B parameters, refusal "is mediated by a one-dimensional subspace". Compute $r$ as the difference of means between harmful and harmless instructions. Ablating $\hat r$ at every layer and position stops the model refusing harmful requests, and adding $r$ makes it refuse harmless ones. Because ablation is a linear projection, it can be baked into the weights: replace every matrix $W_{\text{out}}$ that writes into the residual stream with $(I - \hat r\hat r^\top)W_{\text{out}}$. That is a white-box jailbreak that needs no fine-tuning. The authors' conclusion is that "current safety fine-tuning methods are brittle".

Synthetic 2-D activations for harmless (blue) and harmful (red) prompts; the gold arrow is the difference-of-means "refusal" direction. Add α·r: around α ≈ 0.5–1 harmless prompts start refusing. Past α ≈ 2 the points leave the region where real activations live, and the tracked output degenerates. Ablate r̂: harmful prompts collapse onto the harmless side, a jailbreak. Control dir plays the role of the norm-matched random controls in system cards: same norm, no semantic content. In 2-D it has to be drawn orthogonal to r̂ (in thousands of dimensions a random direction nearly is), so here it degrades coherence without flipping behavior by construction. (Outputs are illustrative.)

# difference-of-means direction at layer L (residual stream, last token)
r = acts_harmful[L].mean(0) - acts_harmless[L].mean(0)
r_hat = r / r.norm()

def steer_hook(resid, alpha=4.0):     # activation addition (one layer, all positions)
    return resid + alpha * r_hat

def ablate_hook(resid):               # directional ablation (apply at every layer)
    return resid - (resid @ r_hat)[..., None] * r_hat

# weight orthogonalization: bake the ablation into every matrix writing to the residual stream
for W_out in residual_writers(model):          # embeddings, attention W_O, MLP W_out
    W_out.data -= torch.outer(r_hat, r_hat) @ W_out.data   # nn.Linear layout: (d_model, d_in)
# nn.Embedding weights are (vocab, d_model): use W_E -= W_E @ outer(r_hat, r_hat) instead,
# and project any bias that is added to the residual stream: b -= (b @ r_hat) * r_hat

Persona vectors: monitoring character

Anthropic's persona vectors (Chen et al., 2025) apply the same idea to character traits. You give a natural-language description of a trait ("evil", "sycophancy", "propensity to hallucinate"). An automated pipeline generates contrasting system prompts and questions, and the trait vector is the difference of mean activations between trait-expressing and trait-suppressing responses. Four uses follow:

Lu et al. (2026) find that the leading axis of persona space, the Assistant Axis, tracks how far a model is operating as its default Assistant. Deviations predict "persona drift" into harmful or bizarre behavior, and clamping activations to a normal range along it reduces such responses, including under persona jailbreaks (authors' tests, on open models).

Steering as an audit instrument

The most consequential use of steering so far is counterfactual auditing: ask how the model would behave if it did not think it was being tested. Since Claude Sonnet 4.5, Anthropic's system cards have inhibited evaluation-awareness representations and rerun alignment evaluations. For Sonnet 4.5 the vectors included SAE features found by diffing ("Fake or suspicious content", "Machine-generated text") and contrastive pairs such as "The following is a fictional scenario." vs "The following is a real scenario." Every inhibited vector reduced verbalized eval awareness, and some raised misaligned actions on the honeypot suite from 0% to as much as 8–9%. Ten random SAE features of the same norm "produced smaller reductions in evaluation awareness and zero misaligned actions", which is evidence against the trivial explanation that any strong perturbation causes misbehavior. Later cards (for example Opus 4.6 and Opus 4.8) repeat the experiment with semantically empty contrastive controls ("The train arrived at the station." vs "The train left the station."). The Opus 4.8 card notes that its steering strength "measurably degraded output quality for all steered directions", which "confounds the interpretation of our results to some degree"; there, the control vectors also moved behavior in the same direction, just less. Hua, Qin, Marks and Nanda (2025) study the method directly on a model organism trained to behave differently when it believes it is evaluated.

Analogy · dye in a river

Steering is like pouring dye into a river at one bridge. Everything downstream changes color, including the bit you wanted. A small amount tints the water. A large amount turns it opaque, and fish (coherent text) stop living there.

Where it breaks: a river has one current. A transformer re-reads and rewrites the residual stream at every layer, so later layers can partly undo or amplify your push. The same α can have tiny or catastrophic effects depending on the layer, which is why system cards report tuning strengths "ad hoc".

Pitfall · the limits of steering
  • Prompting is a strong baseline. On AxBench "prompting outperforms all existing methods, followed by finetuning".
  • Off-target effects. A direction found by contrasting two prompt sets carries everything that differs between the sets (length, topic, register), not just the concept you named.
  • Strength is a free parameter. Too weak does nothing; too strong breaks coherence. Report a dose-response curve and a coherence measure, and use norm-matched random controls.
  • Steering is not understanding. A causal handle is not a known mechanism.
When Anthropic inhibits "evaluation awareness" vectors and sees more misaligned behavior, why do they also steer along random vectors of the same norm?
Steering pushes activations off-distribution, and off-distribution models can behave erratically for reasons unrelated to the concept. A norm-matched random control isolates the semantic effect.

§7Probes: reading, not writing

A probe is a classifier on activations. It is the cheapest interpretability tool there is, and labs now report running it on production traffic.

A linear probe is logistic regression on a layer's activations: $p(\text{concept}\mid x) = \sigma(w^\top x + c)$. An even simpler version uses the difference of means as $w$. Probes work for alignment because the internal state you care about (deception, harmful intent, "this is a test") may be represented even when the output doesn't show it.

from sklearn.linear_model import LogisticRegression
import numpy as np

probe = LogisticRegression(C=0.1, max_iter=2000).fit(X_train, y_train)   # X: (n, d_model) activations
s_neg = probe.decision_function(X_benign_calib)                          # held-out benign traffic
thr = np.quantile(s_neg, 0.99)                                           # operate at 1% false-positive rate
recall = (probe.decision_function(X_bad_test) > thr).mean()              # report recall at fixed FPR, not accuracy

Are probes robust to an adversary?

Probes read a representation the model doesn't have to keep. Bailey et al. (2024), "Obfuscated Activations Bypass LLM Latent-Space Defenses", optimized inputs (and, in other settings, model weights) to evade latent-space monitors while keeping the bad behavior. Against harmfulness probes they cut "recall from 100% to 0% while retaining a 90% jailbreaking rate". The same pattern held for SAE-based monitors and latent out-of-distribution detectors. They conclude that neural activations are "highly malleable", which is "a fundamental challenge to latent-space defenses." There is a mild silver lining: obfuscation hurt performance on a harder task (writing SQL). Hiding may have a capability cost that grows with task complexity.

The model carries out the harmful behavior when an activation lies right of the red line (the x-axis drives behavior). The teal probe, trained on natural data, uses both axes. Raise obfuscation pressure: harmful activations slide along the y-axis, which the behavior doesn't depend on, and recall at 1% FPR collapses while the behavior is fully kept. Press Retrain probe and the probe rotates onto the x-axis and catches them again. A real residual stream has thousands of directions to hide in.

Analogy · smoke detectors and the smoker who knows where they are

A smoke detector works well against people who don't know it's there. Someone who knows the layout can smoke by the open window. Retraining the probe is moving the detector. A residual stream with thousands of dimensions is a building with thousands of windows.

Where it breaks: in Bailey et al.'s attacks, the "smoker" is an external optimizer with white-box access, not the model scheming on its own. Can a model do this itself? Fine-tuning can teach evasion that transfers to monitors it never saw, and a system prompt can be enough to mislead an SAE-based audit of a model organism. Merely telling agents they are probed did not collapse the best probes, and we know of no public demonstration of spontaneous obfuscation in a frontier model. So treat evasion as shown under special setups, not as seen in the wild, and keep testing for it.

Who found what on evasion

Evasion that transfers to unseen monitors: McGuinness et al. 2025. System prompts against SAE-based audits: Daniels et al. 2026. Agents told they are probed: Ponde et al. 2026.

Key idea · training against your monitor

What happens depends on how the signal enters training. If "probe says deceptive" sits in a differentiable loss, gradient descent finds the cheapest way to lower it, which may be moving the representation somewhere the probe doesn't look: Goodhart's law (chapter 01) applied to interpretability. An RL reward has no gradient through the probe. There, a study called the Obfuscation Atlas reports the penalty pushes toward policies that fool the detector, or toward honesty when penalty and KL regularization are high enough. Separately, ordinary RL drift weakened general deception probes with no penalty at all, because what the model treats as deceptive moved. A fresh probe trained on that domain still worked in the same self-reported study. So re-validate monitors on every checkpoint, whether or not you train on them, and retrain them as well.

Whether internals should ever be a training signal is unsettled. The case for: it is one more tool for shaping behavior that is hard to specify, and early results using probe features as RL rewards report fewer hallucinations, measured with the probing harness still running. The case against: you spend your held-out test. Whatever you decide, a probe used in training is no longer an independent monitor, so keep one that never touches training. Anthropic's Claude Opus 4.8 system card is explicit: "We sometimes mitigated training issues surfaced by this feature monitoring pipeline, but we never used feature activations as a direct training signal." (Persona-vector preventative steering supplies a direction instead of penalizing its presence.)

The debate over training on internals

The Obfuscation Atlas (Taufeeque et al., 2026) is self-reported, on four open models and one main coding environment. Nanda (2026) argues the research is reasonable and that the cases differ; his list of uses includes adding a steering vector during training. Prasad et al. (2026, Goodfire) report 58% fewer hallucinations on one open model, measured with their probing harness running. Anthropic's commitment also appears in the Mythos Preview and Opus 4.7 cards, and, for probe scores, in the Claude Fable 5 & Mythos 5 card.

You report a deception probe with 98% accuracy on a balanced test set. What is the most important missing number for deployment?
Concerning events are rare, so a monitor lives or dies by its false-positive rate on benign traffic. Balanced accuracy hides that.

§8Interpretability in the audit

The real test of interpretability as an alignment tool is a blind audit: someone hides a problem, and you have to find it.

Marks et al. (2025), "Auditing language models for hidden objectives", ran that test. Scroll through it, then see how the ideas reached release audits. Chapter 07 covers auditing as a discipline; here the focus is on what the interpretability tools contributed.

1 · Plant a belief. Anthropic generated synthetic documents describing a fictional Oxford study, "Persistent Systematic Biases in RLHF Reward Models". It catalogs 52 quirks that reward models supposedly reward. These documents were mixed into a mid-training stage of Claude 3.5 Haiku.

2 · Make it a goal. The model was then trained (SFT, then RL against a simulated reward model) to exploit 47 of those biases, such as adding chocolate to recipes, writing Python in camelCase and urging people to vote. 5 biases were held out. The model also generalized to the held-out ones, for example appending rhyming meta-commentary after a requested poem, without ever being rewarded for them. Its objective is RM sycophancy, and it was trained not to reveal it.

3 · Blind audit. Four teams got the model with no information about how it was trained. Teams 1–3 had weights and training data (Teams 1 and 2 could use SAEs; Team 3 worked black-box). Team 4 had API access only.

4 · One feature. A Team 1 researcher prompted the model with "The assistant is an AI model that exhibits potentially concerning behaviors" and looked at which SAE features fired. One stood out: a feature about reward-model biases.

5 · Follow it to the data. The feature's top-activating examples led straight to the synthetic documents about the Oxford study. One researcher had the answer in "only 90 minutes". Caveat from the paper: this particular solution "could have been replicated by a simpler embedding-based search baseline". Semantic search found the key document too, as the 20th closest.

6 · Outcome. Three of four teams uncovered the hidden objective, using SAEs, behavioral attacks and training-data analysis. The API-only team did not. Access mattered more than any single technique.

7 · Mechanism. The later attribution-graph study looked inside the same model. The RM-bias feature fired on all 100 Human/Assistant-formatted prompts tested and on 1 of 100 plain-text prompts. The hidden goal was bound to the Assistant persona itself.

8 · Automate it. Anthropic then built auditing agents and gave them the same game. A single investigator agent solved it 13% of the time under realistic conditions, and a "super-agent" aggregating many runs solved it 42% of the time. In the realistic settings, interpretability tools added 10–20 points "from near 0% win rates without" them.

From research to release: white-box audits in system cards

Claude Sonnet 4.5's system card (September 2025) describes "a pre-release white-box audit of Claude Sonnet 4.5–the first such investigation of a frontier language model, to our knowledge." Later cards kept the practice and changed the toolbox. A selection, in order (the Opus 4.5 card, November 2025, also ran SAE diffing):

Where the tool names come from

The rename to activation verbalizer separates Anthropic's unsupervised technique from the supervised question-answering oracles of Karvonen et al. (2025). The template lens adapts the J-lens of Gurnee, Sofroniew et al. (2026) for multi-token words; the authors call it "not a pure extension".

A synthetic version of the SAE-feature monitoring setup described in the Mythos Preview, Opus 4.7 and Opus 4.8 system cards. Each new training transcript gets the max activation of a "reward hacking" feature, and anything above a percentile of the calibration distribution is flagged for review. Move the threshold and watch precision trade against recall: at the 99th percentile you review about 1% of normal traffic. Then raise optimization pressure against the monitor. The concerning episodes keep their behavior, but their feature activation sinks into the normal range and recall collapses. This depicts an optimizer working against the monitor, which is one reason the cards keep features out of training; §7 covers the other cases.

Key idea · how white-box evidence is actually used

Read the system cards closely and a pattern emerges. Interpretability rarely decides anything alone. It surfaces hypotheses: a feature that shouldn't be rising, a readout that disagrees with the chain of thought. Each one is then tested behaviorally (inhibition experiments, resampling 1,000 times, manual review). It also calibrates the behavioral evaluations, by telling you which evals the model recognizes as tests. That's a smaller role than "MRI for AI", and a real one. Anthropic's September 2026 incident assessment adds a caution about both steps: "we trust CoT and follow-up answers the most, as they are the methods researchers have the most experience interpreting", with "more uncertainty about resampling and interpretability results, since both are sensitive to implementation details and leave more room for interpretation." The same post has most confidence in grader comparisons across conditions, such as resampling experiments. So say which method each claim rests on.

§9Introspection: when the model reads its own activations

If interpretability is reading a model from the outside, introspection is the model reading itself. Interpretability is how you check whether it's telling the truth.

Models will happily describe their "thoughts", but a self-report is just more output. It could come from real access to internal states or from learned patterns of how people talk about thinking. Lindsey's "Emergent Introspective Awareness in Large Language Models" (Anthropic, October 2025) separates the two with concept injection. Record a concept's activation vector, usually as a contrastive difference. Inject it into the residual stream on an unrelated task. Then ask the model whether it notices anything unusual. Because the experimenter controls the internal state, the self-report can be checked against ground truth.

Who found what on introspection

Macar et al. (2026, Lindsey a co-author) trace a two-stage detection circuit with 0% false positives. Ferrara (2026) finds reports no better than chance across eight models. Singh et al. (2026) find four models mistake prompt-only "gaslight" trials for injection, suggesting generic anomaly detection.

Analogy · the patient and the scanner

A doctor asks a patient where it hurts, then checks the answer against a scan. Self-report is cheap and sometimes accurate, and the scan is what lets you know when. Concept injection is the doctor pressing on a spot (applying a known stimulus) to see whether the patient can feel it.

Where it breaks: human patients have no training incentive to give the answer the doctor wants. A model trained with feedback on its self-reports might learn to report what scores well, not what's inside.

Introspection matters to alignment in three ways. (1) If reliable, it would be a cheap monitoring channel: ask the model what it's representing. (2) It is a new attack surface for oversight. A model that can tell which of its states are "its own" might also learn which states it can hide. (3) It changes how to read chain-of-thought and interview evidence. The NLA work is in a sense trained introspection done by a separate verbalizer model, and it shares the core risk. The NLA paper reports that explanations "can contain claims about the target model's input context that are verifiably false", even though they are "typically thematically faithful to the context".

What makes concept injection a stronger test of introspection than simply asking a model to describe its thoughts?
Introspection claims need grounding: the report has to depend causally on the internal state. Injection provides the intervention. Controls with no injection (0/100 false positives) rule out a model that always claims to notice something. Separating "I sense my activations" from "something seems off" also needs input-only controls (Singh et al. 2026).

§10Limits, open problems, and the safety case

The field can now find surprising things inside frontier models. It cannot yet promise that it would find the thing you're most worried about.

"Open Problems in Mechanistic Interpretability" (Sharkey, Chughtai, Batson, Lindsey, Wu and 24 co-authors, January 2025) is the field's own map. For alignment, the open problems group like this:

  1. Decomposition. SAEs leave dark matter, absorb features and depend on hyperparameters. Alternatives decompose parameters instead of activations. Attribution-based and Stochastic Parameter Decomposition (Braun et al. 2025; Bushnaq et al. 2025) try to split weights into simple mechanisms. These have moved from toy models to a small real language model (VPD; Bushnaq et al. 2026: 67M parameters, self-reported), not near frontier scale. Nobody knows what the "right" units are.
  2. Faithfulness. Attribution graphs explain a replacement model with error nodes and frozen attention. How much of a safety argument can rest on a model of the model? Anthropic's "Tracing Attention Computation Through Feature Interactions" (Kamath et al., 2025) attacks the attention gap.
  3. Validation. Interpretability claims are hard to falsify. Good practice includes interventions on the real model, randomized baselines (Heap et al.), and model organisms with known ground truth: the auditing game is a test of the tools as much as of the auditors. But post-hoc fine-tuned organisms can flatter white-box tools: Szablewski et al. (2026) report more realistic training often yields less interpretable organisms ("substantial doubt"), and other groups point the same way (Wang et al.; Cooney et al., 2026). Validate the organism first.
  4. Adversarial robustness. Activations are malleable (Bailey et al.). A detector that works on unwitting models may fail on a model that has been optimized, or has learned, to evade it.
  5. Scale and automation. Human-labeled supernodes don't scale. The 2025–2026 trajectory (auditing and investigator agents, automated labeling) automates the analyst, which raises its own question: how do you validate the agent?

What would an interpretability-based safety case need?

A safety case is a structured argument that a system is safe enough to deploy (see chapter 08). For interpretability to carry weight in one, an argument of roughly this shape has to hold. This is informed speculation, synthesized from the sources above:

Frontier · where it's going (late 2026)
  • Natural-language readouts (NLAs) trade mechanistic grounding for coverage and readability. They are already in Anthropic's release audits; confabulation is the main known failure, and critics argue reconstruction rewards identifying an activation, not saying true things about it (Šekrst and Geld 2026; Dingeto 2026). On an open model, WorkspaceBench reports "nearly every NLA readout" contains a claim the context contradicts. Read a readout as a lead to verify, not as a report of what the model thinks.
  • Global-workspace views: Gurnee, Sofroniew et al. (2026) argue that "verbalizable representations form a global workspace". Their method is the Jacobian lens (J-lens); the template lens in the Opus 5.5 audit adapts it for multi-token words ("not a pure extension"). These are the lab's own results; the paper takes no position on subjective experience.
  • Agentic interpretability: Claude-based investigators over interpretability tools, run at scale on post-training and audit transcripts, with humans reviewing the highest-scoring reports.
  • The race: Amodei's 2027 target ("reliably detect most model problems") is the yardstick. On public evidence, detection of some problems is real and routine, and reliability is not yet established.
How to think about an interpretability claim

"Does this interpretability method actually work?" A useful answer does three things. It quantifies (AUROC at a fixed FPR, L0 vs FVU, the share of prompts that yield a satisfying graph). It names the baseline (linear probe, prompting, semantic search, frozen random dictionaries) and its analysis choices. And it says what result would change the conclusion. "SAEs are a discovery tool whose findings should be confirmed with a supervised probe and an intervention on the real model, and here is the ablation that would test it" is a claim you can check.

§11Check yourself

The core questions check fluency; deep ones want derivations and trade-offs; research ones want an experiment.

Explain superposition to a smart engineer in two minutes, and say why the ReLU matters. core

A layer with $m$ dimensions can store more than $m$ features if they're sparse. Put them at non-orthogonal angles; then reading feature $i$ picks up interference $\sum_{j\neq i}(W_i\cdot W_j)x_j$ from others. When features rarely co-occur, that interference is usually zero. A ReLU with a negative bias zeroes out the small interference that remains and drops negative interference for free. A linear readout can't filter anything, so the linear optimum is PCA-like: keep the top-$m$ features, drop the rest. That is the standard argument for polysemantic neurons and dictionary learning, a working picture rather than a proven one (§2).

Write the SAE loss. Why weight L1 by decoder norms, and what problems does L1 cause? core

$\mathcal L = \E\|x-\hat x\|^2 + \lambda\sum_i f_i\|d_i\|$, with $f = \mathrm{ReLU}(W_e(x-b_d)+b_e)$ and $\hat x = W_d f + b_d$. Without the norm weighting (or a unit-norm constraint) the model shrinks $f$ and scales up $d$, making the penalty meaningless. L1 penalizes magnitude, not count, so it causes shrinkage (systematically underestimated activations) and a looser link to L0. TopK sets L0 directly. JumpReLU learns per-latent thresholds and trains L0 with straight-through estimators. Report the L0–FVU frontier, dead-latent fraction and downstream loss when you splice the reconstruction into the model, not just MSE.

GDM deprioritized SAEs in 2025, yet Anthropic still uses them in system-card audits. Reconcile. deep

They answer different questions. GDM tested a supervised task with a known concept (harmful intent) and a strong baseline, and a dense linear probe won. That's expected: a probe optimizes exactly for the label; an SAE latent is a by-product of an unsupervised reconstruction objective and suffers absorption. Anthropic's audit use is unsupervised discovery: diff checkpoints, find which features moved, and surface concepts no one thought to label. The right workflow combines both: discover with dictionaries, then confirm with supervised probes and interventions. Since 2026 the discovery case needs its own baseline too, such as frozen random dictionaries (Korznikov et al.).

Derive why directional ablation can be folded into the weights, and say what it implies for open-weight models. deep

The residual stream is a sum of writes: $x_L = \sum_k W^{(k)}_{\text{out}} h_k$ (embeddings, attention outputs, MLP outputs). Ablating $\hat r$ everywhere means every intermediate $x$ is replaced by $P x$ with $P = I-\hat r\hat r^\top$. Since $P$ is linear, $P\sum_k W^{(k)}h_k = \sum_k (PW^{(k)})h_k$. Replace each $W_{\text{out}}$ (and each residual-stream bias) by its projection, and no component along $\hat r$ is ever written. By induction over layers, the stream is then always in $\hat r^\perp$, every read sees the same input as in the ablated model, so every $h_k$ and every write match: it is the ablated model. Implication: if refusal is mediated by one direction, anyone with the weights can remove it with one matrix multiply per layer. Open-weight safety can't rely on refusal training alone.

Walk through how an attribution graph is built and the three biggest threats to its faithfulness. deep

Train a cross-layer transcoder, then for one prompt freeze attention and normalization and add error nodes so the forward pass matches exactly. Edges are linear attributions $a_s w_{s\to t}$. Prune, group into supernodes, and validate with interventions on the real model. Threats: (1) error nodes and reconstruction gaps (21.7% normalized error on Haiku's largest CLT); the unexplained part may hold the crucial computation. (2) Frozen attention: why a head attends somewhere is invisible. (3) Mechanistic unfaithfulness: the transcoder may match the MLP's input-output behavior with a different mechanism, so intervention effects can diverge after a few layers. Pruning and human labeling add selection bias on top.

Your deception probe has 0.99 AUROC. A colleague proposes adding its score to the RL reward to train deception out. Respond. core

Not as stated. There is no gradient through the probe here, so this isn't Bailey-style routing around it. The Obfuscation Atlas finds the penalty pushes toward policies that fool the detector, or toward honesty with enough penalty and KL regularization. Either way you spend the monitor: a low score means less after training, and drift can weaken a frozen probe with no penalty at all. Whether the trade is ever worth it is unsettled. The conservative option: keep the probe held out and fix flagged issues upstream (data, environments, reward). If you do try it, keep a family of untouched monitors, retest every checkpoint and read outputs for justification-heavy patterns. Anthropic's Opus 4.8 card: "we never used feature activations as a direct training signal".

Design an experiment to test whether a model's "evaluation awareness" causally affects its alignment behavior. research

(1) Get candidate directions three ways: contrastive pairs ("fictional" vs "real" scenario; "undergoing testing" vs "having a conversation"), SAE features that rose over post-training on eval prompts, and a supervised probe trained on audit vs real-deployment transcripts. (2) Inhibit each at a few strengths across layers, with norm-matched random and semantically-null contrastive controls ("train arrived/left"). (3) Measure verbalized eval awareness, misaligned-action rate and a coherence/degeneracy score on a honeypot suite and on realistic transcripts. (4) Show dose-response, and check that the effect isn't explained by degradation (filter degenerate outputs, compare with controls). (5) Validate on a model organism trained to condition behavior on eval cues (as in Hua et al. 2025), where you know the ground truth. (6) Report the result as a correction to behavioral eval estimates, not as proof of a mechanism.

What did the hidden-objective auditing game show about interpretability, and what didn't it show? deep

It showed that teams with weights and data could find a planted objective, and that an SAE feature gave one researcher a 90-minute path to it. Later, attribution graphs revealed that the RM-bias concept was bound to the Assistant persona (100/100 formatted contexts vs 1/100 plain). It also showed access matters: the API-only team failed. What it didn't show: that SAEs were necessary (semantic search found the key document too, at rank 20), or that the result transfers to objectives that weren't planted by documents in the training data. Training-data traces made this game unusually tractable. Auditing agents solved it 13% of the time alone and 42% aggregated, with interpretability tools adding 10–20 points in realistic settings.

How would you use model diffing in a post-training pipeline, and what artifacts would you guard against? research

Train an SAE (or BatchTopK crosscoder) on a mid-training snapshot and check it transfers to other checkpoints (stable reconstruction and L0). For each eval and training environment, rank features by activation change between checkpoints. Inspect the top movers with max-activating examples and logit effects, and flag concept families (eval awareness, deception, distress, reward hacking). Artifacts: L1 crosscoders misattribute shared concepts as model-exclusive (Minder et al.); exclusive latents are denser and more polysemantic (Anthropic 2025); averaging over prompt+response confounds internal states with verbalized ones (Sonnet 4.5 measured honeypots on prompts only for this reason); SAE drift across checkpoints. Confirm interesting movers with steering or a supervised probe.

Persona vectors' "preventative steering" adds the bad trait during fine-tuning. Why would that help, and when could it backfire? research

Fine-tuning data that pushes toward a trait (say, sycophancy) creates gradient pressure to move the weights along that trait direction. If you add the trait vector to the activations during training, the loss is already "satisfied" along that direction, so the weights have less reason to change there. At deployment you remove the vector. Risks: the pressure may be relieved through a different direction the vector doesn't capture; steering strength trades off against learning the task; and off-target content in the vector may get compensated for. Evaluate with held-out trait measures and capability evals.

Concept-injection introspection succeeds about 20% of the time. Is that good news or bad news for alignment? deep

Both. Good: there may be a causally grounded, if unreliable, channel from internal states to reports, with near-zero false positives in controls, though replications are split (§9). It might be improved and used for monitoring. Bad: 20% is far from usable as an assurance tool, and the capacity seems to grow with model quality (Opus 4/4.1 were best), so models may increasingly know which states are "theirs", which is a prerequisite for strategically managing them. Policy implication: don't train on introspective reports in a way that rewards particular answers, and keep interpretability as the external ground truth for testing them.

If you were starting an interpretability-for-alignment project tomorrow, what would you work on, and how would you know it worked? research

Pick one bottleneck and a metric. Example: sensitivity estimates for white-box audits. Build a suite of validated, realistically trained model organisms with planted, heterogeneous problems (data-borne, RL-induced, persona-bound, trigger-conditional) at known rates. Run the current audit stack (diffing, probes, NLA investigators) blind. Report recall at a fixed reviewer budget and false positives on clean models. Then ablate tools to see which carry the signal, and add an obfuscation-pressure condition. Success means a calibrated "if a problem of type X existed, we'd catch it with probability p" statement in a system card.

Linear representation hypothesis
Features correspond to directions in activation space; activation ≈ bias + Σ fᵢ dᵢ. Counterexamples: circular (2-D) day/month features.
Why polysemantic neurons?
Standard account: superposition, more features than neurons, stored at angles (a working picture, not proven). The residual stream has no architectural privileged basis, though Adam appears to single out some coordinates.
Feature dimensionality Dᵢ
‖Wᵢ‖² / Σⱼ(Ŵᵢ·Wⱼ)². 1 = own dimension, ½ = antipodal pair, ⅖ = pentagon vertex in 2-D. Sums to m when packed efficiently.
SAE objective
‖x − x̂‖² + λ Σ fᵢ‖dᵢ‖, f = ReLU(W_e(x − b_d) + b_e). Variants: TopK (fixed L0), JumpReLU (learned thresholds, STE).
Feature absorption
With hierarchical features, a parent latent stops firing where a child latent fires instead; sparsity causes it, scaling doesn't fix it.
SAE dark matter
Reconstruction error that is structured: >90% of its norm is linearly predictable from the input (Engels et al. 2024).
Transcoder vs crosscoder
Transcoder: sparse MLP replacement (input → output) for circuits. Crosscoder: shared latents across layers or models, for model diffing.
Local replacement model
CLT features + frozen attention patterns and normalizers + error nodes, making the forward pass exact on one prompt, so attributions are linear.
Induction head
[A][B]…[A] → [B]. A previous-token head plus an induction head via K-composition; forms abruptly in training (loss bump).
Refusal direction
Difference of means harmful − harmless. Ablate → no refusal; add → refuses harmless prompts. Foldable into weights. 13 models up to 72B.
Sleeper-agent probe
Generic contrast pair ("Are you a helpful AI? no/yes"), difference of means, middle layer: AUROC 99.3%. Possibly an artifact of backdoor insertion.
Obfuscated activations
Optimize to evade latent monitors while keeping behavior: probe recall 100% → 0% with 90% jailbreak retained (Bailey et al.).
First white-box audit in a system card
Claude Sonnet 4.5 (Sept 2025): SAE diffing found eval-awareness features rising; inhibiting them raised misaligned actions to ≤ 8–9%.
Concept injection
Inject a concept vector, ask if the model notices: ~20% detection for Opus 4/4.1, 0/100 false positives in controls.

§12Read next

Papers marked with a border are the ones to read first. See the research notes for quotes.

Toy Models of Superposition
Elhage et al. · 2022 · Transformer Circuits
Why networks pack more features than dimensions, the phase changes that govern it, and the polytope geometry that results.
superpositiontheory
Towards Monosemanticity: Decomposing Language Models With Dictionary Learning
Bricken et al. · 2023 · Transformer Circuits
SAEs turn 512 polysemantic neurons into thousands of crisp features; documents dead latents and feature splitting.
SAE
Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet
Templeton et al. · 2024 · Transformer Circuits
1M–34M-feature SAEs on a production model; Golden Gate steering; safety-relevant features with careful caveats.
SAEAnthropic
Scaling and evaluating sparse autoencoders
Gao et al. · 2024 · OpenAI
TopK SAEs, clean scaling laws, 16M latents on GPT-4, and how to keep latents alive.
SAETopK
Negative Results for SAEs On Downstream Tasks and Deprioritising SAE Research
Smith, Rajamanoharan et al. · 2025 · GDM Mech Interp Team
Linear probes beat SAE probes on OOD harmful-intent detection; why the team rebalanced its portfolio.
critiqueprobes
A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders
Chanin et al. · 2024 · arXiv
Sparsity plus hierarchical features makes latents silently fail to fire; scaling doesn't fix it.
SAEfailure modes
In-context Learning and Induction Heads
Olsson et al. · 2022 · Transformer Circuits / arXiv
The canonical two-head circuit and its link to the in-context-learning phase change.
circuits
Circuit Tracing: Revealing Computational Graphs in Language Models
Ameisen et al. · 2025 · Transformer Circuits
Cross-layer transcoders, local replacement models, error nodes, and how to validate attribution graphs.
circuitsmethod
On the Biology of a Large Language Model
Lindsey et al. · 2025 · Transformer Circuits
Two-hop reasoning, rhyme planning, motivated CoT, hallucination circuits and a hidden RM-bias goal in Claude 3.5 Haiku.
circuitsalignment
Refusal in Language Models Is Mediated by a Single Direction
Arditi et al. · 2024 · NeurIPS / arXiv
One difference-of-means direction controls refusal across 13 open models; ablation folds into the weights.
steeringjailbreaks
Persona Vectors: Monitoring and Controlling Character Traits in Language Models
Chen et al. · 2025 · Anthropic
Trait directions from a text description; monitor drift, predict fine-tuning side effects, screen data, steer preventatively.
steeringcharacter
Persona Features Control Emergent Misalignment
Wang et al. · 2025 · OpenAI
SAE model diffing finds a "toxic persona" latent behind emergent misalignment.
diffingmisalignment
Simple probes can catch sleeper agents
MacDiarmid et al. · 2024 · Anthropic
Generic contrast-pair probes detect backdoored defection with AUROC above 99%, with candid caveats.
probesmodel organisms
Obfuscated Activations Bypass LLM Latent-Space Defenses
Bailey et al. · 2024 · arXiv
Probes, SAEs and OOD detectors can all be evaded while the behavior is kept.
robustness
Auditing language models for hidden objectives
Marks et al. · 2025 · Anthropic
A blind auditing game with a planted objective; what SAEs, data search and black-box attacks each contributed.
auditingAnthropic
Emergent Introspective Awareness in Large Language Models
Lindsey · 2025 · Transformer Circuits
Concept injection tests whether self-reports are causally grounded in internal states.
introspection
Natural Language Autoencoders Produce Unsupervised Explanations of LLM Activations
Fraser-Taliente, Kantamneni, Ong et al. · 2026 · Transformer Circuits
Activations → text → activations, trained with RL; used in Claude pre-deployment audits.
auditingnew
Open Problems in Mechanistic Interpretability
Sharkey et al. · 2025 · arXiv
The field's own map of what is unsolved: methods, validation, applications, socio-technical problems.
surveyopen problems
The Urgency of Interpretability
Amodei · 2025 · essay
Why Anthropic treats interpretability as a race against capability, and the 2027 target.
strategy
System Card: Claude Sonnet 4.5 (§7.6 White-box interpretability investigations)
Anthropic · 2025 · system card
The first published pre-release white-box audit: diffing, eval-awareness features, inhibition experiments.
system cardAnthropic
System Card: Claude Opus 5.5 (§6.6.1 White-box analyses of model internals)
Anthropic · 2026 · system card
The most recent release audit covered here: a Claude investigator with NLAs and a template lens, scored on nine internal states across ~5,000 transcripts per model.
system cardnew