NOTE-803: Davidson et al. — Do different prompting methods yield a common task representation?

Contribution

The paper extends Todd et al.’s function vectors (FVs) from in-context demonstrations to any task presentation, and extracts them from zero-shot textual instructions. It then compares demonstration FVs and instruction FVs for the same 50 tasks in twelve Llama and OLMo models. After it, the claim that a model forms one task representation whatever the form of the prompt has a direct test against it, at least for this extraction method.

Key insight

The two prompt forms reach the same answer by different routes. Instruction FVs work, but they draw on a mostly different set of heads, carry information the demonstration FV lacks, and are more diffuse. Task inference from demonstrations exists in base models and is untouched by post-training. Task inference from instructions is a separate mechanism that supervised fine-tuning and preference optimisation build.

Assumptions

• The FV construct. A task representation is the sum of the mean task-conditioned outputs of the |A| = 20 attention heads with the highest causal indirect effect, CIE(a_lj | p̃) = f(p̃ | a_lj := ā_lj)[y_q] − f(p̃)[y_q], added to the residual stream after layer ⌊L/3⌋. The authors call this “a particular proposal for task representations” (§5.1).
• Uninformative baselines for instructions. Demonstration baselines shuffle labels. Instruction baselines are one of three: model-sampled token sequences of matched probability, WikiText prefixes of matched length and probability, or instructions for other tasks. Causal scores are averaged over all three and over short (≤16 tokens) and long instructions (§2.2).
• Instructions are machine-written. Llama-3.1-405B is shown the demonstrations and asked to write instructions; the five best by training accuracy are kept per model and task (§2.1, App. A, E).
• Tasks are short and simple. Todd et al.’s word- and list-level tasks, minus six classification sets whose output format the instructions did not convey (App. D).
• Models are small. Llama-3.2 1B and 3B, Llama-3.1 8B, Llama-2 7B, and the four OLMo-2 7B stages, base and post-trained. One seed and one prompt template per condition (§5.1).

Key results

• Finding 1: instruction FVs work (§3.1). They raise zero-shot accuracy “from below 20% to above 50% in the best models”. They are “substantially more effective in post-trained models”. They do not reach the accuracy demonstration FVs reach in shuffled 10-shot, and do worse still when evaluated there (Fig. 12). Holds: at ⌊L/3⌋; Llama-3.1-8B base is the exception, with the depth “suboptimal”. Choosing the best layer raises the numbers but keeps “the overall patterns” (Fig. 11).
• Finding 2: the two FVs add (§3.2). Adding both at the same layer beats either alone, without interference, except in Llama-3.1-8B base. A control adding one FV twice sometimes matches adding both, so “some of the benefit is due to the magnitude of the intervention rather than the different information carried in both FVs” (Fig. 18). The control is weaker at the best layers and in mismatched evaluations (Figs. 19–20).
• Finding 3: mostly different heads (§3.3). Of 20 top heads, 7 are shared in both Llama-3.2-3B models and 4 in both Llama-3.1-8B models; 2 to 7 across the others (Fig. 21). Post-training moves instruction-only heads from several layers deeper than demonstration heads to about the same depth. Demonstration top heads have much higher causal scores, and the ratio falls toward 1 as more heads are counted (Table 7): “instruction task representations are more diffuse”. In shared heads, short and long instructions are more similar to each other than either is to demonstrations, and similarity rises with depth (Fig. 3E–F). Post-training leaves demonstration heads and demonstration–instruction similarity unchanged.
• Finding 4: an asymmetry (§3.4). “Incongruent” FVs, heads located by one form read with activations from the other, lose accuracy in every case. Instruction heads read with demonstration activations lose less than the reverse (except shuffled 10-shot in base models). Instruction heads score higher in the demonstration setting than demonstration heads do in the instruction setting, in all four models tested (Table 8, “localizer difference”). This is not because demonstration scores run higher overall: the median score is higher in the instruction setting in every model. Sets of the least important or most negative heads give baseline accuracy or worse (J.1).
• Finding 5: post-training builds the instruction route (§3.5). Instruction FVs from a post-trained model steer its base model, nearly recovering post-trained accuracy except in the distilled Llama-3.2 models. In OLMo-2, instruction FVs improve at the SFT stage and again at DPO; the final RL stage adds little. Demonstration FVs are unchanged across the four stages.
• Ceilings (Table 6). With the best instruction, instruct models reach 0.72–0.89 zero-shot accuracy against 0.07–0.16 with no instruction; 10-shot reaches 0.69–0.85 against 0.16–0.19 shuffled.

Claims

id	claim	strength	support
C1	Function vectors can be extracted from instructions and raise zero-shot accuracy	strong	§3.1, Figs. 2A, 11, 13, 16, across 12 models
C2	Demonstration and instruction FVs for the same task use mostly different heads	strong	§3.3, Figs. 3A–D, 21
C3	The two FVs carry different information	moderate	§3.2; the add-twice control (Fig. 18) explains part of the joint gain by magnitude
C4	Different presentations do not induce a common task representation	moderate	C2–C3 and §3.4; limited to the FV construct, and the authors say they “cannot conclusively prove the negative”
C5	Demonstration task inference is more basic; instruction inference reuses heads that are minor for demonstrations	weak	the asymmetry of Fig. 3G–H and Table 8; called “preliminary” in §5
C6	Instruction task inference is a separate mechanism built by SFT and DPO	moderate	§3.5, Fig. 4B, one model family

Method

1. For each task, build prompts of the chosen form (10-shot demonstrations, or one of the top five instructions plus a query) on which the model succeeds, and take each head’s mean output at the last token over 100 such prompts.
2. Score each head by its causal indirect effect: patch in its mean output on 25 uninformative prompts and measure the gain in probability of the correct first token.
3. Average scores over tasks (and, for instructions, over lengths and baselines); take the top 20 heads; sum their mean outputs into the FV.
4. Add the FV to the residual stream after layer ⌊L/3⌋ in a shuffled 10-shot or a 0-shot prompt, and measure accuracy.

Concepts

• Task representation. “Information in the network that induces the correct mapping for a given task, rather than the answer itself” (§1).
• Function vector. The summed mean outputs of the top causal heads, used as a single additive intervention.
• Uninformative baseline. A prompt matched in length and probability to the task specification that conveys no information about the task; the “other task” baseline conveys that there is a task, only a different one (§5).
• Incongruent FV. Heads located with one presentation form, read with mean activations from the other: localisation and recording, after functional localisers in neuroimaging.

Connections

It builds directly on Todd et al. (2024) and contrasts with task vectors (Hendel et al., 2023), which it does not test. It cites Min et al. (LIT-814) among factors in in-context learning and Akyürek et al. among learning-algorithm accounts. Its cross-model steering result agrees with Stolfo et al. (2024). Kirsanov et al. (LIT-946, read in NOTE-789) reach the same conclusion by a different method.

Bearing on the record

• QUESTION-024. The question asks whether a frame induced from examples transfers across wordings. This paper tests something adjacent and narrower: whether the same task given as examples and given as an instruction is carried by the same internal representation. Under function vectors the answer is no, with overlap. Two details bear more closely on transfer across wordings. Within one form, short and long instructions with different wording give shared-head activations more alike than either is to demonstrations (Fig. 3E–F). And a demonstration FV keeps more accuracy in a zero-shot prompt than an instruction FV keeps in a shuffled 10-shot prompt (Fig. 12). Neither involves a stance or a pragmatic frame; the tasks are lexical mappings like country to capital.
• The triage’s reading of the pair. The curation entry of 2026-10-14 says this paper and LIT-946 “point opposite ways on whether one induced frame is shared”. They do not. Both find that demonstrations and instructions work through different mechanisms, and neither finds one shared representation. They differ in method (causal heads here, representational geometry there) and in model (instruction-tuned here, base models there).
• CLAIM-029 treats a model’s response to a context as a parameterised frame. If “frame” means one internal state that the context sets, this paper counts against a frame common to the forms of a context: what the context sets depends on how it is presented. It does not count against a frame per presentation form.
• CLAIM-118 separates conditioning from adapting the interpreter. Finding 5 bears on it from an unexpected side: the instruction route is built into the interpreter by post-training, while the demonstration route is not changed by it. So what a given context can do depends on the interpreter’s training history, which fits CLAIM-074.
• THEORY-169 (conditioning as training an inner learner) is stated for attention layers on demonstrations. It has no account of instructions, and this paper suggests none falls out of it: the instruction route is a learned mechanism of its own.
• Files THEORY-264.
• The paper ends with prompt-design advice (combine instructions and demonstrations; steer at several layers). That is practice for the anthology, and is not carried here. The LIT’s anthology-candidate flag stands.

Limitations

• One construct. Task vectors and other extraction methods are not tested. “We cannot conclusively prove the negative, that common task representations do not exist; we can only demonstrate that our methods did not identify them” (§5.1).
• Fixed depth. ⌊L/3⌋ is “arbitrary”; the best-layer results are in the appendix.
• Simple tasks, small models, one seed, one template. The authors defend the single seed by Todd et al.’s consistency.
• Part of the joint gain is magnitude, per the add-twice control.
• The instructions were written by another model from the demonstrations, which ties the two forms closer than human instructions might.

Open questions

• Would task vectors, or a learned per-layer representation, find a common component the FV construct misses?
• What do the instruction-only heads do, and do they respond to the words that convey an instruction, as Wu et al. would predict?
• Does the dissociation hold for open-ended tasks, and for presentations other than these two (role prompts, explanations)?