Span-attention confound normalization: sinks, position, recency, and length

This is the deliverable for #862, the second prior-art survey under the reward-over-spans epic (#860). The question is not whether attention has any signal; #861 answers that. The question here is what a span-attention reward must subtract before the remaining mass can be treated as content evidence.

Verdict:

A span reward must be excess attention over a null model, not raw attention. The null model must account for sink tokens, non-creditable prompt infrastructure, span length, relative position, and distance from the consuming query.

The shape already matches the local shadow scorer:

reward(s,T) =
    success_gate(T)
  * recency_discount(s,T)
  * max(0, raw_attention_mass(s,T) - expected_attention_mass(s,T))

The work of #862 is defining expected_attention_mass.

Confounds to subtract

Confound Prior-art basis What goes wrong with raw attention Required normalization
Attention sinks StreamingLLM observes that initial tokens can receive strong attention even when they are not semantically important. Source: https://arxiv.org/abs/2309.17453. A span that contains BOS, the first prompt token, or another sink-like prefix token receives fake credit. Mark sink/preamble positions as non-creditable infrastructure; subtract a sink baseline or exclude them from positive reward.
Massive activations / outlier tokens Massive Activations in LLMs finds very few activations can be extremely large and can concentrate attention probabilities on corresponding tokens. Source: https://arxiv.org/abs/2402.17762. A token can attract attention because it is an architectural/bias carrier rather than task-relevant content. Track outlier/special tokens as a sink class; cap per-token contribution or subtract an empirical per-position/per-token-class baseline.
Beginning/end position bias Lost in the Middle shows performance often peaks when relevant information is at the beginning or end and degrades in the middle. Source: https://arxiv.org/abs/2307.03172. Beginning/end spans look better than middle spans even when relevance is held constant. Subtract an expected attention curve by relative position bucket.
U-shaped positional attention bias Found in the Middle ties lost-in-the-middle behavior to a U-shaped attention bias favoring leading and ending contexts regardless of relevance. Source: https://arxiv.org/abs/2406.16008. A raw attention reward learns the layout preference instead of content value. Calibrate by position: compare a span only against same-length spans at the same relative position/distance bucket, or subtract the learned U-shaped baseline.
Recency / end-of-context bias Attention Sorting reports that sorting highly attended documents later can improve long-context performance, exposing recency-sensitive use of context. Source: https://arxiv.org/abs/2310.01427. Recently appended spans draw mass because they are near the query, not necessarily because they are useful. Include distance-to-query or turn-age in the null model; keep semantic recency discount separate from raw recency attention.
Span length A longer span owns more key positions and can collect more row mass by surface area. Big spans look useful by size. Expected mass must scale with visible token count; the fallback baseline is uniform-visible mass for the span length.
Prompt role / pinned roots Local system, developer, policy, and pinned spans may be required infrastructure. Required setup text gets rewarded because every turn depends on it. Treat pinned/root spans as protected or separately accounted; do not let them compete with candidate working-memory spans unless the benchmark explicitly asks for root credit.

Normalization contract

For every candidate span s consumed by turn/task T, compute:

raw_mass(s,T) =
  sum attention(l,h,q,p)
  for consumer query rows q in T
  for all observed layers l and heads h
  for key positions p owned by span s

expected_mass(s,T) =
  E[raw_mass | model, task_class, query_shape,
              span_length_bucket,
              relative_position_bucket,
              distance_to_query_bucket,
              token_class/sink_class,
              prompt_role]

excess_mass(s,T) = max(0, raw_mass(s,T) - expected_mass(s,T))
reward(s,T) = success_gate(T) * semantic_recency_discount(s,T) * excess_mass(s,T)

The null model can be implemented in rungs:

  1. Uniform-visible fallback. If no empirical baseline exists, expected mass is the per-row uniform attention share for the span’s visible token count. This is the existing safe fallback in internal/model/span_reward_shadow.go.
  2. Position-length baseline. Bucket by relative position and span length, then subtract the mean attention mass for spans with the same geometry.
  3. Distance/age baseline. Add distance from the consuming query and turn age. This separates “recent therefore attended” from “content useful despite age.”
  4. Sink/preamble mask. Mark BOS/special-prefix/system/policy/pinned roots as non-creditable or use a dedicated sink baseline that cannot produce positive reward.
  5. Per-head/layer calibration. If a head or layer is sink-dominated, subtract its own baseline before summing, or downweight it in a documented calibration run.

The first rung is enough for a fail-closed shadow experiment. The second and third rungs are the minimum for a quotable reward claim on long-context agent traces.

Concrete spec for fak

Use this producer contract for the #866 experiment:

  1. Score only consumer/probe rows, not rows emitted while the span is being constructed.
  2. Attribute rows to semantic spans through the From/Len ledger.
  3. Compute raw_attention_mass per span.
  4. Compute expected_attention_mass from the best available baseline:
    • empirical same-position/same-length/same-distance baseline if present;
    • otherwise uniform-visible baseline;
    • sink/preamble spans are excluded from positive reward unless explicitly allowed.
  5. Compute normalized_reward = max(0, raw_attention_mass - expected_attention_mass) * success_gate * recency_discount.
  6. Run exact-eviction LOO on top/bottom spans and record whether normalization improved Spearman correlation versus raw attention.

The acceptance signal is already named locally: SpanRewardReport.ConfoundNormalizationImproved must be true for an attention producer to graduate. If raw attention beats normalized attention, the normalization is wrong or the null model is too coarse; do not promote the reward.

What not to normalize away

Not every correlation with position is a defect. Fresh tool output may genuinely matter more than an old plan. A pinned system rule may genuinely be necessary. The rule is:

This is why recency appears twice. A distance-to-query baseline removes content-agnostic recency attention. A separate semantic recency discount can still be used as a product choice when fresher evidence should matter more.

Failure cases

Mapping to current code

Downstream rule

Any downstream result that quotes a span reward must report four fields:

If expected_attention_mass is omitted, call the number raw telemetry, not reward.

Sources

Primary sources:

Local source files: