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FlashTrace makes multi-token attribution for reasoning LLMs single-pass and recursive, cutting cost by over 130x while keeping faithfulness.

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T0 review · deepseek-v4-flash

2026-08-03 05:30 UTC pith:QKW37XGU

load-bearing objection The speedup is real and the span-wise aggregation is a genuine trick, but the faithfulness claims overreach the paper's own numbers. the 4 major comments →

arxiv 2602.01914 v4 pith:QKW37XGU submitted 2026-02-02 cs.LG

Towards Long-Horizon Interpretability: Efficient and Faithful Multi-Token Attribution for Reasoning LLMs

Wenbo Pan , Zhichao Liu , Xianlong Wang , Haining Yu , Xiaohua Jia This is my paper
classification cs.LG
keywords multi-token attributioninterpretabilityreasoning LLMschain-of-thoughtlong-contextspan-wise aggregationrecursive attributionfaithfulness
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Modern LLMs increasingly answer after long chains of reasoning, and existing token-attribution methods—which explain one output token at a time—become prohibitively slow and systematically mispointed: reasoning tokens absorb the importance, so the original inputs that drove the answer are never identified. This paper claims both problems yield to one algorithmic move. Aggregating attention and residual contributions over the whole target span before applying the importance metric drops attribution cost from O(M*N) to O(N) per hop; then re-targeting the high-scoring reasoning tokens with a weighted span pushes importance back through the chain to the input. Experiments on long-context retrieval, math, multi-hop QA, and code editing show over 130x speedup against the best prior method while maintaining or improving faithfulness, with one recursive hop sufficient. If the claim holds, faithful multi-token attribution for reasoning LLMs becomes practical rather than prohibitive.

Core claim

The paper's central claim is that multi-token attribution for a reasoning LLM collapses to one forward-like pass per hop: because a source token's value vector is the same for every target, summing attention contributions over a span factors into that vector times the span's aggregated attention weights, reducing cost from O(M*N) to O(N). Recursive attribution then weights the high-scoring reasoning tokens as a new span and traces their importance back to the original input, accumulating input-token scores across hops. On long-context retrieval, math, multi-hop QA, and code-editing tasks this matches or beats per-token baselines on faithfulness while running over 130x faster.

What carries the argument

The load-bearing identity is span-wise aggregation for attention: for a target span S, the summed contribution from source token j is v_j * (sum_{i in S} alpha_{i,j}), where v_j is the value vector that depends only on j. This factorization moves the expensive vector transform out of the loop over target tokens, turning per-hop cost from O(M*N) to O(N). The same idea extends to weighted spans, so a recursive hop can target the reasoning tokens weighted by their previous attribution scores. Importance is scored with the L1 proximity metric Prox(z,y)=max(0, -||y-z||_1 + ||y||_1), which estimates how much a target's magnitude falls if a contribution is removed. Final input attribution is the ma

Load-bearing premise

The load-bearing premise is that the L1-proximity of aggregated span vectors faithfully equals the average of per-token attributions; the paper's only direct test of this, on 100 MorehopQA samples, shows FlashTrace 10% worse on RISE than exhaustive token-level rollout.

What would settle it

Run FlashTrace and the exhaustive token-level rollout on the same reasoning chains at 1K, 5K, and 32K context lengths; if the RISE/MAS gap widens beyond the reported 10% or the ground-truth recovery rate drops below a per-token baseline as the chain grows, the span-wise approximation is not faithful at scale.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A 5,000-token generated explanation can be attributed in seconds rather than tens of minutes, with cost that scales linearly in context length and stays independent of the span being explained.
  • Attribution stops pointing at the last reasoning step: re-targeting the important reasoning tokens recovers the original input tokens, which is exactly what reasoning-chain interpretability needs.
  • The same span mechanism applies to code and other structured intermediate output, so agent tool-use traces can be attributed back to user instructions and codebase context.
  • Because one recursive hop resolves most of the information absorption, a production explanation needs only two attribution passes, keeping overhead close to a single forward pass.
  • On long-context multi-hop QA, ground-truth evidence recovery rises substantially over per-token baselines, supporting use cases like auditing which retrieved context caused an answer.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the factoring trick relies on the value vector being target-independent, so the efficiency gain should transfer to most transformer attention variants but would break under target-dependent value computations; testing such an architecture would isolate the source of the speedup.
  • Beyond the paper: the only direct span-wise-vs-exhaustive check was on 100 samples and showed a 10% RISE gap; repeating it at 1K, 5K, and 32K context lengths would establish whether the approximation's faithfulness degrades with reasoning length.
  • Beyond the paper: the recursion can be applied to tool-call outputs and environment observations as if they were reasoning tokens, potentially explaining agent-environment interaction loops rather than only internal thought chains.
  • The paper itself notes that caching all attention maps costs O(L*N^2) memory; the advertised O(N) working memory assumes recomputation or chunking, so the speedup carries a compute-for-memory trade-off that long-context deployments should re-measure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. FlashTrace proposes two mechanisms for multi-token attribution in reasoning LLMs: span-wise aggregation, which attributes an entire target span in one pass by factoring the value transform and pre-aggregating scalar attention weights, and recursive attribution, which re-weights reasoning tokens as targets for subsequent hops and accumulates input scores. The paper reports large efficiency gains (up to 130x over IFR) and favorable faithfulness on RULER, MATH, MorehopQA, and Aider, and claims O(N) complexity and that even one recursive hop improves faithfulness.

Significance. Attribution for long chain-of-thought and agentic outputs is a timely and important problem. The core factorization in Eq. (8) is a genuine algorithmic idea: because the transformed value vector depends only on the source token, summing scalar attention weights over target positions removes the D-dimensional vector loop from the per-target iteration. The measured speedups are plausible if the implementation follows the algorithm. However, the paper currently overstates both the complexity and the faithfulness results: the O(N) claim conflicts with the paper's own Appendix B, the single-hops improvement claim is contradicted by Table 7 for RISE, and no faithfulness experiment actually uses long contexts. With corrected claims and additional validation, the method could be a useful contribution; in its current form the headline claims are not established.

major comments (4)
  1. [§4.2; Eq. (8); Appendix B.1] The main text and abstract state that span-wise aggregation reduces complexity from O(M·N) to O(N). Appendix B.1 gives T_FlashTrace = O(L·N·(M+D)), i.e., the O(M·N) scalar attention-aggregation term remains; the speedup comes from removing the D factor, not from eliminating the M dependence. Since M can be thousands of reasoning tokens, the claim that the method scales linearly with context length and the O(N) entry in Table 3 are not supported. Please correct the complexity statement throughout, or provide a quantitative bound under which the scalar term is negligible.
  2. [§5.2, Table 3; Eq. (7)] The faithfulness claim rests on the span-wise aggregation in Eq. (7), but no bound or monotonicity result is given for Prox(Σz_j, Σy_i) versus Σ Prox(z_j,y_i). The only empirical check is 100 MorehopQA samples: FlashTrace RISE is 0.128 versus 0.116 for the exhaustive rollout (about 10% worse), and MAS is 0.205 versus 0.193 (about 6% worse), with no confidence intervals, yet the text calls this a match. This does not support 'maintaining superior faithfulness,' and the approximation error may grow with target-span length. Please provide a more extensive validation (more samples, varying M, long contexts) or substantially weaken the claim.
  3. [Abstract; Appendix H, Table 7] The abstract states that 'even a single recursive hop improves faithfulness.' Table 7 shows the opposite for RISE: 0.127 with 0 hops versus 0.128 with 1 hop (slightly worse), while MAS improves from 0.209 to 0.205. Thus the claim is metric-specific and not uniformly supported. Please rephrase to report the metric-specific effects and discuss the RISE degradation.
  4. [Appendix E.1; Table 1; Figure 5] The paper motivates long-horizon interpretability, but Appendix E.1 states that all RULER faithfulness runs in Table 1 use a fixed context length of 1024 tokens. Table 1 and Figure 5 therefore do not demonstrate faithfulness at long context; only the efficiency experiments in Figure 4 use longer sequences. The claim of 'superior faithfulness' in long contexts is unsupported. Please add long-context faithfulness experiments or restrict the claims to the 1024-token setting.
minor comments (5)
  1. [Table 1] Several entries are run together without spacing, e.g., the IFR row for NIAH reads '0.0120.5750.452'. Please fix the table formatting.
  2. [Figure 4(e); Appendix C] IG and IG-Attn are included in the 'Pareto front' plot even though their faithfulness values are unavailable due to OOM. Appendix C explains this, but the main text should state that their positions reflect efficiency only.
  3. [Appendix B.2] The memory claim in §5.1 ('avoids memory overhead that scales with target span') should be qualified: Appendix B.2 notes that the working memory is O(N+D), but caching attention maps requires O(L·N^2). The distinction should be made in the main text.
  4. [Appendix H] The number of recursive hops K=1 is selected using the MorehopQA ablation (Table 7) and then MorehopQA results are reported with that K. This is a mild form of test-set hyperparameter selection; please use a separate validation set or report sensitivity across datasets.
  5. [Appendix E.4] Only 100 correctly answered samples per dataset (and 66 for HotpotQA) are used for evaluation. Please state this in the main text and, ideally, provide confidence intervals for the headline faithfulness numbers.

Circularity Check

0 steps flagged

No construction-level circularity: span aggregation is an algebraic identity, and the main approximation is explicitly tested against an exhaustive rollout.

full rationale

FlashTrace's derivation chain is self-contained. The span-wise aggregation in Eqs. (5)-(8) rests on the linearity of attention contributions: the transformed vector v_j depends only on the source token and not on the target position, so swapping the order of summation is exact algebra rather than a fit to the evaluation metrics. The recursive weighting in Eqs. (9)-(12) is a transparent algorithmic rule. No parameter is fitted to RISE, MAS, or Recovery Rate; all attribution scores are computed from cached activations and attention maps. The only load-bearing approximation—replacing the average of per-token proximity scores with the proximity of aggregated span vectors (Eq. 7 vs. the per-token average)—is not asserted as an identity; the paper explicitly tests it in Table 3 against an exhaustive token-level rollout, reporting RISE 0.128 vs. 0.116 and MAS 0.205 vs. 0.193. That is an approximation-quality weakness, not circularity. The choice K=1 is informed by the MoreHopQA ablation in Table 7, so reporting MoreHopQA with K=1 is mild test-set hyperparameter selection, but the central derivation does not reduce to that choice, and the efficiency and long-context faithfulness measurements stand independently. No load-bearing self-citation or uniqueness theorem is invoked; ALTI/IFR are external prior work, and the paper's claim to improve on them is grounded in external perturbation metrics. Therefore no construction-level circularity is present.

Axiom & Free-Parameter Ledger

1 free parameters · 5 axioms · 0 invented entities

The method inherits the ALTI/IFR proximity heuristic, linearizes normalization layers, and postulates a 'flow of probability mass' aggregation with no derivation. The main free parameter is the hop count K, tuned on the MorehopQA test set. No invented entities.

free parameters (1)
  • K (number of recursive hops) = 1
    Set to 1 in all experiments; chosen based on ablation Table 7 on MorehopQA test set, and the same dataset is reported in main results. K=0 vs K=1 difference is within noise; this is test-set hyperparameter selection.
axioms (5)
  • domain assumption The L1-norm proximity metric Prox(z,y)=max(0, ||y||_1 - ||y-z||_1) is a valid measure of causal contribution of z to y.
    Inherited from ALTI/IFR (Ferrando et al. 2022); not proven to equal causal importance. Used in Eq. (4) and all attribution scores.
  • ad hoc to paper LayerNorm/RMSNorm can be linearized as element-wise scaling Norm(x) ≈ x ⊙ s(x) with fixed s from forward pass.
    Eq. (13); approximation needed for the decomposition; nonlinearity effects are ignored.
  • ad hoc to paper The attribution flow through reasoning tokens is a linear Markov chain: final input importance is the discounted sum of per-hop input attributions with multipliers ρ_k (Eq. 12/24).
    Asserted as 'flow of probability mass'; no derivation. The discounting formula is chosen by hand and not validated against exhaustive rollout other than one aggregate comparison.
  • domain assumption The aggregated span proximity Prox(Z_S, Y_S) approximates average per-token attribution within acceptable error.
    Core of span-wise aggregation; only empirical check is Table 3 on 100 MorehopQA samples, showing 10% RISE degradation vs exhaustive token-level rollout.
  • domain assumption Correctly-answered generations only: attribution of incorrect answers is invalid/noisy.
    Appendix E.4; filters out incorrect answers, which may bias the evaluation toward easy samples.

pith-pipeline@v1.3.0-alltime-deepseek · 21905 in / 17385 out tokens · 151823 ms · 2026-08-03T05:30:46.611213+00:00 · methodology

0 comments
read the original abstract

Token attribution methods provide intuitive explanations for language model outputs by identifying causally important input tokens. However, as modern LLMs increasingly rely on extended reasoning chains, existing schemes face two critical challenges: (1) efficiency bottleneck, where attributing a target span of M tokens within a context of length N requires O(M*N) operations, making long-context attribution prohibitively slow; and (2) faithfulness drop, where intermediate reasoning tokens absorb attribution mass, preventing importance from propagating back to the original input. To address these, we introduce FlashTrace, an efficient multi-token attribution method that employs span-wise aggregation to compute attribution over multi-token targets in a single pass, while maintaining faithfulness. Moreover, we design a recursive attribution mechanism that traces importance through intermediate reasoning chains back to source inputs. Extensive experiments on long-context retrieval (RULER) and multi-step reasoning (MATH, MorehopQA) tasks demonstrate that FlashTrace achieves over 130x speedup over existing baselines while maintaining superior faithfulness. We further analyze the dynamics of recursive attribution, showing that even a single recursive hop improves faithfulness by tracing importance through the reasoning chain.

Figures

Figures reproduced from arXiv: 2602.01914 by Haining Yu, Wenbo Pan, Xianlong Wang, Xiaohua Jia, Zhichao Liu.

Figure 1
Figure 1. Figure 1: Motivation for FLASHTRACE. Top: Naive token-by￾token attribution requires expensive per-token computation, while FLASHTRACE performs efficient span-wise recursive attribution. Bottom: (a) With extended reasoning, attribution weight on rea￾soning tokens increases significantly (from approximately 80% to over 90%); (b) This causes recovery rate of ground-truth input tokens to drop substantially (from 26% to … view at source ↗
Figure 2
Figure 2. Figure 2: Overview of FLASHTRACE span-wise attribution. The method pre-aggregates causal attention and residual contributions within target spans at each layer, enabling efficient multi-hop attribution through chains of intermediate reasoning. Identification (Wang et al., 2023), their application to com￾plex, multi-token generations remains underexplored. In the following section, we demonstrate that the presence of… view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of recursive attribution across hops. Hop 1: Initial attribution concentrates on reasoning tokens nearest to the output. Hop 2: Attribution shifts toward earlier reasoning tokens and input context. ∆ (Hop2 - Hop1): The difference map shows how importance propagates backward: green regions indicate tokens gaining attribution in the second hop (typically input tokens), while red regions show to… view at source ↗
Figure 4
Figure 4. Figure 4: Efficiency comparison across methods. (a-b) Time cost vs. input and generation length. (c-d) Memory consumption vs. input and generation length. (e) Pareto front of speed vs. faithfulness. FLASHTRACE achieves the most efficient scaling in both time and memory, while gradient-based methods (IG, IG-Attn, Perturbation) encounter OOM at longer contexts. Dashed lines indicate OOM. 130× faster than the most effi… view at source ↗
Figure 5
Figure 5. Figure 5: Faithfulness (MAS) across reasoning lengths. FLASH￾TRACE maintains stable performance and consistently outperforms baseline methods. 5.2. Discussion and Ablations Compare with Exhaustive Token-Level Rollout To assess how well FLASHTRACE approximates the com￾plete multi-hop information flow, we compare it against a computationally intensive baseline we term Exhaustive Token-Level Rollout. This method repres… view at source ↗
Figure 6
Figure 6. Figure 6: Token-level attribution heatmaps on MATH dataset samples. Hop 1 attributes the output directly to the context. Hop 2 recursively attributes through the reasoning chain. ∆ (Hop2 − Hop1) shows the change: green indicates increased attribution (input tokens), red indicates decreased attribution (reasoning tokens). 0 1 2 3 Recursive Hops 0.0 0.2 0.4 0.6 0.8 1.0 Attribution Weight Input tokens take majority of … view at source ↗
Figure 7
Figure 7. Figure 7: Attribution mass shift during recursive hops. From hop 0 to hop 1, the attribution mass on reasoning tokens de￾creases while attribution shifts toward input tokens. Aggre￾gated across 100 samples from the MoreHopQA dataset. We conduct our pilot study using the multi-hop retrieval task from RULER (Hsieh et al., 2024)’s VT subset. Specifically, we use one example from the validation set and prompt Qwen-3 8B … view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

12 extracted references · 2 linked inside Pith · cited by 1 Pith paper

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    Let wi be a scalar weight for token i (for the first hop, wi = 1; for recursive hops, wi is determined by the previous iteration)

    Aggregated Target Definitions.Instead of attributing each token i∈S individually, we define aggregated target vectors for the attention and MLP blocks. Let wi be a scalar weight for token i (for the first hop, wi = 1; for recursive hops, wi is determined by the previous iteration). The aggregated post-attention target is: Xmid S = X i∈S wi ·x mid i .(16) ...

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    Doing this for all pairs (i, j)where i∈S is computationally expensive

    Attention Contribution (The Efficiency Key).Standard attribution requires computing the contribution of source token j to target token i, which involves the attention weight αi,j. Doing this for all pairs (i, j)where i∈S is computationally expensive. We optimize this by swapping the order of summation. First, we compute the transformed value vector for so...

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    For each layer, we calculate: •Token Importance (e tok,j):The proximity of sourcej’s contribution to the target span

    Computing Proximity Scores.We use the L1-based proximity metric Prox(c,t) = max(0,−∥t−c∥ 1 +∥t∥ 1). For each layer, we calculate: •Token Importance (e tok,j):The proximity of sourcej’s contribution to the target span. etok,j =Prox(C j→S ,X mid S ).(19) •Residual Importance (e res):The proximity of the residual stream bypass. RS = X i∈S wi ·x in i ⇒e res =...

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    The score for token j at layer l is normalized by the sum of all token contributions plus the residual importance at that layer

    Normalization and Aggregation.The raw proximity scores are normalized to form a valid probability distribution. The score for token j at layer l is normalized by the sum of all token contributions plus the residual importance at that layer. We sum these normalized scores across all heads and layers to obtain the global importance distribution w(k) for the...

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    This produces a new distribution w(k) describing which inputs caused the specific reasoning tokens that were important in the previous step

    Execute Span-Wise Pass:We run the span-wise attribution with target span Sthink and token weights w(k) t . This produces a new distribution w(k) describing which inputs caused the specific reasoning tokens that were important in the previous step. 13 Efficient and Faithful Multi-Token Attribution for Reasoning LLMs Final Accumulation.The final attribution...

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    We store the forward cache (Key/Value states), which is inherent to inference:O(N·D)

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    For attribution, we store the pre-aggregated attention weights:O(N)

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    We store the aggregated target vector:O(D)

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    needles” (key-value pairs in the format “The special magic number for X is Y

    During chunked computation, we process small blocks of sizeB. Memory usage isO(B·D). Thus, the peakworking memoryfootprint during the attribution computation (excluding the fixed model weights, KV cache, and attention maps) is: Mwork FlashTrace =O(N+D).(29) This working memory is independent of the target span length M, allowing efficient processing of lo...

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    URL https://proceedings.mlr.press/ v235/achtibat24a.html. Chen, J., Li, X., Yu, L., Dou, D., and Xiong, H. Be- yond intuition: Rethinking token attributions inside trans- formers.Transactions on Machine Learning Research,