{"id":"258842d4-c2db-44e9-8a76-20ac2bd40b67","arxiv_id":"2508.18763","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"MCSU-based vocabulary alignment plus distance-based dynamic selection (DDS) lets several LLMs vote token-by-token, beating single models and prior ensemble baselines on multiple reasoning benchmarks without training.","lead":"Several language models can cooperate at the level of single words: each proposes its next-word probabilities, the most mutually consistent proposals are averaged, and the next word is chosen from that blend. The paper reports that this training-free strategy, called DDS, improves accuracy on math, common-sense, and symbolic reasoning benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"DDS selection rule is not well-defined as written: top-k truncation plus union support makes the KL divergences in Eqs. 3–5 infinite/unnormalized, so the reported gains are not traceable to the specified algorithm.","rationale":"I read the paper in good faith: the idea of token-level collaboration via aligned minimal semantic units is sensible, the experiments consistently favor DDS, and the failure analysis in Appendix F is honest. The reader's clustering-assumption concern is real, but I think there is a more immediate, formal problem. The DDS selection rule in Eqs. (3)–(5) is not actually a well-defined KL divergence: top-k truncation leaves zeros inside the union support, producing infinite values for typical pairs, and the vectors are not normalized after truncation. Also, MCSU probabilities from Eq. (2) are prefix probabilities, not probabilities of disjoint next-semantic-unit events, so they need not sum to one. Any of these issues would make the 'retain if DKL<ε' criterion arbitrary or non-computable as stated. This is not an attack on the empirical results; the implementation may have used sensible smoothing and renormalization, but the paper does not say so and no code is available. A direct implementation check would settle whether the published equations can reproduce the reported behavior. I therefore keep the conditional verdict: the paper should be accepted only if the authors clarify/correct the definitions and release code that reproduces Tables 1–8.","tokens_in":22003,"tokens_out":11013,"duration_ms":113209,"concrete_test":"Re-implement or obtain the authors' code and run Qwen-2-7B, Llama-3-8B, and GLM-4-9B with greedy decoding on 500 GSM8K examples. At every autoregressive step, compute Eq. (2) for the top-5 MCSUs per model and then apply Eqs. (3)–(5) exactly as written. Record (i) the fraction of pairwise KL values that are infinite or NaN; (ii) the fraction of steps where the retained set changes when each P*_i is properly renormalized and all zero-probability entries (not just entries outside U) are smoothed to 1e-9, with KL computed symmetrically. If >5% of steps contain infinite KL or >1% of selections change, the published equations do not specify the method behind Tables 1–8, and the manuscript must be revised before the central claim can be evaluated.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section 3.2 defines the core selection statistic in a way that cannot be computed. After Eq. (3) truncates each model's MCSU distribution to its top-k (k=5 in experiments), Eq. (4) sets P*_i(x)=P_top-k_i(x)=0 for every x in the union U that is not in model i's top-k. The KL sum in Eq. (5) then contains terms P*_i(x) log(P*_i(x)/P*_j(x)) with P*_i(x)>0 and P*_j(x)=0, giving +∞, or vice versa. With k=5 and vocabularies of tens of thousands, this is the normal case, so the 'retain if DKL<ε' rule is undefined for most pairs. Independently, P*_i is not renormalized after truncation and 1e-9 filling, so it is not a probability distribution; DKL of unnormalized vectors is not a divergence and its value is sensitive to each model's missing probability mass. The same problem affects Eq. (2): the product of conditional token probabilities for a multi-token MCSU is only one prefix probability, not the probability of the next MCSU as a disjoint semantic unit, so the sum over MCSUs is not 1. Thus the central empirical claim—that DDS's KL-based filtering improves reasoning—is not formally connected to the algorithm described. If the code silently renormalizes and adds smoothing to all zeros, the paper must say so; otherwise the experimental tables cannot be interpreted.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DDS (Distribution Distance-based dynamic Selection), a training-free token-level ensemble method for heterogeneous LLMs. To handle vocabulary misalignment, it introduces Minimal Complete Semantic Units (MCSUs), aligning models at the level of words/numbers rather than raw tokens. At each autoregressive step, each model's next-MCSU distribution is top-k truncated; pairwise KL divergences over the union support are used to discard outlier distributions; the retained distributions are averaged and decoded greedily. Experiments on 12 reasoning benchmarks (math, commonsense, symbolic), plus code, Chinese, and reliability evaluations, report consistent accuracy gains over single models and output-level/token-level baselines. The paper also presents anecdotal cases where DDS is correct though all member models are wrong, and discusses failure cases in Appendix F.","tokens_in":22409,"tokens_out":2803,"duration_ms":32939,"significance":"If the method works as claimed, token-level distribution blending is a valuable training-free direction for combining heterogeneous LLMs, and the MCSU concept is a sensible way to reduce vocabulary mismatch without learned projections. The paper ships a broad benchmark suite and several ablations, and explicitly discusses limitations, including the failure mode where divergent-but-correct reasoning breaks the clustering assumption. These are genuine strengths. However, the central algorithm as written is not computable, and the empirical support lacks statistical grounding; the headline gains are small and depend on a validation-tuned threshold. The significance therefore hinges on a few fixes plus a clearer statement of the implemented selection rule.","major_comments":[{"comment":"The KL divergence used for selection is undefined as written. Eq. (3) sets all but the top-k MCSUs to zero; Eq. (4) only replaces values outside the union U with 1e-9, but for x∈U not in model i's top-k, P*_i(x) remains 0. Since the sum in Eq. (5) runs over U, and with k=5 and vocabularies of tens of thousands, each pair almost always has x where P*_i(x)>0 and P*_j(x)=0 (or vice versa), giving DKL=+∞. Additionally, P*_i is not renormalized after truncation, so it is not a probability distribution and DKL is not a valid divergence. The experimental tables therefore cannot be traced to the specified algorithm. The authors should either redefine P*_i to assign small mass to every element of U and renormalize, or explicitly state that the implementation smooths all union elements; the current text is inconsistent with the reported results.","section":"§3.2, Eq. (2)"},{"comment":"The MCSU probability is defined as the product of conditional token probabilities over the tokens in the MCSU. This is a prefix probability, not the probability of a disjoint next-MCSU event; the sum over MCSUs is not 1, so the 'distribution' used in Eq. (5) is not normalized even before top-k truncation. This compounds the KL issue in Eq. (5). The paper should clarify how these quantities are normalized (if at all) before divergence computation, and justify why the resulting value is a meaningful distance.","section":"§3.2"},{"comment":"The central claim that DDS 'significantly enhances' reasoning is not supported by statistical evidence. Tables 1–3 report no error bars, confidence intervals, or significance tests; for several benchmarks the DDS gain over the best single model is under 1 point (e.g., Table 1: AddSub 65.5 vs. Qwen 65.5; Table 3: Penguin 83.0 vs. GLM 81.5, but with no variance estimate). Moreover, Table 7 shows the method is sensitive to ε, and ε=0.1 is selected via validation (Appendix A), so the test numbers are conditional on a tuned hyperparameter. The authors should report standard deviations over repeated runs or bootstrap intervals, and state whether ε was fixed before seeing test sets. Without this, the consistent but small gains may be within noise.","section":"Tables 1–3, Table 7"},{"comment":"The selection rule 'if DKL<ε then retain' is pairwise and non-transitive; for three models, A-B and B-C may be close while A-C is not, and the paper does not specify how the retained set is formed in that case. More fundamentally, the core assumption that correct distributions cluster while incorrect ones are scattered is acknowledged in Appendix F to fail when models produce divergent but correct continuations. Since that failure occurs at 'critical stages' such as key numbers/options, the proposed filtering can discard useful distributions exactly when cross-model reasoning styles differ. The authors should state the exact selection procedure and quantify how often the fallback 'retain all' is triggered; otherwise the reported gains cannot be attributed to the filtering mechanism rather than to simple averaging.","section":"§3.2 / Appendix F"}],"minor_comments":[{"comment":"The definition of MCSU relies on whitespace for English and on the assumption that Chinese tokens are complete words. This is reasonable for the tested benchmarks but should be stated as a design assumption; the claim that these two cases cover 'the majority of language types' is broad and unsupported.","section":"§3.1"},{"comment":"The reliability evaluation reports ROUGE, BLEU, and BLEURT on TruthfulQA. These are reference-based generation metrics; the standard TruthfulQA evaluation uses multiple-choice truthfulness and informativeness. The authors should clarify the reference set and why higher BLEU/ROUGE/BLEURT is interpreted as greater truthfulness.","section":"Table 5 / §4.4"},{"comment":"The determination of ε by 'data-driven statistical analysis' is described only abstractly (histogram/CDF, mean). Reporting the actual distribution of KL values and the exact validation split would make the procedure reproducible.","section":"Appendix A"},{"comment":"The emergent-capability examples are illustrative but not quantified. A systematic analysis of how often DDS produces a correct final answer when all three members are wrong, and how often it flips a correct member answer to wrong, would strengthen the claim.","section":"§4.6"},{"comment":"Minor typos and inconsistent notation: 'emsembling' in section headings, 'distrition' in §3.2, 'DSS' used in place of 'DDS' in Appendix C, and 'CommonseQA' for CommonsenseQA. The acronym DSS at line 'using DSS ensemble method' should be corrected.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for a venue interested in efficient inference-time LLM ensembling. The MCSU idea is a useful contribution. However, the current version cannot be accepted because the central selection statistic is undefined as written; the experiments need a clear statement of the implemented smoothing/renormalization, and ideally error bars. The code release (promised but not yet available) will be important for verifying the exact selection rule."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this one. First, the MCSU idea is genuinely nice: using whitespace-delimited words instead of tokens gives a simple, low-cost way to align heterogeneous tokenizers, and the paper shows it works on English and Chinese. Second, the core selection rule in Section 3.2 has a formal hole that looks fatal as written. Eq. (3) truncates each model's distribution to its top-5 MCSUs, Eq. (4) only fills 1e-9 for items outside the union U, and then Eq. (5) computes KL divergences over U. But for any x in model i's top-5 that isn't in model j's top-5, the sum has P*_i(x)>0 and P*_j(x)=0, giving +infinity. With k=5 and vocabularies in the tens of thousands, this is the normal case. Also, neither the truncation nor the 1e-9 fill renormalizes, so P*_i isn't a probability distribution and the KL is not a divergence. The paper's headline results therefore cannot be traced to the algorithm it specifies. The stress-test note is correct.\n\nThat said, the paper does other things well. The experimental sweep is broad—12 reasoning benchmarks plus code and Chinese C-Eval—and DDS beats the baselines consistently, even if only by a few points. The ablation on epsilon (Table 7) is honest enough to show sensitivity. Appendix F acknowledges the central clustering assumption fails when models have different styles, which is a real empirical limitation. The authors also give credit to prior token-level ensemble work and don't oversell the emergent-capability examples as more than anecdotal.\n\nThe soft spots beyond the formal flaw: epsilon is tuned on a validation set with a procedure that is not fully specified; there are no error bars or significance tests; code is promised but not released; and loading all models simultaneously makes the method expensive. These are addressable, but the KL issue is not a minor typo—it undermines the method's definition.\n\nWho should read this? People working on inference-time ensembling will want to know about MCSU as an alignment device. But the submission needs a serious referee to force a rewrite of Section 3.2 and ideally code release. I would not cite it in its current form.\n\nMy recommendation: send it to peer review, but only with a clear request that the authors either repair the KL definition (e.g., renormalize over the union with proper smoothing) or provide code showing what was actually computed. As it stands, it's a promising but unexecutable recipe.","headline":"Clever MCSU alignment and consistent few-point gains, but the KL-based selector as written is mathematically undefined, so the experimental numbers don't yet pin down a working method.","tokens_in":22873,"tokens_out":2678,"would_cite":false,"duration_ms":29285,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Token-level probability blending lets three LLMs outreason any one of them.","keywords":["large language models","token-level ensembling","minimal complete semantic units","distribution distance","dynamic selection","training-free reasoning enhancement","KL divergence","multi-model collaboration"],"falsifier":"Take a benchmark with multiple valid answer phrasings (or rewrite GSM8K solutions so two models reach the same answer through different wording) and record, at each step, the pairwise KL divergence among the three MCSU distributions. If DDS accuracy on steps where the pairwise KL exceeds the 0.1 threshold is no better than choosing the single most confident model, the clustering premise is the reason for both the gains and the failures; a second check is whether a single high-confidence wrong MCSU (e.g., one model assigning 0.8 to an incorrect option while others disagree) reliably flips the f","tokens_in":21950,"feed_emoji":"🔀","tokens_out":5148,"duration_ms":54386,"temperature":0.7,"pith_summary":"Large language models disagree not only in their final answers but in every next-token probability they assign. This paper argues that those per-step distributions are where each model's knowledge lives, and that combining them at token level can improve reasoning without any training. The obstacle is that different models tokenize text differently, so the paper introduces minimal complete semantic units (MCSU)—words, numbers, or punctuation marks—as a common currency for comparing distributions. On top of that, a distribution-distance-based dynamic selection strategy (DDS) keeps only the distributions that cluster together at each autoregressive step, on the principle that correct answers are usually unique while errors are scattered. A reader should care because if this works, three moderate models can be bolted together at inference time to outperform each of them alone, occasionally producing correct answers that none of them would have produced.","feed_headline":"Dynamic token blending beats any single LLM","feed_subtitle":"Three models aligned on semantic units can answer right even when each is wrong alone.","key_machinery":"The two working parts are MCSU and DDS. MCSU replaces tokens as the alignment unit: a token sequence is grown until it forms a complete word, number, or punctuation mark, and the MCSU's probability is the product of its tokens' conditional probabilities, so different tokenizers can be compared in one semantically aligned space. DDS is the selection mechanism: after top-k truncation and padding to a union vocabulary, pairwise KL divergence between MCSU distributions determines which models are kept; distributions within the threshold cluster near what is presumed to be the correct continuation, outliers are dropped, and the surviving distributions are averaged. The threshold is set globally t","core_discovery":"The central claim is that dynamic, distance-based selection over token-level probability distributions—after aligning models on minimal complete semantic units—reliably improves multi-step reasoning accuracy on math, commonsense, and symbolic benchmarks, and does so without retraining or vocabulary projection. At each step, DDS takes the top-k MCSU probabilities from each model, computes pairwise KL divergences, discards outlier distributions beyond a tuned threshold, and averages the rest; the highest-probability MCSU wins. The paper reports that this beats every single member model, beats output-level voting, and beats token-level ensembling baselines that align vocabularies with anchors o","pith_inferences":["The global epsilon of 0.1 is likely not universal; a testable extension would adapt epsilon per step or per model pair, since distributional spread varies with task and with where in the reasoning process a step sits.","MCSU alignment might be reusable beyond ensembling—for example, in speculative decoding, inter-model verification, or any setting where multiple tokenizers must be compared without learned projections.","The emergence cases suggest token-level idea collision could be studied deliberately: measuring how often the winning MCSU comes from a model whose distribution was in the minority earlier would reveal whether the effect is a union of correct prefixes or a genuine mixture.","If the clustering assumption fails on high-variance or open-ended tasks (synonyms, stylistic diversity), DDS may degrade to selecting the most confident wrong token; measuring accuracy conditioned on pairwise KL at each step would map where the method is safe."],"forward_implications":["On the paper's results, training-free token-level ensemble with dynamic selection outperforms the best single model on all three reasoning families tested, with gains around one point on math and two to four points on commonsense and symbolic reasoning.","More models do not automatically help: adding a third model to a two-model collaboration helped on some tasks and hurt on others, which motivates dynamic per-step selection rather than fixed ensembling.","Correct answers can be produced by token-level recombination even when every member model's final answer is wrong, so token-level collaboration offers a capability that majority voting or answer selection cannot recover.","DDS transfers to code generation and a Chinese knowledge benchmark, and improves truthfulness scores on TruthfulQA, suggesting the mechanism is not confined to one task or language.","Because the method is training-free and needs no referee model, it can be deployed by loading several open-weight models and averaging aligned distributions at inference time."],"supporting_citations":[{"why":"Supplies the DEEPEN token-level ensemble baseline, which aligns vocabularies via anchors and is one of the main approaches DDS must outperform.","marker":"(Huang et al., 2024)"},{"why":"Supplies the GAC baseline, a token-level ensemble that treats token generation as classification and uses anchors for vocabulary projection.","marker":"(Yu et al., 2024)"},{"why":"Supplies UNITE, a top-k union token-level ensemble method, and the observation that participating models' capabilities matter for scaling.","marker":"(Yao et al., 2024)"},{"why":"Supplies LLM-Blender, an output-level ensemble baseline that ranks candidate answers and selects the best, representing the alternative paradigm DDS is compared with.","marker":"(Jiang et al., 2023)"},{"why":"Provides the premise that a model's knowledge is expressed in its output probability distributions, which justifies combining distributions rather than answers.","marker":"(Hinton, 2015)"},{"why":"Supports the view that different LLMs have distinct knowledge boundaries and that output probability vectors can be used to transfer or fuse knowledge.","marker":"(Wan et al., 2024)"},{"why":"Supplies GSM8K, one of the primary math reasoning benchmarks used to measure DDS's accuracy.","marker":"(Cobbe et al., 2021)"},{"why":"Supplies SVAMP, another math reasoning dataset used in the evaluation and comparison against baselines.","marker":"(Patel et al., 2021)"}],"fun_headline_variants":["Token-level multi-model fusion outsmarts solo LLMs","Dynamic token choice from multiple LLMs beats single","Semantic unit alignment makes LLM teamwork click","No retraining: pick best tokens across LLMs for reasoning","Multi-LLM token selection trumps any single model"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing assumption is that at every step the correct continuation is essentially unique and similar across models, so distributions that lie close together in KL divergence are near the truth and outliers can be discarded; the paper's own failure analysis shows styles and reasoning paths can legitimately diverge, and then the selection rule keeps everything and the highest-confidence wrong answer can win.","fun_headline_variants_meta":{"raw":{"variants":["Token-level multi-model fusion outsmarts solo LLMs","Dynamic token choice from multiple LLMs beats single","Semantic unit alignment makes LLM teamwork click","No retraining: pick best tokens across LLMs for reasoning","Multi-LLM token selection trumps any single model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000279,"raw_usage":{"total_tokens":1435,"prompt_tokens":623,"completion_tokens":812,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":367,"completion_tokens_details":{"reasoning_tokens":734}},"tokens_in":367,"tokens_out":812,"duration_ms":9267,"temperature":1.0,"reasoning_tokens":734,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T16:12:42.452029+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a benchmark with multiple valid answer phrasings (or rewrite GSM8K solutions so two models reach the same answer through different wording) and record, at each step, the pairwise KL divergence among the three MCSU distributions. If DDS accuracy on steps where the pairwise KL exceeds the 0.1 threshold is no better than choosing the single most confident model, the clustering premise is the reason for both the gains and the failures; a second check is whether a single high-confidence wrong MCSU (e.g., one model assigning 0.8 to an incorrect option while others disagree) reliably flips the f","supporting_citations":[],"review_version":1}