{"id":"bc1ffda4-c3e3-4db9-b7f9-fbcfbf7b13ca","arxiv_id":"2412.13745","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Complex-valued and quantum-circuit word embeddings trained with a fidelity-based Skip-gram loss match classical word2vec on similarity benchmarks, provided the circuits are fit to the complex embeddings rather than trained directly.","lead":"The authors train word embeddings as complex numbers, and also as states produced by parameterized quantum circuits, using a modified Skip-gram objective. The complex embeddings match the classical baseline on similarity benchmarks, and a two-stage pipeline fits quantum circuits to these embeddings while preserving their quality.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim hinges on per-word PQC fitting quality across the full 426k vocabulary, but the paper only reports aggregate WordSim353 equivalence, which is too coarse to rule out a heavy tail of poorly fit words.","rationale":"The reader's weakest_assumption is exactly the load-bearing point: the two-stage pipeline's central claim depends on the PQC ansatz being expressive enough to fit every word's complex embedding to effectively zero loss. I examined other potential concerns—parameter count comparability (the fitted PQC uses 162 parameters per word for 6 qubits, 3 layers of A5, versus 100 for the classical baseline and 128 for the complex embedder), and the use of WordSim353 for model selection—but these are secondary and do not by themselves invalidate the central claim. The decisive issue is the lack of per-word fitting quality evidence. Identical aggregate correlation on a 353-pair dataset is compatible with substantial per-word errors, and the paper's inference from identical scores back to zero loss is circular in the absence of direct loss statistics. A concrete per-word fidelity check would settle whether the claim holds for the full vocabulary or only for the small subset of words appearing in the evaluation datasets. Since the reader already reached CONDITIONAL on essentially this basis, my stress-test does not move the verdict.","tokens_in":15313,"tokens_out":5028,"duration_ms":49265,"concrete_test":"Re-run the PQC fitting stage on the full 426k vocabulary and report the per-word final fidelity distribution between each fitted PQC state and its target complex vector: the median, 5th percentile, and the fraction of words with fidelity above, say, 0.999 or 0.99. Then recompute the WordSim353, MEN, RG-65, and SCWS correlations both on all pairs and on pairs restricted to words whose fitted fidelity exceeds the chosen threshold. If the restricted scores differ materially from the full scores, or if many words fall below the threshold, the claim that the two-stage process preserves quality for the whole vocabulary is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract claims that quantum word embeddings from the two-stage process perform as well as classical Skip-gram embeddings with comparable parameter counts. This claim requires that the fitted PQCs accurately reproduce the stage-1 complex embeddings for essentially every word in the vocabulary. The paper's evidence is the statement in Section 3.4 that the fitting loss 'effectively went to zero' and the observation that WordSim353 scores for the fitted PQCs are identical to those of the arbitrary complex embeddings. This is not sufficient: WordSim353 contains only 353 word pairs, involving a small fraction of the 426,507-word vocabulary, and a Spearman correlation is a rank-based aggregate that is insensitive to many per-word errors. Table 7 already shows a small divergence on SCWS (65.7 vs 65.9), indicating that the fitted vectors are not exactly identical. If a nontrivial fraction of words have low fitting fidelity, the claim of high-quality quantum embeddings for the full vocabulary fails even though the reported evaluation scores are unchanged. The paper also does not provide code or data that would allow an independent check of the fitting loss distribution.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces complex-valued extensions of the Skip-gram word embedding model, replacing real-valued vectors with complex vectors and the inner product with a fidelity-based overlap. The authors describe a PyTorch implementation for small corpora and a modified C implementation of word2vec for a 3.8B-word corpus with a vocabulary of over 400k. They then train parameterized quantum circuits (PQCs) in two ways: directly, with the PQC producing focal or both focal and context embeddings, and through a two-stage procedure that fits a PQC to each already-trained complex embedding. The models are evaluated on WordSim353, MEN, RG-65, and SCWS. The main empirical findings are that the arbitrary complex embeddings are competitive with the classical Skip-gram baseline and that the two-stage fitted PQCs essentially reproduce the evaluation scores of the complex embeddings. The paper argues that this provides a scalable route to producing quantum word embeddings for large vocabularies.","tokens_in":15551,"tokens_out":9532,"duration_ms":84341,"significance":"If the results are reproducible, the two-stage pipeline is a meaningful practical contribution: it avoids corpus-scale PQC training, scales with vocabulary size rather than corpus size, and yields PQC-parameterized states for hundreds of thousands of words that can be used in QNLP inference or compositional models. The paper also provides a useful empirical comparison of circuit ansatze and layer counts for fitting arbitrary complex vectors. The C implementation that enables training on a 3.8B-word corpus is a nontrivial engineering contribution, and the authors are transparent about the limitations of direct PQC training. However, the absence of code or data release and the lack of per-word fitting evidence currently temper the significance of the claims.","major_comments":[{"comment":"The claim that the fitted PQCs reproduce the arbitrary complex embeddings 'perfectly,' with the loss going to 'effectively zero,' is not backed by per-word evidence. WordSim353 contains 353 word pairs and Spearman correlation is an aggregate rank measure, so identical WordSim353 scores do not rule out a heavy tail of poorly fit words; Table 7 itself shows a 0.2-point gap on SCWS (65.7 vs 65.9), so the fit is not exactly lossless for every word. Please report the distribution of the final fitting loss or fidelity over the full 426,507-word vocabulary (or a random sample), including the fraction of words below a stated fidelity threshold. This is load-bearing for the abstract's claim that the quantum embeddings 'perform as well' for the whole vocabulary.","section":"Section 3.4"},{"comment":"WordSim353 is used both for hyperparameter selection (e.g., the D scaling factor, ansatz, number of layers, learning rate) and as the main evaluation set; Section 3.5 further states that 'WordSim353 is used as a validation set to choose the best-performing model' before reporting the additional datasets. No held-out split or significance tests are provided, and several of the headline differences are small relative to the reported standard deviations (e.g., Table 2: 64.6 vs 63.0 at dimension 64, with SDs of 0.33 and 0.50). Please add paired significance tests (e.g., bootstrap over runs) or a properly separated validation set, and report the scores of all models without selection on the test set.","section":"Section 3.1 and Section 3.5"},{"comment":"The paper introduces a custom C implementation, a newly created 3.8B-word corpus, and per-word PQC fitting code, but no code, embeddings, or fitted parameters are released. This prevents independent verification of both the large-scale training results and the central per-word fitting claim. At minimum, please release the trained complex embeddings and the fitted PQC parameters for the evaluation vocabulary, along with a script that recomputes the evaluation scores, or provide a clear statement about any restrictions.","section":"Sections 3.2-3.4"},{"comment":"The two-stage PQC result is partly by construction: once a PQC is fitted to a complex embedding, its evaluation score is, by design, nearly identical to that of the complex embedding. The abstract's wording could be read as an independent demonstration that quantum embeddings match classical ones, which is not what the experiment shows. The paper should explicitly state that the value of the two-stage method is the scalable production of PQC-prepared states that inherit the semantic quality of the complex embeddings, and that the direct PQC-training results (Tables 3, 4, 6) are the appropriate tests of PQC-based learning.","section":"Abstract and Section 3.4"}],"minor_comments":[{"comment":"The phrase 'to the predict the context word' should be 'to predict the context word'.","section":"Section 2.1"},{"comment":"'Anzatze' should be 'Ansätze'.","section":"Table 4 header"},{"comment":"'in the worse case' should be 'in the worst case'.","section":"Section 3.4"},{"comment":"'WordsSim353' should be 'WordSim353'.","section":"Section 3.5"},{"comment":"The WordSim353 score for the 1-way PQC model (64.0) does not match the corresponding dimension-64 entry in Table 3 (63.5); please clarify whether these are the same best-run weights or different selections.","section":"Table 6"},{"comment":"Section 2.1 says 'a value of around D = 3 works well in practice,' but Section 3.1 states D = 3.5 for all experiments using loss (4); please reconcile this or comment on the sensitivity to D.","section":"Section 2.1 vs Section 3.1"},{"comment":"The abstract's phrase 'comparable numbers of parameters' should be quantified: a 100-dimensional classical embedding has 100 real parameters per word, a 64-dimensional complex embedding has 128, and a 3-layer A5 PQC on 6 qubits has (log_2^2(64)+3 log_2(64))*3 = 162 parameters per word.","section":"Table 7"}],"recommendation":"major_revision","confidential_remarks":"I agree with the reader's conditional verdict. The manuscript has a potentially useful contribution, but the central claim about per-word PQC fitting quality needs direct evidence, and the evaluation would benefit from significance testing and a clearer separation between validation and test sets. I would encourage the editor to ask for code/data release before publication, because the large-scale results cannot otherwise be independently checked."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look if you care about QNLP. The genuinely new thing is the two-stage pipeline: train complex skip-gram on 3.8B words with a modified C implementation, then fit per-word PQCs to those embeddings. That decouples PQC training from corpus size, and it works—WordSim, MEN, RG-65 all come within a few points of the classical baseline. The fidelity-based objective (5) is a clean idea and they show it is competitive with the sigmoid version. Credit also for a serious engineering effort and for openly noting that direct PQC training hurts. The main soft spot is that the abstract overstates parity. Table 7 has classical at 72.5 on WordSim versus 69.3 for the complex and fitted PQC; similar 2–3 point gaps on MEN. That is 'competitive' more than 'as well as.' Minor but worth correcting. The bigger reproducibility gap: no code or data release. The complex C code and the fitting code are core to the claim, and without them the 'loss went to effectively zero' cannot be checked. The paper also uses WordSim353 for model selection and then reports it as the headline result, which inflates the result slightly. They do include three other datasets that mostly confirm the pattern, so overfitting to WordSim is not a load-bearing concern. The stress-test worry about a heavy tail of poorly fit words in the 426k vocabulary is real but probably not fatal. The SCWS row shows 65.7 versus 65.9, so the fitted vectors are not exactly identical, but the drop is tiny across 2,003 pairs. Still, a per-word loss histogram would settle it in two lines, and its absence is the weakest part of the evidence. Worth asking for in revision. Overall: a solid, useful paper for the QNLP community, with one overstated sentence and a reproducibility gap. Send it to a serious referee; ask for code/data and the fitting-loss distribution.","headline":"Useful, honest scaling pipeline for quantum word embeddings, but the headline claim of parity with classical is a few points overstated.","tokens_in":581,"tokens_out":1461,"would_cite":true,"duration_ms":32249,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that complex-valued word embeddings, including quantum states prepared by parameterised circuits, can match classical Skip-gram on similarity benchmarks via a two-stage pipeline that scales to a 426k vocabulary.","keywords":["complex word embeddings","quantum natural language processing","Skip-gram with negative sampling","parameterised quantum circuits","word similarity benchmarks","fidelity overlap","two-stage embedding pipeline","word2vec"],"falsifier":"Compute the final per-word fidelity loss for all 426,507 fitted PQCs and inspect the tail; if a non-negligible number of words, or a distinct semantic class of words, have loss far above zero, the claim that the fitted PQCs reproduce the complex embeddings across the vocabulary fails. A simpler check is to hold out a random set of words from the fitting stage and see whether their PQC embeddings still match the target vectors.","tokens_in":15151,"feed_emoji":"⚛️","tokens_out":5249,"duration_ms":41339,"temperature":0.7,"pith_summary":"The paper tries to show that word embeddings can live in complex vector spaces, and ultimately as quantum states prepared by parameterised quantum circuits, without losing the quality of classical real-valued embeddings. It develops a complex-valued version of Skip-gram with negative sampling, replacing real vectors with complex vectors and the inner product with a scaled fidelity measure, then evaluates on WordSim353, MEN, RG-65, and SCWS. The key result is a two-stage pipeline: train complex embeddings with an efficient C implementation on a 3.8B-word corpus with a 426k vocabulary, then fit a separate PQC to each word. The fitted quantum embeddings reproduce the classical complex embeddings' scores almost exactly, so the paper claims high-quality quantum word embeddings at scale.","feed_headline":"Quantum word embeddings match classical Skip-gram at 426k words","feed_subtitle":"Two-stage pipeline fits a quantum circuit to every word vector, preserving similarity scores on standard benchmarks.","key_machinery":"The two-stage pipeline is the load-bearing mechanism. Stage one is a complex-valued Skip-gram with negative sampling, implemented by modifying the C word2vec code to store real and imaginary parts separately and to feed the scaled fidelity $F_D(v_f,v_c) = D(2|\\langle v_f|v_c\\rangle|^2 - 1)$ into a sigmoid loss; for the PyTorch models the overlap $|\\langle v_f|v_c\\rangle|^2$ is also used directly as a probability in the cross-entropy loss. Stage two fits, for each word, a parameterised quantum circuit—a unitary built from single-qubit Y-rotations and controlled X-rotations, with three layers of Ansatz 5 or Ansatz 14—to the normalised complex vector from stage one, using the overlap as the fitting loss. The fidelity overlap is the object that connects classical complex geometry to quantum states: normalised complex vectors are quantum states, and the squared absolute inner product is the Born-rule probability between pure states.","core_discovery":"On the paper's own terms, the central discovery is that parameterised quantum circuits can serve as word embeddings without a quality penalty, provided they are fitted in a second stage to complex embeddings produced by an efficient classical Skip-gram variant. Directly training PQCs as part of the Skip-gram objective degrades performance, especially when both focal and context words are circuits, but the two-stage procedure—first learn arbitrary complex vectors from the corpus, then fit a PQC to each normalised vector—yields PQC embeddings whose WordSim353, MEN, and RG-65 correlations match the complex vectors exactly, and SCWS within 0.2 points. The paper attributes this to the expressivity of the ansatz: three layers of Ansatz 5 or Ansatz 14 fit the arbitrary complex states with the loss 'effectively going to zero.' Because the fitting stage only touches each vocabulary item and not each token, the route scales with vocabulary size rather than corpus size.","pith_inferences":["If the per-word fit is truly lossless, the quantum circuits inherit the full information of the complex embeddings, making the PQC set a drop-in replacement for complex vectors in any downstream compositional model, not just similarity benchmarks.","The closeness of the 64-dimension complex model to the 100-dimension real baseline, and the lack of gain from 64 to 128 complex dimensions, suggests the fidelity geometry rather than raw dimension is what drives performance; a controlled test with matched parameter counts across more dimensions would clarify this.","A natural extension is to use the same two-stage idea for GloVe-style objectives, where the overlap would predict log co-occurrence counts; success there would broaden the method beyond Skip-gram."],"forward_implications":["If the central claim holds, a 426k-word vocabulary of PQC word embeddings is available for quantum natural language processing models at inference time, without needing a quantum device during training.","Complex-valued Skip-gram with the fidelity overlap can be trained as efficiently as classical word2vec on multi-billion-word corpora, since the overhead is a constant factor and gradients are computed explicitly.","Direct PQC training is not the route to good embeddings; the two-stage fitting procedure is, so future work on quantum embeddings should treat the circuit as a compression of a classically learned complex vector.","On the additional similarity datasets, the fitted PQC matches the complex embedding scores on three of four datasets and stays within 0.2 points on the fourth, so the result is not specific to WordSim353."],"supporting_citations":[{"why":"Supplies the Skip-gram with negative sampling objective and the word2vec training paradigm that all complex and PQC models are based on.","marker":"[MSC+13]"},{"why":"Defines the original Skip-gram model whose inner-product classification the paper replaces with a fidelity overlap.","marker":"[MCCD13]"},{"why":"Provides Ansatz 5 and Ansatz 14 and the expressivity analysis that motivates enough layers to fit arbitrary complex vectors.","marker":"[SJAG19]"},{"why":"Supplies the WordSim353 similarity and relatedness dataset used to select and report the main results.","marker":"[AAH+09]"},{"why":"Supplies the SCWS dataset, one of the additional evaluation sets used to show the results are not WordSim353-specific.","marker":"[HSMN12]"},{"why":"Underpins the claim that preparing an arbitrary quantum state needs exponential circuit depth, motivating the fitting stage rather than direct preparation.","marker":"[ZLY22]"}],"fun_headline_variants":["Quantum word embeddings match classical Skip-gram","Two-stage quantum embeddings rival classic vectors","Vocabulary-scaling route to quantum word embeddings","Direct PQC training hurts; two-stage wins","Complex embeddings go quantum without performance loss"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim that the whole 426k-vocabulary PQC set is high quality rests on the assumption that three layers of the chosen ansatz can fit every word's complex embedding to effectively zero loss; the paper reports that loss 'effectively went to zero' but verifies it mainly through identical WordSim353 scores rather than a per-word fitting-loss distribution.","fun_headline_variants_meta":{"raw":{"variants":["Quantum word embeddings match classical Skip-gram","Two-stage quantum embeddings rival classic vectors","Vocabulary-scaling route to quantum word embeddings","Direct PQC training hurts; two-stage wins","Complex embeddings go quantum without performance loss"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000366,"raw_usage":{"total_tokens":1984,"prompt_tokens":977,"completion_tokens":1007,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":593,"completion_tokens_details":{"reasoning_tokens":952}},"tokens_in":593,"tokens_out":1007,"duration_ms":8448,"temperature":1.0,"reasoning_tokens":952,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:49:43.764159+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the final per-word fidelity loss for all 426,507 fitted PQCs and inspect the tail; if a non-negligible number of words, or a distinct semantic class of words, have loss far above zero, the claim that the fitted PQCs reproduce the complex embeddings across the vocabulary fails. A simpler check is to hold out a random set of words from the fitting stage and see whether their PQC embeddings still match the target vectors.","supporting_citations":[],"review_version":1}