{"id":"a566f2e6-e0ee-4352-89cd-8d325e2085ab","arxiv_id":"2608.03425","paper_version":2,"verdict":"REJECT","confidence":"LOW","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A small complex-valued recurrent model achieves 100% accuracy on three length-16 state-tracking puzzles, but the claim that state propagation alone is sufficient is not tested against any baseline.","lead":"This paper proposes a complex-valued recurrent network that tracks discrete states, like parity and balanced parentheses, by rotating a hidden state through the sequence. It claims this simple state-propagation design solves these toy tasks perfectly, but it never compares against existing recurrent or attention-based models.","discovery_kind":"incremental","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim generalizes but only length-16 evidence is given; no length extrapolation or full enumeration rules out a fixed-length decision rule, and Table 3 contradicts its own text.","rationale":"I read the paper as making a general existence claim: CSP shows that propagating hidden states alone is enough for deterministic state tracking, not merely for three fixed-length datasets. For that claim to hold, the learned mechanism must be a genuine state transition that works for arbitrary input length, or at least for lengths beyond the training distribution. The experiments never check this; length 16 is the only regime. Given the normalization and positive gating coefficients in Sec. 2.4, a finite-length solution could be a lookup or a length-specific decision rule. This is the weakest load-bearing premise because the entire conclusion rests on it. The numerical contradictions in Table 3 versus Sec. 3.3.1 are also serious and independently undermine trust in the reported numbers, but the length-generalization gap is the more direct threat to the central thesis. A single reproduction plus length extrapolation would settle it. I therefore do not change the reader's REJECT verdict; the evidence for the general claim is insufficient rather than proven false.","tokens_in":8863,"tokens_out":6723,"duration_ms":66356,"concrete_test":"Retrain CSP from the released repository with the reported hyperparameters for the three length-16 tasks. Then evaluate the saved checkpoints on all 65,536 length-16 inputs and on length-32, length-64, and length-128 versions of parity, mod-3, and balanced-parenthesis. If accuracy/F1 is not perfect on longer lengths or the full enumeration, the claimed sufficiency of state propagation is not established. Separately, rerun the Sec. 3.3.1 focal-loss comparison with fixed seeds to determine which of the contradictory Table 3 entries are correct.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's thesis is that state propagation alone is sufficient for deterministic state tracking (Sec. 6). The supporting experiments in Sec. 3.1 are restricted to length-16 inputs, trained on 5,000/10,000 samples, and no evaluation is reported on longer sequences or on the full 2^16 input space. Because the CSP recurrence (Sec. 2.4) uses positive softplus coefficients alpha_t, gamma_t and an element-wise normalization to the unit circle, a solution that reaches 100% on length 16 need not implement an exact phase counter: it could rely on the specific depth-16 pattern. Thus the central claim is not supported by the evidence. This is compounded by Sec. 3.3.1, where Table 3 reports Parity accuracy 100% under cross-entropy vs 50% under Focal Loss and identical F1=1.0 for Parenthesis under both losses, while the text says Focal Loss is essential for Parenthesis and that it improves Mod-3; those numbers cannot all be correct, so the empirical record is unreliable.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes the Complex State Propagator (CSP), a recurrent architecture that propagates complex-valued hidden states through stacked blocks, applying an input-dependent element-wise rotation, a first-order recurrence with positive softplus coefficients, a block-level skip connection, and unit-circle normalization at each time step. The authors report 100% accuracy and F1 = 1.0 on parity checking, mod-3 counting, and parenthesis matching for binary sequences of fixed length 16, and conduct ablations to attribute this success to the learned rotation, complex normalization, block skip connections, and Focal Loss. The paper concludes that 'state propagation alone is sufficient' for deterministic state tracking and offers a grokking analysis of the training dynamics. The code is released at the linked repository.","tokens_in":9143,"tokens_out":7064,"duration_ms":60823,"significance":"Should the empirical claims survive verification, the architecture is a useful minimal construction: it is linear-time, parameter-light, and provides a concrete inductive bias for cyclic state tracking, complementing recent theoretical results on negative eigenvalues and complex parameterizations. The open-source release is a concrete asset. However, the paper's current significance is sharply limited by the narrow evidence base (three fixed-length-16 toy tasks), by the absence of any baseline comparison with models that do use output projections, and by internal numerical contradictions that make the ablation story unreliable. The 'state propagation alone is sufficient' thesis is an overgeneralization as written.","major_comments":[{"comment":"The table contradicts the text. Table 3 reports Cross-Entropy Parenthesis F1 = 1.0 and Focal-Loss Parity accuracy = 50%, while the text says that without Focal Loss the model 'entirely fails to identify valid sequences (F1 = 0.0)' and that for Parity and Mod-3 'Focal Loss does not provide additional benefit.' These statements are mutually inconsistent, so the claimed role of Focal Loss is not supported by the reported numbers.","section":"§3.3.1, Table 3"},{"comment":"All tasks use length-16 sequences with 5,000 or 10,000 training samples, and no evaluation is reported on longer sequences or on the full 2^16 input space. Because CSP includes per-step normalization and positive softplus coefficients, a model could reach 100% on a fixed length by memorizing depth-16 decisions rather than implementing a compositional phase counter. The Section 6 conclusion ('state propagation alone is sufficient for deterministic state tracking') therefore goes beyond the evidence; the authors should either add length-generalization experiments or restrict the claim to fixed-length problems.","section":"§3.1/§3.2"},{"comment":"The motivating argument mischaracterizes Mamba. In Mamba the state recurrence is h_t = A h_{t-1} + B x_t and the output is y_t = C h_t; the next layer's B acts on its own input sequence, not as a second projection of the previous layer's output at the same time step. The composition h_{l+1,t} = B_{t+1} C_t h_{l,t} is therefore not the actual Mamba block, and Eq. (6) is essentially a restatement of the CSP recurrence rather than an independent derivation. The central 'projection bottleneck' argument needs to be reformulated.","section":"§1.1 and Eq. (6)"},{"comment":"No baseline comparison is provided. The claim that state propagation alone is sufficient and that output projections are unnecessary requires comparison against at least one architecture with the same recurrent core but with intermediate output projections, or against standard RNN/SSM baselines. As it stands, the paper only demonstrates that CSP succeeds on three tasks, not that the absence of output projections is the operative design choice.","section":"§3.2 and §3.3"},{"comment":"The reported convergence and incubation numbers are internally inconsistent. Table 2 says parity reaches 100% at about 70 epochs, while the main text says about 50; §4.2 says the incubation period for parity is about 30 epochs. For parenthesis matching, Table 2 gives about 40 epochs, §3.2 says about 150, and §4.2 says over 100 epochs before F1 rises. An empirical paper emphasizing grokking dynamics must have internally consistent epoch counts.","section":"§3.1, §4.2"}],"minor_comments":[{"comment":"Eq. (13) defines α_t = softplus(δ_t) and γ_t = softplus(δ_t) with the same δ_t, making α_t and γ_t identical; if this is intended, define one gate, and if not, use separate projections.","section":"Eq. (13)"},{"comment":"The optimization section says gradient clipping is applied only in the later stages of training, while the setup section says all models use gradient clipping at norm 1.0; this should be reconciled.","section":"§2.4.2 vs §3.1"},{"comment":"The statement that 'Mamba-1 and Mamba-2 both employ a diagonal real-valued state transition A' is imprecise for Mamba-2's structured state-space duality formulation; please make the description citation-specific.","section":"§1.1"},{"comment":"The figure caption refers to grokking curves, but the plots appear to show training metrics over epochs; consider labeling axes explicitly and marking the grokking gap defined in §4.2.1.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The numerical contradictions in Table 3 and the epoch counts should be treated as a red flag: if the authors cannot reproduce consistent numbers in a revision, the paper should be rejected rather than accepted in any form. The scope issue (length-16 toy tasks supporting a general 'state propagation alone' thesis) is fixable by reframing the contribution and adding length-generalization experiments, but the current manuscript is not yet a reliable scientific record."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here is my take. The paper's headline claim—that state propagation alone is enough for deterministic state tracking—is not supported by the evidence as reported. The architecture is a reasonable small complex-valued recurrent net, and there are useful pieces here, but the empirical record is self-contradictory and the comparison to Mamba is off.\n\nWhat's actually new: the specific combination of element-wise complex rotations, state-only propagation across blocks (no per-step output projections), block-level skip connections, and complex normalization with SiLU confined to block boundaries. That's an incremental variation on known complex RNN machinery, but the design is clean and the ablations in Table 4 are informative. The grokking observation is a nice addition, and releasing the code helps reproducibility.\n\nNow the soft spots. Table 3 contradicts its own text. The text says cross-entropy gets 67% on Mod-3 and F1=0 on Parenthesis, with Focal Loss fixing both; the table shows CE at 100% on Mod-3, FL at 50% on Parity, and F1=1.0 for Parenthesis under both losses. Those cannot all be correct. Table 2's epoch counts also disagree with Figure 3's grokking curves. That makes the empirical record unreliable. There are no baselines—no LSTM, GRU, S4, or Mamba runs—so the 'attention is overkill' claim is untested. The motivating derivation about Mamba layer composition mischaracterizes the model: the B and C projections live inside a single Mamba layer, not across layers, so fusing them into a single matrix is not a faithful description of how Mamba propagates state. That undermines the conceptual framing.\n\nThe central claim also outruns the evidence. Every task uses sequences of length 16 with 5–10k samples. Without length extrapolation or full enumeration, 100% on length-16 could be a fixed-depth decision rule rather than a compositional state transition. The paper would need either a length generalization experiment or a theoretical argument to support the strong conclusion it draws.\n\nIf the tables were fixed, baselines added, and the claim restricted to the tested setting, this could be a minor empirical contribution. As written, I would not send it to peer review in its current form; the internal contradictions alone justify a desk reject. The idea is not worthless, but the reporting is not trustworthy.","headline":"A clean small complex-valued recurrent model, but the empirical reporting is self-contradictory and the central claim outruns the evidence.","tokens_in":9571,"tokens_out":5581,"would_cite":false,"duration_ms":42854,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"State propagation alone is sufficient for deterministic state tracking, achieving perfect accuracy on parity, modular counting, and parenthesis matching.","keywords":["complex-valued state space model","deterministic state tracking","parity checking","modular counting","parenthesis matching","state-only propagation","grokking","phase rotation"],"falsifier":"Train CSP on parity, mod-3 counting, and parenthesis matching at length 16, then evaluate the same trained model on sequences of length 32, 64, and 128 without retraining; if accuracy degrades toward chance as length grows, the learned rule is length-bound rather than a general state propagator. A second test, using an unbounded counting task where the target is the total number of ones seen so far, would distinguish cyclic phase tracking from genuinely unbounded state.","tokens_in":8571,"feed_emoji":"🔄","tokens_out":5874,"duration_ms":48449,"temperature":0.7,"pith_summary":"The paper tries to establish that deterministic state tracking does not require attention or output projections between layers; a recurrent architecture that only propagates a complex-valued hidden state, updated by learned phase rotations, is enough. On three canonical tasks of length 16—parity checking, mod-3 counting, and parenthesis matching—the proposed Complex State Propagator reaches 100% accuracy and perfect F1 scores. A sympathetic reader would take this as evidence that phase accumulation is the essential inductive bias for exact, compositional reasoning over time. The paper concludes that this class of deterministic functions can be solved by state propagation alone.","feed_headline":"State-only propagation achieves 100% on three deterministic tracking tasks","feed_subtitle":"Complex-valued rotations and block-level skips make attention optional for exact compositional reasoning over time.","key_machinery":"The load-bearing object is the Complex State Propagator (CSP) block, whose recurrence takes the form $h_t = \\alpha_t h_{t-1} + \\gamma_t e^{i\\theta_t} \\odot z_t$, followed by element-wise normalization onto the unit circle. It encodes task state entirely in phase—parity as a 2-cycle, mod-3 as a 3-cycle, and parenthesis balance as accumulated phase—while block-level skip connections and boundary-only SiLU activation keep gradients alive without corrupting the phase memory.","core_discovery":"The central discovery is that a minimal recurrent architecture that only propagates hidden states through depth, representing information in the angle of a complex vector, can exactly solve deterministic state-tracking functions. Each block rotates the current input by a learned angle, runs a complex-valued linear recurrence, adds a block-level skip connection, and normalizes each complex unit to the unit circle; the final phase is decoded. With this design, and with Focal Loss where classes are imbalanced, the model reaches 100% accuracy and F1 of 1.0 on parity, mod-3 counting, and parenthesis matching, and training exhibits grokking—long near-chance performance followed by abrupt perfect generalization.","pith_inferences":["Inference: The length-16 benchmark leaves open whether the model composes state transitions or memorizes a depth-16 decision rule; evaluating on sequences substantially longer than training would separate the two.","Inference: The unit-circle representation suggests CSP should handle cyclic counters but not unbounded ones; a length-generalization test with unbounded counting would reveal whether a fixed-dimension phase state can track an unbounded discrete quantity.","Inference: The same rotation-based state machinery could be tested on state-tracking tasks with larger alphabets or multiple interacting counters, where the phase-accumulation hypothesis makes quantitative predictions about required state dimension.","Inference: The grokking observation might extend to other parameterizations that force exact angles and decay rates, implying that delayed generalization is not specific to this architecture but to the rigidity of the inductive bias."],"forward_implications":["If the claim holds, attention is not required for deterministic state tracking; a simple recurrent phase accumulator matches perfect performance.","The design principles—linear temporal updates, nonlinearity only at block boundaries, and complex normalization—offer a template for state-space models aimed at exact memorization rather than smooth approximation.","The grokking dynamics observed here suggest that structured parameterizations with rigid constraints can exhibit delayed generalization on algorithmic tasks, and that phase-boundary gradients can help escape flat regions.","Focal Loss becomes a necessary ingredient for deterministic tracking under class imbalance, where plain cross-entropy collapses to majority-class predictions.","The paper's matrix formulation of temporal aggregation, input modulation, and depth-wise rotation accumulation gives a compact target for further theory linking recurrent capacity to group representations."],"supporting_citations":[{"why":"Proves that linear RNNs with diagonal non-negative eigenvalues cannot solve parity in finite precision, motivating the need for complex or negative-eigenvalue rotations.","marker":"[14]"},{"why":"Shows that input-dependence alone is insufficient and that the recurrence must combine input-dependent gating with non-positive eigenvalues, setting the precise conditions CSP tests.","marker":"[15]"},{"why":"Provides theoretical grounding that complex diagonal transitions can improve representational capacity without sacrificing stability.","marker":"[16]"},{"why":"Introduces Mamba, the selective state-space model whose output-projection structure the paper analyzes and collapses into state-only propagation.","marker":"[6]"},{"why":"Unifies SSMs and linear attention through State Space Duality, the framework against which the paper positions its minimal alternative.","marker":"[7]"},{"why":"RoPE applies 2D block-diagonal rotations, which the paper contrasts with its element-wise per-dimension complex rotation.","marker":"[17]"},{"why":"Defines grokking, the abrupt late generalization that CSP exhibits on all three tasks.","marker":"[18]"},{"why":"Offers the interpretation of grokking as a phase transition in the loss landscape, which the paper adopts to explain its training dynamics.","marker":"[19]"}],"fun_headline_variants":["Complex state propagation solves three deterministic tracking tasks","State-only model with complex rotations: perfect on three tasks","No attention needed: exact state tracking via complex rotations","Grokking and perfect F1 with minimal recurrent state propagation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The general claim rests on the assumption that perfect results on three length-16 toy datasets imply the model has learned a compositional state transition, rather than a memorized decision rule of depth 16.","fun_headline_variants_meta":{"raw":{"variants":["Complex state propagation solves three deterministic tracking tasks","State-only model with complex rotations: perfect on three tasks","No attention needed: exact state tracking via complex rotations","Grokking and perfect F1 with minimal recurrent state propagation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000274,"raw_usage":{"total_tokens":1584,"prompt_tokens":832,"completion_tokens":752,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":448,"completion_tokens_details":{"reasoning_tokens":688}},"tokens_in":448,"tokens_out":752,"duration_ms":6778,"temperature":1.0,"reasoning_tokens":688,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:17:32.113586+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train CSP on parity, mod-3 counting, and parenthesis matching at length 16, then evaluate the same trained model on sequences of length 32, 64, and 128 without retraining; if accuracy degrades toward chance as length grows, the learned rule is length-bound rather than a general state propagator. A second test, using an unbounded counting task where the target is the total number of ones seen so far, would distinguish cyclic phase tracking from genuinely unbounded state.","supporting_citations":[{"cited_title":"Roformer: Enhanced transformer with rotary position em- bedding.Neurocomputing, 2024","cited_arxiv_id":null,"evidence_quote":"RoPE applies 2D block-diagonal rotations, which the paper contrasts with its element-wise per-dimension complex rotation."}],"review_version":2}