{"id":"45368885-8cfd-4217-9a12-6f358328d406","arxiv_id":"2512.17893","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"Basis rotation of the Ising ground state relocates the target in the NQS parameter space and can cause shallow networks to converge to low-energy but wrong wavefunctions.","lead":"This paper studies why neural-network wavefunctions fail when the basis is rotated, using a tiny exactly-solvable Ising model. It argues the target state moves in an unchanged loss landscape, creating saddle points that trap shallow networks even when the target is representable.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Basis rotation does not leave the parameter-space loss landscape unchanged for a fixed sign-free ansatz, and generic rotated targets are not representable by the real log-RBM/FFNN used; the reported failures therefore cannot be attributed to geometric relocation of a representable target.","rationale":"The reader's verdict (REJECT, moderate confidence) identifies essentially the same weak point: the paper's central conceptual premise confounds the unitarily equivalent state-space energy functional with the actual parameter-space loss, and the sign-free architectures used cannot represent generic rotated targets. I agree. The paper's own text repeatedly asserts 'unchanged loss landscape' (Sec. II, Conclusion) and 'optimization failure can persist even when the rotated target state remains representable' (Abstract), but no representability analysis is given. For a real log-RBM, ψθ(s)=exp[...] is positive; any rotation producing sign changes in the target puts it outside the model's image. This makes the separation of representability from optimization failure impossible with the reported experiments. Independent support is weak: no code/data shipped, result figures are inconsistent/missing in the provided compilation, and no formal verification is claimed. A corrected framing—state-space functional equivalent, parameter-space landscape changed, target often not representable—might motivate future work, but the submission as is overstates the geometric mechanism. The critique concerns the argument, not the authors.","tokens_in":10428,"tokens_out":9989,"duration_ms":112646,"concrete_test":"For N=5, h=0.5, exactly diagonalize the ferromagnetic Ising ground state |ψ0⟩ and compute the rotated coefficient vector v(φ)=U_y(φ)|ψ0⟩ for φ=π/3. Since the real log-RBM image is the strictly positive orthant, record whether min_s v_s(φ)<0; if so, the target is not representable. Then run the same infidelity/QNG training at φ=π/3 and at φ=π (which is the same ray as φ=0 and hence representable) and compare final infidelity. If the failure disappears for the representable case but persists at φ=π/3, the geometric claim is not established; if it also persists at φ=π, the expressivity confound is not the full explanation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that U_y(φ) merely moves the target within an otherwise fixed optimization landscape. For a fixed parameterization ψθ, however, the energy loss with the rotated Hamiltonian is E_φ(θ)=⟨ψθ|U_y(φ)HU_y†(φ)|ψθ⟩/⟨ψθ|ψθ⟩ = ⟨U_y†(φ)ψθ|H|U_y†(φ)ψθ⟩/⟨U_y†(φ)ψθ|U_y†(φ)ψθ⟩. This equals E_0(θ) only if the variational family {ψθ} is invariant under U_y(φ). The real log-RBM/FFNN of Eqs. (2)-(4) have strictly positive amplitudes exp[lnψθ(s)], whereas U_y(φ)|ψ0⟩ generically acquires negative coefficients (U_y(π/2) maps |0⟩↔|1⟩ and |1⟩→-|0⟩). Hence the target lies outside the representable manifold for generic φ, and the set of representable states—and with it the attainable energy/infidelity landscape—changes with φ. The Sec. II statement that basis rotations 'act solely to reposition the exact ground state inside an otherwise unchanged loss landscape' is therefore unsupported. It also assumes the target even has a parameter-space position, which for sign-free RBMs at generic φ it does not. The paper's explicit claim that optimization failure persists 'even when the rotated target state remains representable' is asserted but not demonstrated; no representability certificate or complex-weight control is provided. The observed low-energy/high-infidelity results can be fully accounted for by representational failure.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the basis-rotation sensitivity of shallow neural quantum states (real log-RBMs and small feedforward networks) on the one-dimensional transverse-field Ising model. A sitewise U_y(φ) rotation is applied to the Hamiltonian/ground state, and the paper claims that this leaves the parameter-space loss landscape unchanged while relocating the exact ground state farther from typical initializations. Using quantum natural gradient (stochastic reconfiguration), the authors report that shallow architectures get trapped near saddle points or high-curvature regions, leading to small relative energy errors but low fidelity, and they interpret this as a geometric optimization effect separable from representational limitations. The paper also compares energy and infidelity minimization and discusses information-geometric diagnostics such as the quantum Fisher metric and Fubini-Study distances.","tokens_in":10803,"tokens_out":12802,"duration_ms":135843,"significance":"If correct, the claimed mechanism would be a valuable controlled testbed for separating representational and optimization causes of basis dependence in NQS. The paper has several strengths: exact gradient/expectation evaluations for N<20, a deterministic pretraining to the equal-weight superposition to remove initialization noise, the use of infidelity in addition to energy, and an exactly solvable rotated Ising model. However, the central premise is not valid for the fixed real-valued ansätze actually used, the claimed representability control is absent, and the empirical core is presented only as figure captions without the corresponding plots. As it stands, the reported failures are fully explainable by representational insufficiency, so the paper does not establish its main conclusion.","major_comments":[{"comment":"The central premise is incorrect for the fixed parameterization. For a variational state ψ_theta(s)=exp[lnψ_theta(s)] with real lnψ_theta (Eqs. (2)-(5)), the energy loss for the rotated Hamiltonian is E_phi(theta) = <ψ_theta|U_y(phi) H U_y^†(phi)|ψ_theta> / <ψ_theta|ψ_theta> = <U_y^†(phi)ψ_theta|H|U_y^†(phi)ψ_theta> / ||U_y^†(phi)ψ_theta||^2. This coincides with E_0(theta) only if the variational family is invariant under U_y(phi). The real log-RBM is not U-invariant; the manuscript itself notes that sign structures require complex weights. Therefore the statement that basis rotations 'act solely to reposition the exact ground state inside an otherwise unchanged loss landscape' is unsupported. Moreover, the observed angle dependence of E_phi(theta) is direct evidence that the parameter-space landscape changes with phi.","section":"Sec. II, Eqs. (2)-(6)"},{"comment":"The abstract claims that 'optimization failure can persist even when the rotated target state remains representable,' but no representability certificate is provided for any rotation angle. For generic phi, U_y(phi)|ψ_0> has negative amplitudes and hence lies outside the set of states representable by a strictly positive ψ_theta(s) (Eq. (5)). The text singles out special angles θ_k=0, π/2, π, but at φ=π/2 the target has mixed signs, inconsistent with a sign-free ansatz. Without a demonstrated case where the target is in the representable manifold, the low-energy/high-infidelity results can be fully accounted for by representational failure, and the intended separation of expressivity and optimization is not established.","section":"Abstract; Sec. V"},{"comment":"As submitted, the manuscript contains only captions for Figures 1-7; the actual plots are absent. All quantitative claims—for example, 'RBM fails to converge for all angles except special points' (upper subplots of the missing figure), the log-log saddle-point plot (Fig. 7), and the UMAP comparisons (Figs. 1 and 4)—cannot be checked. The paper's conclusions are empirical, so the missing figures are load-bearing rather than a cosmetic issue.","section":"Sec. V, Figs. 1-7"},{"comment":"The conclusion states that 'basis rotations that leave the loss landscape invariant can nonetheless degrade performance.' This is internally inconsistent with the paper's own numerical results: if the parameter-space landscape were literally unchanged and the initialization were identical, the energy-minimization trajectory would be identical for all phi. The results instead show phi-dependent outcomes, which is only possible because E_phi(theta) changes with phi. The framing needs to be corrected, not merely qualified.","section":"Sec. VI"}],"minor_comments":[{"comment":"The caption uses h=-0.5 while the text and other figures use h=0.5. The sign convention should be reconciled.","section":"Fig. 4 caption"},{"comment":"The bullet refers to the 'quantum Fisher matrix G(alpha)' but alpha is the hidden-unit ratio; the matrix is G(theta).","section":"Sec. IV-B, item 4"},{"comment":"The phrase 'rotates σ_x ↔ σ_z' is only literally true at φ=π/2; for general φ the transformation is a rotation in the σ_x-σ_z plane with angle 2φ. Please state this precisely.","section":"Sec. II"},{"comment":"The text uses L for system size in one passage ('for larger system sizes L>5') and N elsewhere. Use a single symbol throughout.","section":"Sec. V"},{"comment":"The quantity called 'quantum coherence' is defined as the Shannon entropy of the wavefunction coefficients in the rotated basis. This is not a standard coherence measure, and reference [18] does not obviously define it. Please provide a precise definition or use a different name.","section":"Sec. V, Fig. 6"},{"comment":"Data and code availability 'upon request to the authors' is insufficient for reproducibility. A public repository would be more appropriate, especially since the numerical results are central to the paper.","section":"Sec. VII"}],"recommendation":"reject","confidential_remarks":"The paper is a preprint with a genuinely interesting question, but the central premise is formally incorrect for the real-valued ansätze used, and the numerical support is not present in the submitted manuscript. The missing figures alone would block acceptance; combined with the representability issue, the conclusions cannot stand. The authors might be able to reformulate the study using a U-invariant or complex-weight ansatz and provide a clean representability control, but that would be a substantially new paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the rotated-Ising sweep is a nice idea, and the Fisher-distance diagnostic is worth borrowing. But the central premise — basis rotations leave the loss landscape unchanged — is false for a fixed parameterization, and the numerical results that would support the story are not actually in the manuscript.\n\nWhat's new and good: using an exactly solvable Ising chain with sitewise y-rotations gives a clean angle sweep that changes the target state without changing the spectrum or entanglement. The pretraining to the equal-weight superposition is a good control, and exact gradients for N<20 remove sampling noise. Comparing energy and infidelity losses is the right way to expose low-energy/high-infidelity traps. Tracking the target's Fubini-Study distance from initialization is a sensible diagnostic. These pieces are genuinely useful.\n\nThe soft spot is load-bearing. For a fixed ansatz ψθ, the rotated energy is E_φ(θ)=⟨ψθ|UHU†|ψθ⟩, which explicitly depends on φ; it equals the unrotated energy only if the variational family is invariant under U. The real log-RBM has nonnegative amplitudes, so generic rotated targets, which acquire negative or complex coefficients, are outside the representable manifold. That means the observed failures can be explained by representability, not by 'relocation within an unchanged landscape.' The claim that optimization fails 'even when the rotated target remains representable' is asserted; no representability certificate or complex-weight control is given. Figures 5–7 are only captions; the main numerical evidence is absent from the manuscript. Code is 'available upon request,' which in practice means not available.\n\nThe correct framing is more modest and still interesting: a basis rotation moves the target in state space relative to the variational manifold, and the induced geometry can make optimization hard even when the target is representable. That version needs complex-valued or sign-carrying ansätze and actual data.\n\nBottom line: this deserves a desk reject in current form, not because the idea is bad but because the central claim is unsupported and the results are absent. If the authors fix the framing, ship the figures and code, and test with a complex RBM, I'd be happy to look again. The reader who might get value is someone working on NQS optimization, but they should wait for a corrected version. As a referee, I would not spend time on this submission.","headline":"Nice testbed, but the central claim is false for a fixed ansatz and the main figures are missing.","tokens_in":11315,"tokens_out":5321,"would_cite":false,"duration_ms":51024,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Local basis rotations can leave an Ising model's loss landscape effectively unchanged while shifting the exact ground state in parameter space, and shallow neural quantum states trained with quantum natural gradient often stall at saddle po","keywords":["neural quantum states","basis rotation","quantum natural gradient","restricted Boltzmann machine","Fubini-Study distance","quantum Fisher information","transverse-field Ising model","variational optimization"],"falsifier":"For a small system (e.g., N=5), compute the actual energy landscape E_φ(θ) for a fixed RBM and compare the critical points before and after rotation: if the set of saddles or local minima moves with φ, the 'unchanged landscape' claim is false for that ansatz. Alternatively, train a complex-valued RBM on the same rotated targets with exact gradients: if optimization always succeeds, representability rather than geometry was the limiting factor; if it still stalls at intermediate fidelities, the geometric mechanism is confirmed.","tokens_in":10327,"feed_emoji":"⚛️","tokens_out":7557,"duration_ms":67223,"temperature":0.7,"pith_summary":"The paper sets out to explain why Neural Quantum States (NQS) are so sensitive to the basis in which the wavefunction is represented, and to separate two candidate causes: representational expressivity versus optimization geometry. Using an exactly solvable one-dimensional transverse-field Ising model, the authors apply a site-wise rotation to the ground state, which preserves the Hamiltonian spectrum and entanglement entropies but relocates the target state inside a supposedly unchanged minimization landscape. For shallow architectures—Restricted Boltzmann Machines and small feedforward networks—trained with quantum natural gradient, the relocated target often drives the optimizer into saddle-point and high-curvature regions, yielding a small relative energy error while the coefficient structure of the wavefunction is wrong. The paper's point is that low energy error is not proof of a good variational state, and that basis dependence in NQS can be a purely geometric optimization effect rather than a simple lack of expressivity.","feed_headline":"Rotating the basis traps neural quantum states in saddles","feed_subtitle":"Low energy error can hide a wrong wavefunction when the target shifts inside an unchanged landscape.","key_machinery":"The central object is the site-wise Pauli-Y rotation U_y(ϕ) = e^{iϕ σ^y} applied at every site, which rotates σ^x into σ^z and vice versa, leaving the Ising spectrum and reduced density matrices unchanged while changing the ground-state amplitudes in the computational basis. The paper uses two information-geometric quantities—the Fubini–Study distance and the quantum Fisher information matrix pulled back to the network parameter space—to track how the rotated target moves away from the typical initialization (the equal-weight superposition). Because the natural-gradient update uses the inverse of this Fisher metric, the induced geometry of the parameter manifold is what steers the optimizer;","core_discovery":"The central claim is that for the transverse-field Ising model, a site-resolved rotation U_y(ϕ)^⊗N maps the ground state to a rotated state |ψ_ϕ⟩ while leaving the Hamiltonian spectrum and all reduced density matrices unchanged; the variational energy functional on the full state space is unitarily equivalent, so the loss landscape 'looks the same' but the target location moves. Measuring Fubini–Study distances and the quantum Fisher information, the authors show that this relocation increases the information-geometric distance from the typical initialization (the equal-weight superposition) and, for shallow ansätze, drives quantum natural gradient trajectories toward saddle points and high-","pith_inferences":["The rotation sweep could be turned into a diagnostic tool: fixing the network and Hamiltonian and varying φ effectively surveys the saddle-point structure of an ansatz's loss landscape, something the paper does not explicitly propose.","A control experiment the paper does not run: repeat the study with a complex-valued RBM (or another ansatz that can exactly represent complex amplitudes) to quantify how much of the observed failure is geometric versus a representability artifact of the real-valued log-RBM.","The 'unchanged landscape' statement is exact for the full state space but approximate for a fixed finite-parameter network; an interesting extension is to test how the critical points of E_φ(θ) move with φ for small network widths."],"forward_implications":["Low relative energy error must not be used alone as a success metric in NQS calculations; infidelity or coefficient coherence (Shannon entropy) should be monitored alongside energy.","Because the rotation does not change the spectrum or entanglement, the observed failure modes imply that spectral structure—especially near-degeneracy in the ferromagnetic case—shapes the optimization landscape independently of representational capacity.","The rotated-Ising framework provides a controlled testbed: with the Hamiltonian and ansatz fixed, sweeping the rotation angle maps where an optimizer gets stuck, which can inform initialization strategies and architecture choice.","Optimization failure can persist even when the rotated target remains representable by the variational family, supporting a geometric (rather than purely expressivity-based) explanation of basis dependence."],"fun_headline_variants":["Basis shift hides wrong wavefunction behind low energy","Rotated basis steers NQS into saddle traps","Same landscape, moved target: NQS optimization fails","Energy low, wavefunction wrong: basis rotation culprit","Basis rotation misleads neural quantum states"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that rotating the basis leaves the network's optimization landscape unchanged, so that any failure must come from where the target state sits within that landscape; if the landscape itself shifts for the fixed network parameterization, the geometric-relocation explanation is not the whole story.","fun_headline_variants_meta":{"raw":{"variants":["Basis shift hides wrong wavefunction behind low energy","Rotated basis steers NQS into saddle traps","Same landscape, moved target: NQS optimization fails","Energy low, wavefunction wrong: basis rotation culprit","Basis rotation misleads neural quantum states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000382,"raw_usage":{"total_tokens":1818,"prompt_tokens":656,"completion_tokens":1162,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":400,"completion_tokens_details":{"reasoning_tokens":1101}},"tokens_in":400,"tokens_out":1162,"duration_ms":9169,"temperature":1.0,"reasoning_tokens":1101,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T15:07:59.104676+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For a small system (e.g., N=5), compute the actual energy landscape E_φ(θ) for a fixed RBM and compare the critical points before and after rotation: if the set of saddles or local minima moves with φ, the 'unchanged landscape' claim is false for that ansatz. Alternatively, train a complex-valued RBM on the same rotated targets with exact gradients: if optimization always succeeds, representability rather than geometry was the limiting factor; if it still stalls at intermediate fidelities, the geometric mechanism is confirmed.","supporting_citations":[],"review_version":1}