{"id":"c0648e75-75e8-43ff-a2b1-fd383653ccc7","arxiv_id":"2505.09789","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A two-layer implicit neural network with sinusoidal activations compresses and reconstructs real power-system waveforms with roughly 1-2% MSE, outperforming an equal-size single-layer Fourier-like network.","lead":"This paper brings implicit neural representations, a machine learning technique for continuous functions, to power grid voltage and current waveform data, showing that a two-layer network with sine activations can reproduce real waveforms with 1-2% error and fewer stored numbers than raw samples. The approach also models three-phase and synchro-waveform data with shared neural layers, and tracks oscillation frequencies in the reconstructed signals.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The '4–6x compression' claim compares parameter counts to raw samples, not bytes; with float32 weights the real ratio is ~1.5–2.2x and may vanish after quantization.","rationale":"I focused on the compression metric rather than the reader's nominated weakest assumption (single-sensor representativeness). Dataset breadth is a real limitation, but the core two-layer-versus-one-layer advantage is demonstrated on the included captures and does not collapse if the data are unrepresentative. The compression ratio, by contrast, is a headline number in the abstract and Section IV-D, and it is computed with an unconventional and potentially misleading metric: parameter counts versus raw sample counts. A reader relying on the abstract would infer storage savings that the paper does not actually show. This is a concrete, checkable issue rather than a speculation about generalization. Because the fix is rephrasing and re-reporting rather than invalidating the architecture or its accuracy results, I keep the reader's CONDITIONAL verdict rather than moving to ACCEPT or REJECT.","tokens_in":8195,"tokens_out":7253,"duration_ms":82385,"concrete_test":"Reproduce the Fig. 7 byte-level ratio: encode the INR weights at 32-bit, 16-bit, and 8-bit precision and reconstruct; compute actual storage (weights plus needed metadata) versus raw int16 waveform samples, and also versus a wavelet or transform-coder baseline at matched MSE. If the byte-level ratio is below 2x at 32-bit or degrades sharply after quantization, revise the abstract and Section IV-D to say 'parameter-count reduction' rather than 'compression'.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline quantitative claim of '4–6x compression' is not established by the reported numbers. Section IV-D states that 23,808 raw parameters over three phases versus 5,503 INR parameters 'achiev[es] 4–6× compression', but this equates one raw sample with one parameter and ignores numeric precision. For a single 62-cycle phase at 128 samples/cycle, the raw signal has 7,936 samples. A h1=h2=50 two-layer INR has 2,651 parameters. Raw WMU samples are typically 16-bit integers (15,872 bytes/phase); float32 INR weights need 10,604 bytes/phase, i.e., only 1.5x compression. For the combined three-phase model, 5,503 float32 weights are 22,012 bytes versus 47,616 bytes raw, i.e., about 2.2x. No quantization, entropy coding, or bitstream is specified, and training compute is not charged to the representation. Thus the central 'model size' advantage is overstated as a practical compression ratio; it is only a parameter-count reduction. The conclusion's acknowledgement that a 'more comprehensive comparison with state-of-the-art waveform modeling techniques' is future work does not repair the specific byte-level claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes the use of implicit neural representations (INRs) with sinusoidal activations to model power-system voltage and current waveforms. It compares single-hidden-layer and double-hidden-layer INRs, arguing that the former behaves like a Fourier series and cannot capture transients while the latter achieves roughly 3x lower MSE at equal parameter count. It further proposes a shared-hidden-layer INR to represent three-phase and synchro-waveform measurements, and reports 4-6x 'compression' relative to raw samples. Experiments use 30 real-world waveform captures from a 480V SEL 735 sensor, with sensitivity analysis for h1 and h2, comparisons of separate versus combined models, and two oscillation-monitoring case studies.","tokens_in":8426,"tokens_out":7899,"duration_ms":76969,"significance":"The core representation claim is plausible and supported by the experiments: on the presented data, two-layer sine INRs outperform equal-parameter one-layer INRs and ReLU, and the combined three-phase model is more parameter-efficient than three separate models. The use of real waveforms and the averaging over 300 and 900 training runs are strengths. However, the headline compression gain is measured in parameter counts rather than bytes, the dataset is a single-sensor collection, and there is no comparison with existing waveform-modeling or compression methods. With those corrections and scoping, the paper would be a useful contribution to waveform analytics.","major_comments":[{"comment":"The claimed '4–6× compression' is not supported by the reported numbers as a storage ratio. Section IV-D compares 23,808 raw 'parameters' with 5,503 INR parameters, but raw waveform samples are not parameters and their storage cost depends on numeric precision. For a 62-cycle capture at 128 samples/cycle, one phase has 7,936 samples; at the typical 16-bit WMU resolution this is 15,872 bytes, while a float32 INR for that phase (h1=h2=50, 2,701 parameters) needs 10,804 bytes, a factor of only 1.47. For the three-phase combined model in Section IV-D, 5,503 float32 weights need 22,012 bytes versus 47,616 raw bytes, a factor of about 2.16. The '4–6×' figure also does not match the stated parameter ratios: 23,808/8,103 = 2.94 and 23,808/5,503 = 4.33. Please report byte-level compression with the actual precision of the INR weights, or explicitly relabel the claim as parameter-count reduction and avoid the word 'compression' in the abstract.","section":"Abstract; Section IV-D"},{"comment":"The hyperparameters used for the separate and combined models in Fig. 7 are not stated, and the reported parameter counts are inconsistent with the earlier sensitivity setup. Three separate phase models with h1=h2=50 give 8,103 parameters by Eq. (4), but a combined three-output model with h1=h2=50 gives 2,803 by Eq. (6), not 5,503; the 5,503 figure corresponds to h1=50, h2=100. Please specify the exact h1 and h2 used for each curve and recompute the comparison on an equal-size or matched-accuracy basis.","section":"Section IV-D and Fig. 7"},{"comment":"The abstract claims 'accuracy (<1–2% MSE)', but Section IV-A states that the MSE varies from 0.77% to 2.85% across the nine displayed examples, and Fig. 5 shows MSE values well above 2% for some configurations. Please either define the range over which the <1–2% claim is made or correct the abstract, because the headline accuracy is part of the central claim.","section":"Section IV-A and Abstract"},{"comment":"All quantitative results are based on 30 waveform captures from a single SEL 735 sensor at one 480 V location. Since both the reported MSE values and the roughly 3× advantage of the two-layer INR are averages over this one-sensor dataset, the conclusion that INRs are generally effective for power-system waveforms is not yet established. Please add data from additional sensors, locations, or voltage classes, or explicitly limit the claims to the studied dataset.","section":"Sections IV and V"}],"minor_comments":[{"comment":"In Eq. (3), the bias inside the second sine is written as b2,i, but the summation index is j; it should be b2,j (or a separate bias per second-layer neuron). Please fix the notation.","section":"Eq. (3)"},{"comment":"The training-details paragraph mentions the largest INR model with h1=50 and h2=70, but Figs. 5(a)–(c) only show h1 up to 30 and h2 up to 50. Please reconcile the text and the figure, or clarify that the compute-time example is outside the plotted sensitivity range.","section":"Section IV-B"},{"comment":"The paper should define what 'paramter' means when comparing to raw samples, and state the numeric precision (e.g., float32 vs 16-bit) used in any reported compression. This is essential for reproducibility and for interpreting the 'model size' claims.","section":"Section II and IV"},{"comment":"The training setup is not fully specified: the optimizer, learning rate, number of epochs, SIREN initialization scale (ω0), and loss function are not reported, even though these are known to be important for INR training. Providing them would strengthen the reproducibility of the results.","section":"Section IV-A"},{"comment":"The limitation that no comparison with state-of-the-art waveform modeling or compression techniques is performed is acknowledged only in the conclusions; since the paper positions INRs against Fourier- and wavelet-style representations, a baseline comparison (even on the same dataset) would substantially strengthen the novelty claim.","section":"Section V"}],"recommendation":"major_revision","confidential_remarks":"The manuscript does not mention data or code availability, and the core frequency-convergence premise is cited to a prior work by one of the co-authors [21]; the empirical results appear to stand independently, so I do not see this as a circularity problem, but the compression claim needs a careful rewrite before acceptance. The paper fits the journal's scope, and the central modeling idea is worth publishing once the load-bearing quantitative claims are corrected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a genuine first application of INRs to power-system waveform measurements, not a repackaging. The paper shows that a two-hidden-layer sinusoidal MLP can represent real voltage/current captures at 1-3% MSE, and that sharing layers across phases cuts parameters by about 2x. The core modeling claim is believable.\n\nNew and good: they fit time-to-waveform SIREN-type MLPs, compare one vs double hidden layer, show two layer captures transient sub-cycle events with ~3x lower MSE at equal parameter count, and extend to combined three-phase/synchro-waveform models. Results are on real SEL 735 captures, 30 signatures averaged over 10 runs. The 1 vs 2 layer comparison is a clean design contribution. Citation pattern is appropriate: it builds on Sitzmann, Roddenberry, plus power-waveform background. No code or data, but the experimental setup is transparent enough to reproduce roughly.\n\nSoft spots: headline '4-6x compression' is a parameter-count ratio, not bytes. Raw samples are usually 16-bit; float32 weights run about 1.5-2.2x. If they quantize and entropy code, maybe, but none is specified. They need to state bitrate or bytes. Also all results are from one 480V SEL 735 sensor; the MSE numbers and the two-layer advantage may not generalize to other sensors/event classes. There are no classical baselines (Fourier/wavelet/Slipstream) against the reconstructed quality; the conclusion acknowledges this but only as an apology. Hyperparameters and training details are missing, and the abstract's '<1-2% MSE' doesn't match the 0.77-2.85% range in Section IV. The 'single-layer = Fourier transform' claim is a useful intuition but overstated; a single-layer sine MLP with trained frequencies is not literally DFT and can approximate transients with enough terms. Those are real soft spots, but none of them sinks the central representation claim.\n\nBottom line: if you want a careful byte-level compression paper, this isn't it. If you want an applied first look at INRs for waveform analytics with some honest empirical design, this is useful. I would send it to peer review, because the application is timely and the one-vs-two-layer result is worth a serious referee's time despite the needed compression correction. My own cite: maybe for context, though I'd wait for code/data.","headline":"First genuine INR-to-power-waveform application with a solid two-layer vs one-layer empirical case; the headline compression ratio is inflated until you count bytes.","tokens_in":8945,"tokens_out":2762,"would_cite":true,"duration_ms":27824,"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":"A double-hidden-layer sinusoidal INR can represent real power-system voltage and current waveforms with 1–2% mean-squared error and 4–6× parameter compression, preserving transient and frequency content that an equal-size…","keywords":["waveform analytics","implicit neural representation","sinusoidal activation","power system monitoring","synchro-waveform measurements","three-phase measurements","oscillation monitoring","model compression"],"falsifier":"Collect a diverse set of event captures from multiple sensors, voltage levels, and event types, such as voltage sags, capacitor-switching transients, and inverter trips, and rerun the equal-parameter one-layer versus two-layer comparison; the central claim is falsified if the two-layer MSE advantage over one-layer drops to the run-to-run noise level, or if a one-layer model matches two-layer accuracy on the sub-cycle portion of any capture.","tokens_in":7976,"feed_emoji":"⚡","tokens_out":8154,"duration_ms":78809,"temperature":0.7,"pith_summary":"This paper argues that a small neural network can serve as a compact, continuous mathematical model of raw power-system voltage and current waveforms, replacing bulky waveform captures with a few thousand parameters. The key claim is that the network needs two hidden layers with sinusoidal activations: a one-hidden-layer version is essentially a Fourier series and misses sub-cycle transient distortions, whereas the two-layer version captures them, giving roughly three times better accuracy at the same model size. The authors test this on 30 real-world event captures from a 480-volt three-phase sensor, reporting 1–2% mean-squared error and four to six times compression, and they show a shared-layer version can model three phases or synchronized waveforms together with fewer parameters. The motivation is that high-rate waveform monitoring, especially synchro-waveform streaming, can exceed a gigabyte per sensor per day, so a faithful compact representation would make waveform analytics practical.","feed_headline":"Two-layer neural net captures grid waveform transients","feed_subtitle":"Sinusoidal layers preserve transient distortions and oscillation modes a Fourier-style model misses.","key_machinery":"The load-bearing object is the double-hidden-layer sinusoidal MLP, an implicit neural representation mapping time $t$ to a waveform value $x(t)$. The single-layer model reduces to a sum of sinusoids, i.e., a truncated Fourier series, while the two-layer model composes sinusoids of sinusoids, which the authors connect to a larger reachable frequency space. The second machinery piece is the shared-hidden-layer multi-output extension, where several correlated waveforms, such as three phases or synchro-waveforms at multiple locations, are produced from one network, reducing parameter count when correlations exist. Sinusoidal activation is what lets both networks represent periodic signals compactly; replacing it with ReLU raises MSE to 18.88% on the initial case study, so the activation choice is central to the representation.","core_discovery":"The central claim is that an implicit neural representation with two sinusoidal hidden layers is the right model class for power-system waveform measurements. With one hidden layer the output has the form $x(t) = \\sum_{i=1}^{h} a_{2,i} \\sin(a_{1,i}t + b_{1,i}) + b_2$, so the learned parameters play exactly the roles of Fourier frequencies, magnitudes, and phases, and the model cannot represent non-stationary sub-cycle events. With two hidden layers the nested composition $x(t) = \\sum_{j=1}^{h_2} a_{3,j} \\sin(\\sum_{i=1}^{h_1} a_{2,i,j}\\sin(a_{1,i}t + b_{1,i}) + b_{2,j}) + b_3$ no longer resembles a Fourier transform; the second layer introduces spectral diversity that lets the network represent transient distortions. On a real 62-cycle capture containing a sub-cycle oscillatory event, the same-parameter-count comparison moves MSE from 2.40% (one layer) to 0.82% (two layers). Across 30 voltage and current event signatures, the two-layer INR reconstructs waveforms with MSE between 0.77% and 2.85%, and in the oscillation case studies it reproduces the DFT spectrum of both a 900 Hz single-mode oscillation and a dual-mode $60$ Hz $\\pm f_{\\mathrm{sideband}}$ modulation while compressing the raw three-phase data by $4$–$6\\times$.","pith_inferences":["A natural next test is whether the same two-layer architecture yields a fixed-length embedding of an event; if so, INR weights could themselves become features for classifying fault types or locating disturbances, without computing spectra.","The reported compression counts model parameters against raw samples and ignores the cost of encoding those parameters; a fair comparison with Fourier or wavelet codecs would need a bitrate-versus-distortion curve on the same captures.","Because the second layer is what creates spectral diversity, the architecture may also apply to other non-stationary power signals, such as traveling-wave fault records or inverter switching transients, where a Fourier basis is known to be inefficient.","A testable prediction follows from the sensitivity analysis: for a fixed parameter budget, optimal width allocation should favor $h_2$ over $h_1$; one could check this by grid-searching widths on a larger multi-site dataset."],"forward_implications":["Waveform captures can be stored and transmitted as INR parameters rather than raw samples, cutting the per-sensor data footprint by roughly four to six times while keeping reconstruction error below a few percent.","Event analysis that relies on the frequency spectrum, such as locating a dominant 900 Hz oscillation mode or resolving sidebands around 60 Hz, can be run on the INR reconstruction without losing the modes visible in raw data.","Modeling three-phase or multi-location waveforms with one shared network is more parameter-efficient than modeling each channel separately, especially when channels are correlated.","Because a one-hidden-layer INR is mathematically a Fourier representation, any waveform-analytics pipeline that needs sub-cycle transient detail should use at least two hidden layers.","The accuracy saturation observed in the sensitivity analysis indicates that for a fixed parameter budget, increasing $h_2$, the second-layer width, buys more accuracy than increasing $h_1$, the first-layer width."],"supporting_citations":[{"why":"Supplies the sinusoidal activation function that gives the INR its periodic representation capacity.","marker":"[10]"},{"why":"Supports the claim that two hidden layers enlarge the frequency space the INR can converge to, enabling transient capture.","marker":"[21]"},{"why":"Provides the waveform-measurement background and the differential-waveform definition used in the oscillation case studies.","marker":"[4]"},{"why":"Documents synchro-waveform data volumes, over a gigabyte per sensor per day, that motivate compact waveform models.","marker":"[2]"},{"why":"Introduces the MLP-based continuous function approximation approach that the paper adapts to power-system waveforms.","marker":"[6]"}],"fun_headline_variants":["Two sinusoid layers pack Fourier punch plus transients","Neural two-layer model trims grid waveform error threefold","Power waveforms get 4-6x compression via implicit neural maps","Sub-cycle grid events decoded by two-layer sinusoidal INR","INR with sinusoidal activations sees dual-mode oscillations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"All reported numbers come from 30 waveform captures taken by a single 480-volt three-phase sensor, and if those captures are not representative of grid waveforms in general, the claimed accuracy and the two-layer advantage will not generalize.","fun_headline_variants_meta":{"raw":{"variants":["Two sinusoid layers pack Fourier punch plus transients","Neural two-layer model trims grid waveform error threefold","Power waveforms get 4-6x compression via implicit neural maps","Sub-cycle grid events decoded by two-layer sinusoidal INR","INR with sinusoidal activations sees dual-mode oscillations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000981,"raw_usage":{"total_tokens":4202,"prompt_tokens":1022,"completion_tokens":3180,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":638,"completion_tokens_details":{"reasoning_tokens":3099}},"tokens_in":638,"tokens_out":3180,"duration_ms":24883,"temperature":1.0,"reasoning_tokens":3099,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:24:06.089990+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Collect a diverse set of event captures from multiple sensors, voltage levels, and event types, such as voltage sags, capacitor-switching transients, and inverter trips, and rerun the equal-parameter one-layer versus two-layer comparison; the central claim is falsified if the two-layer MSE advantage over one-layer drops to the run-to-run noise level, or if a one-layer model matches two-layer accuracy on the sub-cycle portion of any capture.","supporting_citations":[{"cited_title":"Implicit neural representations with periodic acti- vation functions,","cited_arxiv_id":null,"evidence_quote":"Supplies the sinusoidal activation function that gives the INR its periodic representation capacity."},{"cited_title":"Mohsenian-Rad, Smart Grid Sensors: Principles and Applications","cited_arxiv_id":null,"evidence_quote":"Provides the waveform-measurement background and the differential-waveform definition used in the oscillation case studies."},{"cited_title":"Synchro-waveforms: A windo w to the future of power systems data analytics,","cited_arxiv_id":null,"evidence_quote":"Documents synchro-waveform data volumes, over a gigabyte per sensor per day, that motivate compact waveform models."},{"cited_title":"Nerf: Representing scenes as neural radiance fields for view synthesis,","cited_arxiv_id":null,"evidence_quote":"Introduces the MLP-based continuous function approximation approach that the paper adapts to power-system waveforms."}],"review_version":1}