{"id":"be3d490f-5647-4735-bfdf-1428907f5337","arxiv_id":"2502.10070","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"AirTNN treats wireless channel fading and noise as part of the topological convolutional filter, improving robustness over graph-based and communication-agnostic baselines in synthetic source localization.","lead":"AirTNN is a new neural network for data living on cell complexes that deliberately builds wireless fading and noise into its message-passing layers, tested on a source localization task. It matters because it fuses over-the-air computation with topological deep learning, aiming to make distributed intelligence on edge-flow data robust to real radio channels.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported AirTNN advantage over AirGNN is not causally identified: Figs. 2-3 show absolute accuracy, not degradation from each model's ideal-setting baseline, so the claimed 'enhanced robustness' may reflect extra capacity or upper-neighborhood information rather than resilience to channel…","rationale":"The reader's weakest assumption concerns the practical feasibility of deploying two independent communication topologies over shared physical wireless links. That is a legitimate external feasibility concern. My concern is internal and more directly tied to the central claim: the experimental comparison does not control for the extra expressivity of AirTNN (two shift operators, more filter parameters) and does not report degradation from ideal performance, so the observed absolute-accuracy advantage does not by itself demonstrate robustness to channel disturbances. This is an evidentiary gap rather than a demonstrated flaw in the architecture or mathematics; with the missing measurements supplied, the claim could be fully supported. The appropriate disposition therefore remains CONDITIONAL, unchanged from the reader's verdict, with the condition being the additional robustness and ablation analyses described above.","tokens_in":9040,"tokens_out":11205,"duration_ms":118331,"concrete_test":"Re-analyze the saved model outputs from Figs. 2-3 by computing, for each model and each tested (delta, SNR) point, the accuracy drop relative to that model's own ideal-setting accuracy; report these drops with error bars over at least 10 random seeds. If AirTNN's drop is not consistently smaller than AirGNN's under matched conditions, then Figs. 2-3 do not establish 'enhanced robustness' over the state of the art.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is empirical: AirTNN is more robust to channel impairments and outperforms AirGNN. But Figs. 2-3 plot absolute accuracy, not robustness measured as accuracy drop from each model's own noiseless operating point. The 'Ideal setting' curve is a single unlabeled horizontal line; the paper does not report per-model ideal accuracy, error bars, or the degradation from ideal to each tested (delta, SNR) point. Because the AirTNN layer in Eq. (13) uses two shift branches (lower and upper) while AirGNN uses one graph shift, AirTNN has more filter parameters and additional topological information. A model with higher representational capacity can achieve higher absolute accuracy yet degrade just as much or more under channel randomness; the figures as presented would still look favorable. The text attributes the gain to 'two distinct neighborhoods that experience different channel and noise conditions at each step' (Sec. 4), but this causal attribution requires showing the dual-neighborhood design specifically reduces sensitivity to channel randomness, not merely that it is a stronger classifier. Without degradation curves, matched parameter budgets, or an ablation that removes upper neighborhoods, the robustness claim is not distinguishable from an expressivity claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes AirTNN, a topological neural network architecture for edge signals over regular cell complexes that incorporates over-the-air wireless communication into the topological filtering operation. The filter aggregates information over lower and upper neighborhoods through channel-dependent shift operators with Rayleigh fading and AWGN, and the network is trained by sampling channel coefficients and noise at each training step. Numerical experiments on a synthetic edge-flow source localization task compare AirTNN with AirGNN, GNN, and TNN baselines across fading severity δ and SNR, reporting higher accuracy for AirTNN and attributing this to the exploitation of two distinct neighborhoods with different channel conditions.","tokens_in":9319,"tokens_out":9064,"duration_ms":77655,"significance":"The paper extends over-the-air graph neural networks to topological neural networks, which is a natural and useful step for distributed processing of edge-flow data over wireless networks. The architectural definitions are explicit, the training procedure is simple to reproduce (a code link is provided), and the synthetic data generation is described in detail. The claim that the architecture is robust to channel impairments is plausible and consistent with prior work on training with channel randomness, but the empirical support is incomplete: the reported figures compare absolute accuracies without per-model ideal baselines or ablations, so the causal attribution of the performance gain to channel robustness is not yet established. If the authors supply the missing baselines and an ablation, the paper would be a solid contribution.","major_comments":[{"comment":"The central claim that AirTNN 'consistently demonstrates enhanced robustness against disturbances introduced by wireless communication' is not established by the reported experiments. Figs. 2 and 3 plot absolute accuracy, not the degradation from each model's ideal (noiseless/fading-free) operating point; the 'Ideal setting' line is unlabeled and no per-model ideal accuracies are reported. Because AirTNN in Eq. (13) uses two filter banks (lower and upper neighborhoods) while AirGNN uses a single graph shift, AirTNN has more trainable parameters and additional topological information; a higher-capacity model can achieve higher absolute accuracy while degrading equally or more under channel randomness. To support the robustness attribution, the authors should report per-model accuracy under ideal communication and the accuracy drop versus δ and SNR, include error bars or multiple seeds, and add an ablation that removes the upper-neighborhood branch (or matches the parameter budget) to show that the dual-neighborhood design, rather than expressivity, is responsible for the resilience.","section":"§4, Figs. 2–3 and experimental setup"},{"comment":"The training distribution of the channel parameters is not specified. The figures sweep δ at fixed SNR=20 dB and SNR at δ=1, but the paper does not state over which δ and SNR ranges the stochastic channel coefficients and noise are sampled during training for AirTNN (or for AirGNN). Without this information, the comparison might reflect a mismatch in train/test channel distributions rather than a property of the proposed architecture. The authors should state the training channel model (e.g., Rayleigh scale and SNR values used per mini-batch) and ensure that AirGNN is trained under identical conditions.","section":"§4, 'Experimental setup'"},{"comment":"The architecture rests on the assumption that 'proper resource allocation strategies (e.g., power control, analog beamforming, etc.)' can realize two distinct wireless communication topologies corresponding to the lower and upper neighborhoods, with independent fading across links and transmission rounds. No design, feasibility argument, or reference is provided for this assumption. Since the simulation simply instantiates the assumed independent channels, the numerical results do not validate the wireless feasibility. The authors should add a discussion of how such a resource allocation could be implemented (e.g., time/frequency separation, interference management) or at least state clearly that this is an idealization and discuss its practical limitations.","section":"§3, before Eqs. (4)–(5)"}],"minor_comments":[{"comment":"There are typos in the recursion and noise terms. In Eq. (10), the inner shift should be S_air^(d,p-1), not S_air^(d,P-1), and the final noise term 'n(d,ρ)' should be a specifically indexed term such as n(d,i) or n(d,p). Eqs. (11) and (12) have analogous problems. These equations define the AirTF, so they should be corrected.","section":"§3, Eqs. (10)–(12)"},{"comment":"The filter weights are written as {w_p^{(d)}}_{p=1}^P and {w_p^{(u)}}_{p=1}^P, but the sums in Eqs. (12)-(14) run from p=0 to P; align the indexing and explicitly define w_0.","section":"§3, after Eq. (12)"},{"comment":"The 'Ideal setting' line is not defined in the captions or the text. Specify which model (or which ideal-communication configuration) it represents and its numerical value.","section":"§4, Figs. 2–3"},{"comment":"The dataset paragraph gives the generative model but not the values of η and ψ, the number of training samples, or the number of independent runs; provide these for reproducibility.","section":"§4, 'Dataset design'"},{"comment":"State explicitly which of the five models listed in the setup are represented by the curves labeled 'TNN' and 'GNN' in Figs. 2 and 3; as written, the reader cannot tell whether these are the ideal-communication baselines or the models with channel impairments at test time.","section":"§4, 'Experimental setup'"},{"comment":"The notation T_air(S(d), S(u)) uses S(d), S(u) for both the ideal shift operators from Eq. (2) and the channel-dependent operators in Eqs. (8)-(9); use distinct notation (e.g., S_air^(d,p), S_air^(u,p)) in the AirTF definition to avoid ambiguity.","section":"§3, 'AirTF'"},{"comment":"The phrase 'no previous works investigated TNNs over realistic wireless channels' is a strong claim; it is preceded by 'to the best of our knowledge' in Section 1, but the abstract omits this qualifier.","section":"Abstract and §1"}],"recommendation":"major_revision","confidential_remarks":"The paper is a reasonable fit for a signal-processing or machine-learning venue and the architecture is well motivated. The main gap is experimental: the robustness claim needs per-model ideal baselines, degradation curves, and an ablation of the upper-neighborhood branch. I would be willing to review a revised version. The typos in Eqs. (10)-(12) should also be fixed before resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short take: this is a legitimate incremental extension of AirGNN to regular cell complexes, and I think the architecture is worth building on. But the paper's central empirical claim—that the dual-neighborhood design itself confers channel robustness—is not actually established by the figures as presented.\n\nThe genuinely new piece is the formulation in Eqs. (4)-(12): defining topological shift operations with per-round fading and noise for both lower and upper neighborhoods of a cell complex, then building an AirTF and AirTNN layer that reduce to standard cell-complex filters under perfect channels and to AirGNN when only the lower neighborhood is ke5pt. That reduction is explicitly noted, which I appreciate. The training scheme (sampling channels per training step) follows the AirGNN recipe and is sensible. The paper is clearly written, the synthetic experiment at least demonstrates feasibility, and they ship a code repository.\n\nThe main soft spot is that the robustness story is not causally identified. Figures 2 and 3 plot absolute accuracy; the 'Ideal setting' is a single horizontal line, not per-model ideal baselines. AirTNN has two filter branches and more parameters than AirGNN, so its superior absolute accuracy could simply reflect extra capacity or additional upper-neighborhood information rather than higher resilience to channel fading and noise. To make the claimed mechanism stick, the paper needs degradation curves from each model's own ideal-setting baseline, or an ablation that removes the upper branch, or at least matched parameter budgets. Without that, the text's attribution—that two neighborhoods experiencing different channel conditions drive the gain—is an interpretation, not a result.\n\nA second issue is the premise that the two distinct communication topologies (lower and upper) can be realized in practice with independent fading, separate time slots, and proper resource allocation. This is assumed rather than discussed. If the two topologies share physical links or require synchronization that is not feasible, the whole mechanism does not materialize. A paragraph acknowledging this would go a long way.\n\nMinor but worth noting: Eqs. (10)-(12) contain typos in the recursion index and a stray noise term in the product. The math is conceptually sound, but it needs a cleanup before publication.\n\nOverall, this is a small, honest step. The central idea—train with sampled channels and use both neighborhoods—is plausible and consistent with prior work on AirGNN and AirNet. The experiments are too thin to fully support the robustness claim as stated, but the paper deserves serious referee time. I would send it to review, expecting major revisions: add degradation-based evaluation, an upper-neighborhood ablation, and a discussion of the communication-topology assumption. As it stands, I would cite it as an extension of AirGNN to cell complexes, but not yet as evidence for the robustness mechanism.","headline":"Reasonable incremental extension of over-the-air GNNs to cell complexes, with a clean formulation but an empirical robustness claim that needs sharper causal evidence.","tokens_in":9817,"tokens_out":2057,"would_cite":true,"duration_ms":19878,"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":"Neural networks defined on cell complexes can be trained to perform their convolutional filtering over a wireless channel, absorbing fading and noise into the filter itself, and this makes them more robust than graph-based or…","keywords":["topological neural networks","over-the-air computation","cell complexes","topological signal processing","fading channels","edge flows","source localization","wireless distributed learning"],"falsifier":"Run the same source-localization experiment but force the lower and upper neighborhood transmissions to share a single physical wireless topology with correlated fading, instead of the assumed independent networks: if AirTNN's accuracy collapses to the level of AirGNN or the communication-agnostic baselines, the two-topology independence assumption is the load-bearing part of the claimed robustness. A second, cheaper check is to keep fading gains fixed across all $p$-hop shifts instead of re-sampling them per transmission round, which removes the diversity the architecture relies on.","tokens_in":8828,"feed_emoji":"📡","tokens_out":8180,"duration_ms":68889,"temperature":0.7,"pith_summary":"This paper argues that topological neural networks can be made robust to real wireless communication by putting the channel inside the filter rather than treating it as an external disturbance. It introduces AirTNN, a cell-complex neural network whose convolutional filtering is executed over the air: every message is faded and noised by the channel, and the network learns its filter weights under those same impairments. The claim is that this design keeps accuracy close to the ideal noiseless setting while fading strength grows and signal-to-noise ratio drops, beating both over-the-air graph networks and communication-agnostic graph and topological baselines. The reason to care is that edge-flow data collected by distributed sensors (traffic, hydraulic, or communication network monitoring) must in practice be exchanged over wireless links, and this is a first proposal that builds that exchange into the learning architecture.","feed_headline":"Over-the-air topological networks keep accuracy under fading","feed_subtitle":"Unlike graph-only models, AirTNN folds noise into its filters and outperforms them on edge-flow localization.","key_machinery":"The over-the-air topological shift is the load-bearing object: lower and upper neighborhood aggregation is performed by wireless transmission, so instead of the fixed matrices $\\mathbf{S}^{(d)}$ and $\\mathbf{S}^{(u)}$ the network uses random shift matrices $\\mathbf{S}_{\\mathrm{air}}^{(d,p)}$ and $\\mathbf{S}_{\\mathrm{air}}^{(u,p)}$ whose nonzero entries are the channel gains $h_{ij}^{(d,p)}$ and $h_{ij}^{(u,p)}$. The topological filter over the air is the shift-and-sum operator $y = \\sum_p w_p^{(d)} \\mathbf{x}^{(d,p)} + \\sum_p w_p^{(u)} \\mathbf{x}^{(u,p)}$, which extends cell-complex FIR convolution to noisy random shifts, and AirTNN layers are banks of such filters followed by pointwise nonlinearities. Training treats the channel as part of the computation graph by sampling fading and noise afresh each step, so the learned weights are robust to those impairments at inference.","core_discovery":"AirTNN replaces the ideal cell-complex shift operators with over-the-air shifts whose matrix entries are channel fading coefficients and whose outputs carry additive Gaussian noise. A one-hop shift of an edge signal is $\\mathbf{x}^{(d,1)} = \\mathbf{S}_{\\mathrm{air}}^{(d,1)} \\mathbf{x} + \\mathbf{n}^{(d,1)}$ over lower neighborhoods and $\\mathbf{x}^{(u,1)} = \\mathbf{S}_{\\mathrm{air}}^{(u,1)} \\mathbf{x} + \\mathbf{n}^{(u,1)}$ over upper neighborhoods, and $p$-hop shifts are formed by products of these random matrices with accumulated noise. The paper shows that a topological filter composed of such noisy shifts reduces exactly to a standard cell-complex FIR filter when the channel is perfect, and that training by sampling channel coefficients and noise at each step yields filter weights matched to the channel statistics. In experiments on Stochastic Block Model cell complexes with diffused edge-flow signals, AirTNN retains high source-localization accuracy as the Rayleigh fading scale and noise grow, and it outperforms AirGNN as well as communication-agnostic GNN and TNN baselines.","pith_inferences":["The paper assumes pre-designed resource allocation for the two communication topologies; jointly learning power control or beamforming together with the filter weights is a natural extension that could improve accuracy beyond the reported results.","If the lower and upper neighborhood transmissions share physical links or correlated fading in a real deployment, the diversity that the paper credits for robustness would be reduced, and the performance gap over AirGNN might shrink.","The same over-the-air shift construction applies in principle to signals on higher-order cells (polygons, $k=2$) and to simplicial complexes, where the upper and lower neighborhood structure is richer; the paper does not test those cases.","A matched training distribution is what delivers robustness: if test-time fading or noise follows a different distribution than the training samples, the architecture's advantage would likely degrade, suggesting a distribution-shift experiment as a sharp test."],"forward_implications":["AirTNN generalizes standard cell-complex topological filters, because perfect communication reduces its over-the-air shifts to the ordinary shift operators and recovers the textbook filter.","Because the same noisy channel model is present in training and inference, no retraining or channel estimation is needed at test time for robustness to the channel statistics seen in training.","The architecture uses two distinct communication topologies, one per neighborhood type, whose partially redundant links can make the overall distributed processing more resilient to link failures.","For edge-flow source localization, which matters for anomaly detection in infrastructure networks, the paper's experiments indicate that a wireless-aware topological model beats both graph-only over-the-air models and models trained under ideal-communication assumptions.","This is the first over-the-air topological neural network, extending the over-the-air computation idea from graph neural networks to cell complexes and higher-order data."],"supporting_citations":[{"why":"Supplies the AirGNN architecture and the training strategy of sampling channel fading and noise at each step, which the paper adapts to cell complexes.","marker":"[26]"},{"why":"Defines topological signal processing over simplicial complexes and the local shift operation that the over-the-air shift generalizes.","marker":"[5]"},{"why":"Provides simplicial convolutional FIR filtering, the filter model that the topological filter over the air extends to noisy wireless shifts.","marker":"[7]"},{"why":"Develops signal processing on cell complexes, including upper and lower neighborhood shift operators that AirTSO replaces with channel-dependent matrices.","marker":"[28]"},{"why":"Defines cell complex convolutional neural networks, the layer structure that AirTNN layers are built from.","marker":"[15]"},{"why":"Demonstrates that incorporating channel noise during training improves deep network robustness, motivating the channel-sampling training design.","marker":"[25]"},{"why":"Provides the stochastic block model used to generate the graph and edge-community structure of the source localization dataset.","marker":"[29]"},{"why":"Supplies the cycle-basis algorithm used to extend the generated graph to a regular cell complex with polygon cells.","marker":"[30]"}],"fun_headline_variants":["AirTNN folds channel fading into topological filters for robust edge-flow","Over-the-air TNN beats graphs by learning with noisy shifts","Wireless-aware topological networks: robustness to fading and noise","Cell-complex TNN with over-the-air shifts outperforms on edge-flow"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole mechanism depends on being able to build two separate wireless communication networks, one for lower-neighbor and one for upper-neighbor exchanges, with independent fading across links and transmission rounds; if those two topologies cannot be deployed or synchronized in practice, the over-the-air topological aggregation never materializes.","fun_headline_variants_meta":{"raw":{"variants":["AirTNN folds channel fading into topological filters for robust edge-flow","Over-the-air TNN beats graphs by learning with noisy shifts","Wireless-aware topological networks: robustness to fading and noise","Cell-complex TNN with over-the-air shifts outperforms on edge-flow"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000575,"raw_usage":{"total_tokens":2700,"prompt_tokens":916,"completion_tokens":1784,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":532,"completion_tokens_details":{"reasoning_tokens":1722}},"tokens_in":532,"tokens_out":1784,"duration_ms":12090,"temperature":1.0,"reasoning_tokens":1722,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T19:30:52.365732+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same source-localization experiment but force the lower and upper neighborhood transmissions to share a single physical wireless topology with correlated fading, instead of the assumed independent networks: if AirTNN's accuracy collapses to the level of AirGNN or the communication-agnostic baselines, the two-topology independence assumption is the load-bearing part of the claimed robustness. A second, cheaper check is to keep fading gains fixed across all $p$-hop shifts instead of re-sampling them per transmission round, which removes the diversity the architecture relies on.","supporting_citations":[{"cited_title":"Fading models,","cited_arxiv_id":null,"evidence_quote":"Supplies the AirGNN architecture and the training strategy of sampling channel fading and noise at each step, which the paper adapts to cell complexes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines topological signal processing over simplicial complexes and the local shift operation that the over-the-air shift generalizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides simplicial convolutional FIR filtering, the filter model that the topological filter over the air extends to noisy wireless shifts."},{"cited_title":"Fading types in wireless communications systems,","cited_arxiv_id":null,"evidence_quote":"Develops signal processing on cell complexes, including upper and lower neighborhood shift operators that AirTSO replaces with channel-dependent matrices."},{"cited_title":"Signal processing on higher-order networks: Livin’on the edge... and beyond,","cited_arxiv_id":null,"evidence_quote":"Defines cell complex convolutional neural networks, the layer structure that AirTNN layers are built from."},{"cited_title":"Cell attention networks,","cited_arxiv_id":null,"evidence_quote":"Demonstrates that incorporating channel noise during training improves deep network robustness, motivating the channel-sampling training design."},{"cited_title":"Unsupervised representation learning of structured radio communication signals,","cited_arxiv_id":null,"evidence_quote":"Provides the stochastic block model used to generate the graph and edge-community structure of the source localization dataset."},{"cited_title":"Detection Algorithms for Communication Systems Using Deep Learning","cited_arxiv_id":"1705.08044","evidence_quote":"Supplies the cycle-basis algorithm used to extend the generated graph to a regular cell complex with polygon cells."}],"review_version":1}