DWnet: Deep-Wide Network for 3D Action Recognition

Fuxing Yang; Jianqin Yin; Yonghao Dang

REVIEW 4 major objections 6 minor 34 references

DWnet: Deep-Wide Network for 3D Action Recognition

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Replacing a deep network's final layers with a broad learning readout preserves 3D action accuracy and cuts test time by 100x.

desk verdict The BLS-plus-CNN architecture is a plausible engineering idea, but the paper's headline 100x speedup claim is not supported by the timing evidence, which appears to measure only the BLS readout, not the full pipeline. read the letter →

arxiv 1908.11036 v1 pith:QI2TXYWA submitted 2019-08-29 cs.CV

Yonghao Dang , Fuxing Yang , Jianqin Yin This is my paper · ORCID

classification cs.CV

keywords 3Dskeletonactionrecognitionbroadlearningsystemhierarchicalco-occurrencenetworkdeep-widetest-timeefficiencyridgeregressionenhancementnodes

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to show that a deep convolutional feature extractor and a broad learning system can be combined into one network that recognizes 3D skeleton actions almost as accurately as the deep network alone, but around 100 times faster at test time. The deep half is a pruned hierarchical co-occurrence network (PruHCN), which keeps the convolutional trunk and the first fully connected layer of the original HCN. The wide half is a broad learning readout: randomly initialized enhancement nodes expand the PruHCN feature vector, and the output weights are solved by ridge regression. On the SBU Kinect dataset the combined model reports 97.39% accuracy versus 94.83% for HCN, with average test time 2.17e-4 seconds per sample versus 4.12e-2. On NTU RGB+D, accuracy stays within 0.06 to 0.23 points of HCN while keeping a similar speed advantage.

What carries the argument

The central object is the PruHCN feature mapping feeding a broad learning readout. The feature mapping writes $Z_i = \theta(P(\mathrm{ReLU}(X \otimes W_{ei} + \beta_{ei})))$; the enhancement nodes are $H_j = \xi(Z W_{hj} + \beta_{hj})$ with random $W_{hj}, \beta_{hj}$ and a tansig activation; the final output is the concatenation of $Z$ and all $H_j$ multiplied by ridge-regression weights. This machine carries the argument because the random expansion is what compensates for the two pruned layers, and the closed-form solution is what makes testing fast.

What would settle it

Train DWnet while choosing enhancement-node counts on a validation split rather than the test set, then test under the same preprocessing. If accuracy falls below HCN's by a margin comparable to the reported gains (for example, more than 2.5% on SBU), the claim that random enhancement restores the pruned layers' approximation is refuted. A complementary check is to train a linear classifier directly on the same Fc6 features; if it already matches DWnet, the enhancement nodes add little.

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Extended reading notes

Core claim

The central claim is that replacing the Dropout layer and the final Fc7 softmax layer of a trained HCN with a broad learning system readout preserves learning capacity and improves inference efficiency. The pruned trunk still learns local spatial-temporal and co-occurrence features; the broad readout expands the Fc6 feature vector through random nonlinear enhancement nodes and connects both to an output layer whose weights are obtained in closed form. The reported numbers are 97.39% versus 94.83% on SBU and 84.07% versus 84.30% on NTU cross-subject, with per-sample test times falling from about 4.12e-2 seconds to 2.17e-4 seconds on SBU and from about 1.1e-2 seconds to 2.26e-4 seconds on NTU. The paper interprets this as evidence that the width of the broad readout can restore the approximation ability removed by pruning.

Load-bearing premise

The load-bearing premise is that a single trained PruHCN's Fc6 feature vector, expanded by randomly initialized enhancement nodes and solved with ridge regression, can maintain or improve the classification power of the original HCN's Dropout and Fc7 layers.

Editorial extensions

If this is right

The last fully connected layers of a trained deep CNN can be swapped for a ridge-regression readout without hurting accuracy, so the expensive softmax classifier is not a necessary part of the model.
Skeleton action recognition can run near real time on modest hardware: per-sample times near 2e-4 seconds move the bottleneck from classification to feature extraction.
The enhancement-node count is a dataset-dependent knob; the paper reports optimal values of 550 on SBU and 7500 or 12500 on NTU, so accuracy and speed trade off through a single width parameter.
Because only the readout changes, the same extracted features can be reclassified after retraining just the readout, avoiding a full end-to-end retraining pass.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The recipe generalizes beyond skeletons: any CNN that produces a dense feature vector could have its classifier pruned and replaced by a broad readout for faster inference, but the paper does not test this.
The reported 100x speed gain is tied to the specific enhancement-node counts; for very wide enhancement layers the ridge regression itself may dominate the runtime and weaken the advantage.
The success of random enhancement nodes suggests the Fc6 representation is already close to linearly separable; a simple probe such as a linear classifier on the same Fc6 features could reveal how much of the accuracy comes from the broad readout rather than the deep trunk.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The core idea is a simple, sensible assembly: take a pretrained skeleton CNN (HCN), chop off the last two layers, and replace them with a broad learning system ridge-regression readout. That specific combination is new in the literature, and the accuracy results are genuinely close to the HCN baseline: on NTU you lose less than 0.3% in both CS and CV, and on SBU you even gain a couple points. I believe the accuracy claim, as far as it goes. The paper is also honest about being non-end-to-end and about not being a full theoretical treatment.

The weak spot is the speed claim, and it is not minor. The paper reports DWnet at 2.17e-4 s/sample vs HCN at 4.12e-2 s/sample, about a 190x gap. But DWnet keeps all the convolutional layers and Fc6 from HCN (Fig. 2). Those layers account for virtually all the multiply-adds on a 16x15x3 input; the removed Dropout and Fc7 are a mask and a 256x8 dense product. If both models run the same conv stack, DWnet cannot be two orders of magnitude faster. The timing number for DWnet is suspiciously close to the BLS-alone timing (8.30e-5), which tells me the authors timed only the BLS readout, not the full PruHCN forward pass. The complexity analysis in III.C compares BLS to the pruned layers only, not to the total network, so it does not justify the headline. The paper never states what quantity was timed, and no code is released to check.

Secondary issues: the enhancement-node count is chosen from test-set curves (Figs. 5-7), there are no repeated-run statistics, and the conclusion calls the result state-of-the-art after comparing with exactly one action-recognition baseline (HCN). The BLS and HCNBLS baselines are much weaker by design, so they do not make the SOTA claim meaningful. On the plus side, the related work is fine, the method is described clearly, and the accuracy comparison with HCN on two datasets is a reasonable first evidence.

Verdict: the architecture is worth knowing about, but the speed evidence needs to be redone end-to-end, with a clear statement of what was measured, ideally with timing breakdowns and code. If the speedup survives that, it's a useful practical result, though not a breakthrough. This deserves a serious referee because the core question is empirical and correctable, but I would not cite it in its current form.

Referee Report

4 major / 6 minor

Summary. The paper proposes DWnet, which combines a pruned Hierarchical Co-occurrence Network (PruHCN) with a Broad Learning System (BLS) readout for 3D skeleton-based action recognition. The deep part is HCN with the final Dropout and Fc7 layers removed, and the BLS readout consists of randomly generated enhancement nodes followed by a ridge-regression output layer. On SBU Kinect, the authors report 97.39% accuracy for DWnet versus 94.83% for HCN; on NTU RGB+D they report near-identical accuracies (84.07% vs 84.30% CS; 89.84% vs 89.90% CV). The headline claim is an approximately 100x reduction in per-sample testing time (e.g., 4.12e-2 s vs 2.17e-4 s on SBU). The paper also compares against a plain BLS and an HCNBLS variant with untrained PruHCN modules.

Significance. If the efficiency claim were properly supported, the idea of using a pretrained deep feature extractor with a broad-learning readout for skeleton-based action recognition would be of moderate interest, especially for latency-sensitive applications. The architecture is clearly described, and the experiments cover two standard datasets with a direct comparison to HCN. However, the paper provides no code, no repeated-run statistics, and only one strong deep-learning baseline, so the empirical support for the 'state-of-the-art' conclusion is weak. Crucially, the central speedup claim is not yet established by the reported measurements.

major comments (4)

[Section III.C, Tables II and III] The roughly 100x speedup claim is not supported by the evidence because the paper does not state whether the reported times are end-to-end or only for the readout layers. DWnet retains all of HCN's convolutional layers and Fc6 (Fig. 2), so replacing only Dropout and Fc7 with a BLS readout cannot reduce total inference time by 190x on SBU if both timings include the same convolutional forward pass. Additionally, Dropout is not active at inference time in standard HCN, so pruning it has no effect on test-time cost. Please report end-to-end timings for both models with the same hardware/software stack, and state exactly which operations are included in each measurement.
[Section IV.C, Figs. 5-7] The number of enhancement nodes m is selected by maximizing test-set accuracy: Fig. 5 reports the best average testing accuracy at m=550, and Figs. 6-7 select 7500 and 12500 by the same criterion. This selection on the test set makes the accuracies in Tables I and III optimistic relative to what would be expected on unseen data. Please tune m on a validation split (or report accuracy as a function of m without claiming the maximum as expected performance) and provide repeated-run mean ± std to establish the stability of the reported improvements.
[Section III.C] The complexity argument is incomplete and does not by itself imply the claimed speedup. On NTU RGB+D, the BLS readout with 7500 or 12500 enhancement nodes multiplies a feature vector of dimension 256 plus the enhancement dimension by the 60-class output matrix, yielding far more multiply-adds than HCN's Fc7 (256x60). On SBU, 614x8 operations for the BLS readout exceed 64x8 for Fc7. Thus the statement that 'the computational complexity of the BLS is lower than that of pruned layer of HCN' is not true in terms of multiply-add count for the configurations actually used, and the reported timing difference likely reflects differences in implementation, batching, or measurement scope rather than the architecture change.
[Section V and Section IV.D] The conclusion that DWnet 'can achieve the state-of-the-art performance' is unsupported by the comparisons presented. The only deep-learning baseline is HCN itself, and on NTU RGB+D DWnet is slightly worse than HCN (89.84% vs 89.90% CV; 84.07% vs 84.30% CS). Please either temper the claim to 'comparable to HCN' or add the relevant state-of-the-art baselines from the skeleton-based action recognition literature.

minor comments (6)

[Section III.A and III.B] There are several typos: 'irregualr' in Section III.A, 'spapatial-temporal' and 'sapatial-temporal' in Section III.B, and 'pruned' used as a verb in Fig. 2 caption.
[Section III.B] The text says 'There are 6 layers including 4 convolutional layers and 2 fully connected layers in the PruHCN,' but Fig. 2 shows PruHCN includes five convolutional layers (Conv1-Conv5) and one fully connected layer (Fc6); please correct the layer counts.
[Eq. (2) and Eq. (3)] Equation (2) defines Z_i for i=1,...,n but the paper then uses Z without a subscript in Eq. (3); please clarify whether Z denotes Z_1 given that n=1.
[Table III] The table header is confusing: the columns are labeled 'CV' and 'CS' with 'Testing Time' straddling the accuracy and time columns, making it unclear which number is accuracy and which is time. Please use explicit column headers such as 'CV Acc.' and 'CV Time'.
[References] References [23] and [34] cite the same NTU RGB+D dataset paper; please merge them to avoid duplicate citations.
[Section IV.C] The paper says DWnet 'almost achieves real-time testing' but does not define real-time relative to any frame-rate requirement; please specify the target frame rate and the measurement protocol.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: DWnet accuracy and speedup are empirical comparisons; no equation reduces to its inputs.

full rationale

The paper makes an empirical architecture claim: a trained PruHCN feature extractor followed by a BLS ridge-regression readout. Section III-C defines the feature mapping (Eq. 2) and enhancement nodes (Eq. 3), but no equation defines the output accuracy or testing time in terms of these quantities; accuracy and speed are measured on test sets (Tables I-III). The speed comparison is questionable because both HCN and DWnet share the convolutional stack and Fc6, so the ~100x speedup cannot follow from replacing Dropout/Fc7 with BLS alone; however, this is a correctness or measurement concern, not a circular reduction. The number of enhancement nodes is tuned on test-set curves (Figs. 5-7), which weakens generalization but is not a fitted quantity renamed as a prediction. The one self-citation [28] concerns cement compressive strength and is not load-bearing. The Conclusion's admission that DWnet is non-end-to-end is a limitation, not a circular step. No load-bearing derivation step reduces to its own inputs.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claim rests on two existing machinery blocks (HCN features and BLS readout) plus two hand-set choices: pruning the classifier and selecting the enhancement-node count. The enhancement-node count is fitted to test data, which is the main burden. No new physical or conceptual entities are introduced.

free parameters (3)

Number of BLS enhancement nodes m = 550 (SBU), 7500 (NTU CS), 12500 (NTU CV)
Swept and chosen by highest testing accuracy on the test split, so the reported accuracy is partly a selection result.
Number of feature nodes (PruHCN modules) = 1
Chosen by hand, justified by a redundancy argument, without an ablation comparing 1 vs multiple trained PruHCNs.
BLS random weights W_hj and biases beta_hj = Not specified
Generated randomly with an unspecified distribution; the realization affects enhancement nodes and accuracy, and no seed is reported.

assumptions (3)

domain assumption HCN is an effective feature extractor for skeleton co-occurrence
The paper builds on HCN [19] and assumes its convolutional features are discriminative for the target datasets.
domain assumption BLS ridge regression can restore the approximation ability lost by pruning layers
Assumed from BLS literature [20] and used to justify replacing Dropout and Fc7 with enhancement nodes.
ad hoc to paper Randomly generated nonlinear enhancement nodes provide a sufficiently rich feature expansion
Relied on in Eq. (3); no analysis of the distribution or dimensionality is provided, and the required node count is found by test-set tuning.

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Cite this review

Pith. "Pith review of DWnet: Deep-Wide Network for 3D Action Recognition." pith.science (2026). https://pith.science/paper/QI2TXYWA

@misc{pith2026190811036,
  author       = {Pith},
  title        = {Pith review of: DWnet: Deep-Wide Network for 3D Action Recognition},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QI2TXYWA}},
  note         = {Machine review of arXiv:1908.11036}
}

read the original abstract

We propose in this paper a deep-wide network (DWnet) which combines the deep structure with the broad learning system (BLS) to recognize actions. Compared with the deep structure, the novel model saves lots of testing time and almost achieves real-time testing. Furthermore, the DWnet can capture better features than broad learning system can. In terms of methodology, we use pruned hierarchical co-occurrence network (PruHCN) to learn local and global spatial-temporal features. To obtain sufficient global information, BLS is used to expand features extracted by PruHCN. Experiments on two common skeletal datasets demonstrate the advantage of the proposed model on testing time and the effectiveness of the novel model to recognize the action.

Figures

Figures reproduced from arXiv: 1908.11036 by the authors.

**Figure 2.** The structure of HCN and PruHCN. The struc [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The structure of HCNBLS. It is the other [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: The average confusion matrix. The horizontal [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: The effect of the number of enhancement nodes [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: The effect of the number of enhancement nodes [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: The effect of the number of enhancement nodes [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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