Efficient Implicit Neural Compression of Point Clouds via Learnable Activation in Latent Space

Qianqian Yang; Yichi Zhang

REVIEW 3 major objections 5 minor 50 references

Efficient Implicit Neural Compression of Point Clouds via Learnable Activation in Latent Space

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read PICO, an INR codec with learnable activations, outperforms MPEG point cloud compression by 4.92 dB on geometry.

desk verdict The 4.92 dB BD-PSNR claim is not supportable as written: the decoder is never told which cubes to evaluate, so the reported bpp omits mandatory side information. read the letter →

arxiv 2504.14471 v1 pith:N6Y4VX6I submitted 2025-04-20 cs.CV

Yichi Zhang , Qianqian Yang This is my paper · ORCID

classification cs.CV

keywords pointcloudcompressionimplicitneuralrepresentationlearnableactivationfunctionKolmogorov-Arnoldnetworksgeometryattributeparameterentropycoding

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 proposes PICO, a point cloud codec built on implicit neural representations (INRs), and reframes compression as the task of compressing the network's parameters. It splits the problem into geometry compression, posed as voxel-occupancy classification, and attribute compression, posed as color regression on the reconstructed surface. The central claim is that PICO's geometry compression beats the MPEG standards G-PCC (octree and trisoup) and V-PCC, with an average gain of 4.92 dB in D1 PSNR and about 53.5% bitrate reduction on the 8iVFB dataset, and that joint geometry-attribute compression is competitive. The gain is attributed to LeAFNet, a network whose learnable activation functions fit implicit fields with fewer parameters than conventional MLPs.

What carries the argument

LeAFNet is the central object: a coordinate network whose hidden layers use trainable activation functions of the form $\phi(x) = w_b\,\mathrm{silu}(x) + w_s \sum_i \exp(-\|x-c_i\|^2/h^2)$, replacing the B-spline kernels of Kolmogorov-Arnold Networks with radial basis functions. The argument also depends on three supporting mechanisms: a dynamic threshold $\tau_0$ chosen by golden-section search over a D1-PSNR curve that is empirically unimodal, which decides which voxels count as occupied; a reweighted sampling strategy that keeps occupied and empty voxels balanced despite severe sparsity; and parameter compression by uniform quantization followed by DeepCABAC entropy coding, with rate controlled by $\ell^1$ regularization and a dictionary of model sizes.

What would settle it

Recompute the rate-distortion curves for the four 8iVFB sequences while charging bits for the dynamic threshold (one scalar per sequence) and the model dictionary index (a few bits per rate point); if the BD-PSNR gain over G-PCC (octree) drops below the reported 7.09 dB average, the central claim fails. Alternatively, run the decoder with a fixed threshold derived only from the transmitted model and measure the resulting D1 PSNR loss.

Watch

Extended reading notes

Core claim

The discovery is that a per-point-cloud optimized network with learnable radial-basis activations can, after quantization and entropy coding of its parameters, reconstruct voxelized geometry at higher D1 PSNR than the standardized G-PCC and V-PCC codecs at the same bitrate on the four 8iVFB test sequences. The authors report BD-PSNR gains of 7.09 dB over G-PCC (octree), 3.95 dB over G-PCC (trisoup), and 3.73 dB over V-PCC, and an average 53.54% BD-BR reduction for geometry. For joint geometry and attribute compression they report a BD-PCQM improvement of $2.70 \times 10^{-3}$ over the same anchors, which they take as evidence that the two-stage decomposition preserves perceptual quality while keeping attributes aligned to the reconstructed geometry.

Load-bearing premise

The reported bitrate counts only the quantized and entropy-coded network parameters, and the paper does not state whether the dynamic threshold $\tau_0$ used at reconstruction and the model dictionary selection are also transmitted, so if those side bits are omitted the claimed rate-distortion gains are overstated.

Editorial extensions

If this is right

Geometry bitstreams require roughly 44-68% fewer bits than the three MPEG anchors at matched D1 PSNR across the tested sequences.
Because decoding is just coordinate queries through the network, a single bitstream can be evaluated at arbitrary sampling resolution without re-encoding.
Improvements in neural network quantization and entropy coding transfer directly into point cloud compression gains, since the signal is only a set of weights.
Splitting geometry and attribute compression means attribute quality is bounded by the reconstructed geometry, but color optimization can proceed independently once geometry is fixed.

Reading between the lines

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

If the dynamic threshold $\tau_0$ and the model dictionary index are not counted in the bitrate, the reported rate-distortion gains are optimistic; a fair comparison should cost these side parameters explicitly.
Because LeAFNet's activation is a generic replacement for fixed activations, the same quantization-and-entropy-coding pipeline could be applied to other INR tasks such as image or video compression.
The unimodality of D1 PSNR as a function of the threshold is verified on only three trained models; testing the golden-section search on sparser and more varied LiDAR scenes would show whether the dynamic threshold remains reliable.
Using the same codec on larger-scale block-wise scenes would test whether the per-sequence optimization cost, which is not included in the reported bitrate, remains acceptable in practice.

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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

Colleague,

The headline number – 4.92 dB BD-PSNR over MPEG anchors – is not load-bearing as written. The decoder cannot reconstruct the geometry it promises. In Algorithm 1, the sampling space V is defined from the original point cloud X via the occupied cube set W, and both encode and decode steps use V. But the bitstream contains only the compressed network parameters (line 17). Nothing tells the decoder which 32x32x32 cubes are occupied. Without W (or an equivalent signal), the decoder does not know where to evaluate f_g, and f_g was never trained on voxels outside V. Querying all of S is not the described algorithm and is far more expensive; it also may produce arbitrary outputs outside the training domain. The same goes for tau_0 and the model dictionary selection, though those are small scalars. W is not small: it is a 32768-cube occupancy pattern. So every bpp in Table 1 and Figure 2 omits a mandatory part of the bitstream, and the BD gains are computed against understated bitrates.

This is a fixable problem in principle – transmit W as side information – but as written the codec is internally inconsistent. That is the main thing you should know.

What the paper does well: the LeAFNet activation using RBFs is a sensible, KAN-inspired modification, and the ablations are thoughtful. The two-stage geometry/attribute split is a reasonable way to handle class imbalance, and the dynamic threshold search is a nice touch. If the rate accounting were fixed and the method still beat the MPEG anchors, this would be an interesting contribution to INR-based point cloud compression.

But there are other soft spots. Only the first frame of each 8iVFB sequence is used, there are no error bars or learned baselines, no code or data is released, and hyperparameters like lambda values and exact model sizes for each RD point are absent. None of that is disqualifying by itself; the V/W omission is.

Who is this for? A practitioner in learned point cloud compression who wants to track INR codec progress. It deserves a serious referee because the methods and results are plausible enough to warrant scrutiny, but the paper needs major revision and explicit bitstream accounting before any of the headline numbers can be taken at face value. I would send it to review, and I would tell the authors exactly what I wrote above.

Referee Report

3 major / 5 minor

Summary. The paper proposes PICO, an implicit neural representation (INR) framework for static point cloud compression, decomposed into two stages: geometry compression and attribute compression. The geometry stage trains a neural network to predict voxel occupancy probabilities over a restricted sampling space, applies a dynamically optimized threshold, and the attribute stage regresses colors on the reconstructed geometry. The network architecture, LeAFNet, replaces conventional MLP activations with learnable radial-basis-function (RBF) inspired activations in the KAN style. The network parameters are quantized and entropy-coded with DeepCABAC, framing compression as neural parameter compression. Experiments on the first frames of four 8iVFB sequences report large BD-BR savings and BD-PSNR/BD-PCQM gains over G-PCC (octree), G-PCC (trisoup), and V-PCC, including the headline average 4.92 dB D1 PSNR improvement.

Significance. If the reported bitrate accounting is correct, PICO would be a noteworthy INR-based codec that beats the MPEG standards on this benchmark with a parameter-efficient KAN-inspired architecture. The paper includes a detailed algorithm, several ablations (threshold selection, sampling, positional encoding, model selection), and public baselines. The main strengths are the clean two-stage formulation, the demonstration of LeAFNet's parameter efficiency over an MLP, and the effort to control rate via L1 regularization and entropy coding. However, the central claim depends critically on the completeness of the transmitted bitstream, and the experimental validation is narrow. As written, the bitrate accounting has a load-bearing gap that must be resolved before the headline results can be accepted.

major comments (3)

[Algorithm 1, Section 3.2.2, Eqs. (11)-(12)] The decoder in Algorithm 1 reconstructs X at lines 19-20 by querying f_g and f_a over the sampling space V, but V (and its defining cube occupancy set W) is computed from the original point cloud X in Eqs. (11)-(12) and is never included in the bitstream: line 17 entropy-encodes only the quantized network parameters. The decoder therefore cannot determine which of the 2^{3M}=32768 cubes (for M=5) contain points, so W is mandatory side information whose bitrate is absent from every bpp value in Table 1 and Figure 2. This omission can be large at low bpp and directly inflates the reported BD-BR savings and the headline 4.92 dB average D1 PSNR gain. The scalar threshold tau_0 from Algorithm 1 line 10 and the model dictionary index from SelectModel (line 3) are also not specified as transmitted. The paper must report the full bitstream including all side information, or explain how the decoder regenerates V without ground-truth geometry, and include that cost in all rate values.
[Section 4.1.3, Section 3.5.2] The rate-distortion experiments are not reproducible as reported. Section 4.1.3 gives training steps, quantization steps, and optimizer settings, but does not give the L1 regularization strengths lambda_g and lambda_a used for each RD point, the entries of the model dictionary (hidden dimensions, number of RBF centers), the RBF bandwidth h, or the number and bpp values of the RD points in Figure 2. Section 3.5.2 states that a model dictionary M enables adaptive selection by target bpp but never lists the dictionary. Without these parameters, the RD curves in Figure 2 and the BD metrics in Table 1 cannot be verified, weakening the claim that PICO achieves precise rate control through joint tuning of lambda and Delta.
[Section 4.2, Section 1] The experimental evaluation is limited to the first frame of each of the four 8iVFB sequences, with no error bars or repeated trials. The paper motivates the method with LiDAR-acquired large-scale point clouds in the Introduction, but all results are on a single dataset of human bodies at 1024^3 resolution. The absence of multi-frame statistics and the absence of any large-scale outdoor dataset make the broad claims of 'superior compression performance' and 'state-of-the-art' insufficiently supported, particularly since the method's complexity (training an INR per point cloud) is not evaluated for scalability.

minor comments (5)

[Table 1 caption] The caption 'Static PCC Performance of PICO (MLP), G-PCC (octree), G-PCC (trisoup) and V-PCC against PICO' is ambiguous. It should clarify that each column pair reports the BD gains of the proposed PICO (LeAFNet) relative to the named baseline, with the first pair being the LeAFNet-versus-MLP ablation.
[Eq. (22)] In Eq. (22), the two directional errors are both written as e(B,A); one should be e(A,B) to define the symmetric point-to-point error correctly.
[Eqs. (13)-(14)] The sampling strategy notation in Eqs. (13)-(14) is confusing: Eq. (13) uses V-X while Eq. (14) uses U(V), and the relationship between the calibrated rate alpha-hat and the original alpha is not explained in the main text.
[Figure 3(b)] The unimodality experiment in Figure 3(b) should specify the sequence, model configuration, and the range of thresholds used, since only the lambda values are currently identifiable.
[Section 2.2, References] The paper cites Ruan et al. [32] as prior work on implicit neural compression of point clouds but does not compare against it in the experiments; adding this baseline (or justifying its exclusion) would strengthen the state-of-the-art claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: benchmark gains are empirical comparisons, and the only author-overlapping citation is not load-bearing.

full rationale

The paper's central claims are empirical codec evaluations rather than closed-form derivations, so no predicted quantity reduces to an input by construction. The geometry INR is trained on voxel occupancy, and the dynamic threshold is selected by golden-section search on D1 PSNR; using the original point cloud at the encoder for this selection is standard rate-distortion optimization, not a self-fulfilling prediction. The BD-PSNR and BD-BR numbers in Table 1 are computed from rate-distortion curves against independent MPEG anchors using the paper's stated bitrate accounting, so the reported gains have independent empirical content. The only author-overlapping citation, reference [32], appears in a general list of multimodal INR techniques and is not used to justify LeAFNet, PICO, or the headline benchmark gains; therefore the self-citation is not load-bearing. The architecture borrows KAN, RBF, and NeRF components by acknowledged inspiration, not through a uniqueness theorem that forces the choices. A real concern is that Algorithm 1 derives the sampling space V and threshold tau_0 from the original geometry but appears to entropy-encode only the quantized network parameters, which may omit mandatory side information from the reported bitrates; that is a correctness and bitrate-accounting risk, not circularity, and does not raise the circularity score.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a set of hand-chosen hyperparameters (alpha, gamma, L, M, Delta, lambda values) and empirical assumptions (unimodality, generalization from sampled cubes, zero-cost side information, nearest-neighbor targets). No new physical entities or exotic axioms are introduced. The largest burden is the unstated rate accounting and model configuration, which directly affects the headline 4.92 dB claim.

free parameters (9)

alpha (sampling target ratio) = 0.5
Target non-empty voxel ratio in each training batch, Section 3.2.2 and Section 4.1.3. Chosen by hand, affects geometry training.
gamma (focal loss modulation) = 2
Modulation coefficient in focal loss, Equation 20 and Section 4.1.3. Chosen by hand.
L (positional encoding length) = 64
Number of octaves in NeRF-style positional encoding, Section 3.4.1. Ablations show sensitivity to L.
M (cube resolution bits) = 5
Partition of the voxel space into 32x32x32 cubes, Section 4.1.3. Controls the sampling space V.
Delta_g (geometry quantization step) = 1/2^10
Quantization step for geometry INR parameters, Section 4.1.3.
Delta_a (attribute quantization step) = 1/2^12
Quantization step for attribute INR parameters, Section 4.1.3.
lambda_g, lambda_a (L1 regularization strengths) = not stated (varied)
Regularization terms in Equations 20 and 21 control the rate, but the values used for each RD point in the main curves are not reported.
hidden dimensions for model dictionary = 24/36/48 in ablation; main curves unspecified
The adaptive model selection from dictionary M (Section 3.5.2) requires knowing which model produced each RD point; the main experiments do not specify this.
RBF bandwidth h and center count = not stated
The learnable activation phi(x) in Equation 19 has bandwidth h and N centers; neither is specified for the reported results.

assumptions (5)

domain assumption The quality metric D(O, tau) is unimodal in the threshold tau.
Section 3.2.3 and Figure 3(b) rely on this for golden-section search; only three models are tested.
domain assumption An INR trained on voxels from non-empty cubes W generalizes to all voxels in V.
The sampling strategy in Section 3.2.2 only queries voxels in W; the reconstruction assumes the network's occupancy predictions are valid for all of V.
domain assumption The decoder knows tau_0 and the model configuration with negligible or zero bitrate cost.
Algorithm 1 uses tau_0 at decode time and the model dictionary M for selecting architecture, but the paper never specifies how these are transmitted.
domain assumption Nearest-neighbor projection of attributes from original geometry to reconstructed geometry provides valid training targets.
Equation 17 defines the attribute regression ground truth; if the reconstructed geometry is poor, this projection introduces label noise.
standard math Kolmogorov-Arnold representation theorem supports the expressiveness of learnable activations.
Section 2.3 motivates the architecture, but the theorem is not used to guarantee compression performance and is not load-bearing.

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Pith. "Pith review of Efficient Implicit Neural Compression of Point Clouds via Learnable Activation in Latent Space." pith.science (2026). https://pith.science/paper/N6Y4VX6I

@misc{pith2026250414471,
  author       = {Pith},
  title        = {Pith review of: Efficient Implicit Neural Compression of Point Clouds via Learnable Activation in Latent Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N6Y4VX6I}},
  note         = {Machine review of arXiv:2504.14471}
}

abstract

Implicit Neural Representations (INRs), also known as neural fields, have emerged as a powerful paradigm in deep learning, parameterizing continuous spatial fields using coordinate-based neural networks. In this paper, we propose \textbf{PICO}, an INR-based framework for static point cloud compression. Unlike prevailing encoder-decoder paradigms, we decompose the point cloud compression task into two separate stages: geometry compression and attribute compression, each with distinct INR optimization objectives. Inspired by Kolmogorov-Arnold Networks (KANs), we introduce a novel network architecture, \textbf{LeAFNet}, which leverages learnable activation functions in the latent space to better approximate the target signal's implicit function. By reformulating point cloud compression as neural parameter compression, we further improve compression efficiency through quantization and entropy coding. Experimental results demonstrate that \textbf{LeAFNet} outperforms conventional MLPs in INR-based point cloud compression. Furthermore, \textbf{PICO} achieves superior geometry compression performance compared to the current MPEG point cloud compression standard, yielding an average improvement of $4.92$ dB in D1 PSNR. In joint geometry and attribute compression, our approach exhibits highly competitive results, with an average PCQM gain of $2.7 \times 10^{-3}$.

Figures

Figures reproduced from arXiv: 2504.14471 by the authors.

**Figure 1.** Model Architecture of LeAFNet. 3.3 Attribute Compression We formulate attribute compression as continuous regression over sparse coordinate samples. In our approach, each coordinate sample is mapped to its corresponding attribute value through an INR 𝑓𝑎. To implement this idea, we redefine the operator introduced in Equation 8 as follows: 𝑓𝑎 : (𝑥, 𝑦, 𝑧) ∈ [−1, 1] 3 → 𝒄 ∈ [0, 1] 3 , (15) Cˆ = {𝑓𝑎 (𝒙 ′ ) | 𝒙 ′ = 𝒙/2 𝑁… view at source ↗

**Figure 2.** Rate-distortion curves of PICO, PICO (MLP), G-PCC (octree), G-PCC (trisoup) and V-PCC on Static PCC. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** (a) PCQM RD curve of LeAFNet with different parameter sizes. (b) Unimodal property of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

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Reviewed August 16, 2026 · model on record in the stance chip above.

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