DSCD: Dual-Serialization Consistency Distillation

• DSCD is an order-regularization mechanism that stabilizes 3D point cloud models by addressing serialization-induced instability.
• It enforces consistency at both representation and decision levels using dual serializations (e.g., Hilbert and Trans-Hilbert) in a frozen-backbone framework.
• Empirical results show that DSCD notably reduces feature and prediction discrepancies while enhancing overall accuracy and efficiency on 3D tasks.

Searching arXiv for the cited Mantis paper and related work on Mamba-based 3D point cloud models and consistency regularization. Dual-Serialization Consistency Distillation (DSCD) is an order-regularization mechanism introduced within Mantis, a Mamba-native parameter-efficient fine-tuning framework for 3D point cloud foundation models. It addresses a specific failure mode of frozen Mamba backbones on point clouds: the same unordered point set admits multiple valid serializations, and changing the scan order changes the input-dependent operator chain in the state space model, which alters hidden-state propagation and the effective transfer kernel. DSCD therefore constructs two complementary serializations of the same point cloud and enforces consistency at both the representation and decision levels, while the pre-trained backbone remains frozen and adaptation is carried by trainable modules such as the State-Aware Adapter (SAA) and the task head (Guo et al., 5 May 2026).

1. Problem setting and motivation

In Mamba-based 3D point cloud processing, serialization denotes the conversion of an inherently unordered point cloud into a 1D causal sequence so that it can be scanned by a state space model. Because any permutation of points is valid for the causal scan, multiple serializations exist for the same input. Geometry-aware serializations such as Hilbert and Z-order better preserve locality and are empirically more stable than random permutations, but the core instability remains: different valid orders induce different state-transition chains and therefore different transfer matrices $W^{(k)}$ (Guo et al., 5 May 2026).

Appendix A.1 formalizes this sensitivity by showing that, for a branch $k$ with discretized operators, the output at time $t$ depends on the chain

$\prod_{j=i+1}^{t} A_j^{(k)},$

so the order itself directly affects the hidden-state evolution. This is the basis of what the paper terms serialization-induced instability. The issue becomes particularly acute when the Mamba backbone is frozen and adaptation is attempted with Transformer-native PEFT methods that operate at the token or feature level rather than at the level of selective state-space dynamics.

Mantis situates DSCD alongside SAA as a complementary remedy to this mismatch. SAA performs state-level modulation of Mamba’s operators, whereas DSCD penalizes divergence across valid serializations. A plausible implication is that DSCD is not merely a generic regularizer but a mechanism targeted at order sensitivity that arises specifically from causal selective state propagation in Mamba backbones.

2. Formal definition and optimization objective

DSCD is defined over two serialization functions $s_1$ and $s_2$, which map a point cloud $X \in \mathbb{R}^{M \times 3}$ to two sequential inputs. Let $k \in \{1,2\}$ index the dual branches. For each branch, the serialized token features are $E^{(k)} \in \mathbb{R}^{n \times d}$, and the SAA-enhanced encoder produces final-layer features $Z^{(k)} \in \mathbb{R}^{n \times d}$ (Guo et al., 5 May 2026).

The representation-level regularizer uses a branch-shared projection $k$0 on average pooled final features: $k$1

The decision-level regularizer uses a shared task head and softened logits: $k$2

With downstream loss $k$3, the total objective is

$k$4

Several design choices are explicit. DSCD uses no teacher-student network and no EMA teacher. The task head weights are shared across branches, and the KL term is symmetric. The paper applies DSCD only at the final encoder layer for efficiency; it does not specify per-layer feature alignment beyond that point. This suggests that DSCD is intended as a lightweight regularization layer on top of state-level adaptation rather than a deeply interleaved multiscale consistency scheme (Guo et al., 5 May 2026).

3. Serialization choices and training integration

The pipeline processes exactly two serializations per point cloud in parallel. The default choice is Hilbert and Trans-Hilbert, which the ablations identify as the best-performing dual curves. Z-order and Trans-Z-order are also evaluated, as are mixed combinations such as Hilbert + Z-order and Trans-Hilbert + Trans-Z-order. Random serialization is used only as a control baseline and performs worst (Guo et al., 5 May 2026).

A single iteration is described as follows. The input point cloud $k$5 is sampled with FPS to obtain $k$6 keypoints; KNN patches are gathered; and two serializations $k$7 and $k$8 produce dual token sets $k$9 and $t$0. Learnable order embeddings $t$1 are added, and per-branch features may be fused through a lightweight operation, optionally including cross-order channel-wise fusion to form $t$2. Each encoder block then applies normalization, projection, depthwise convolution, and SAA-modulated selective state-space updates: $t$3

$t$4

After the final encoder layer, DSCD computes feature consistency from pooled $t$5 and prediction consistency from softened logits $t$6. Gradients flow into the SAA controllers, order embedder, cross-order fusion, task head, and DSCD heads, while the pre-trained Mamba backbone remains frozen. The default hyperparameters are $t$7, $t$8, and $t$9. The optimizer is AdamW; typical learning rates are $\prod_{j=i+1}^{t} A_j^{(k)},$0 for ModelNet40 classification, $\prod_{j=i+1}^{t} A_j^{(k)},$1 for few-shot learning, and $\prod_{j=i+1}^{t} A_j^{(k)},$2 for segmentation, with cosine scheduling, 10-epoch warm-up for ModelNet40 classification, and weight decay $\prod_{j=i+1}^{t} A_j^{(k)},$3. The reported environment includes PyTorch 2.7.1+cu128 and often a single RTX 5090 GPU (Guo et al., 5 May 2026).

The compute cost is also characterized explicitly. DSCD adds two forward passes of the encoder and task head per sample and small projection heads $\prod_{j=i+1}^{t} A_j^{(k)},$4. The backbone’s linear-time property is preserved, and the memory and throughput overhead are described as marginal compared to full fine-tuning.

4. Empirical behavior and ablation evidence

The principal empirical claim for DSCD is a reduction in cross-serialization discrepancy. On ScanObjectNN, Table 11 reports that for the PB_T50_RS split, baseline Mamba3D full fine-tuning has feature discrepancy $\prod_{j=i+1}^{t} A_j^{(k)},$5 and prediction discrepancy $\prod_{j=i+1}^{t} A_j^{(k)},$6, whereas Mantis with SAA+DSCD reduces these to $\prod_{j=i+1}^{t} A_j^{(k)},$7 and $\prod_{j=i+1}^{t} A_j^{(k)},$8, corresponding to $\prod_{j=i+1}^{t} A_j^{(k)},$9 and $s_1$0, respectively. Similar reductions are reported on OBJ_BG and OBJ_ONLY (Guo et al., 5 May 2026).

These regularization effects are accompanied by downstream accuracy gains. On ScanObjectNN PB_T50_RS, Mamba3D full fine-tuning achieves $s_1$1 OA, while Mamba3D + Mantis reaches $s_1$2, a gain of $s_1$3. Similar improvements are reported on PointMamba and ZigzagPointMamba, including a $s_1$4 gain in one cited case. Table 4a further shows that DSCD alone yields modest improvements, whereas the combination of SAA with both feature-level and prediction-level consistency achieves the best result, again with final OA $s_1$5.

The paper also provides qualitative evidence. Figure 1 attributes tighter clusters in t-SNE and more coherent part boundaries in segmentation to the inclusion of DSCD. Large-scale scene segmentation and few-shot experiments are described as confirming that Mantis maintains or improves performance with small parameter budgets and that DSCD contributes to prediction stability. Since Mantis uses only about $s_1$6 trainable parameters overall, a plausible implication is that DSCD helps recover robustness that would otherwise be lost when full backbone adaptation is replaced by lightweight trainable modules.

5. Relationship to SAA and to broader consistency methods

Within Mantis, DSCD is explicitly paired with SAA rather than treated as a substitute for it. SAA modulates selective state-space operators and thereby adapts sequence dynamics at the state level; DSCD complements this by encouraging those SAA-modulated dynamics to remain robust across serialization choices. In practice, DSCD is computed on the outputs of the SAA-enhanced encoder and the shared task head, so its effect is to regularize the trainable adaptation layers rather than the frozen backbone directly (Guo et al., 5 May 2026).

The paper compares DSCD to consistency regularization and distillation in self-supervised learning, especially cross-view consistency. The resemblance lies in using two views of the same input and enforcing agreement across them. The distinction is that the two views are not augmentations in the ordinary sense but dual serializations of the same point cloud, chosen to probe Mamba’s order-sensitive dynamics. The method is also explicitly not teacher-student: both branches are aligned symmetrically at the feature and prediction levels.

The claimed novelty is therefore narrower and more specific than generic consistency training. DSCD addresses the fact that different valid serializations produce different operator chains and transfer kernels in Mamba-based 3D PFMs. Token-level PEFT and augmentation-based consistency methods do not target that failure mode. This suggests that DSCD’s main conceptual contribution is the recasting of serialization choice as a structured source of view variation tied to state-space dynamics rather than to semantic invariance in the usual augmentation sense.

6. Practical use, limitations, and terminological ambiguity

The paper identifies several circumstances in which DSCD is most beneficial: noisy, cluttered, or partially corrupted real-world point clouds, exemplified by ScanObjectNN PB_T50_RS, and fine-grained tasks such as part segmentation, where stable feature aggregation is important. It recommends geometry-aware curves that preserve locality and provide complementary views, with Hilbert + Trans-Hilbert as a strong default and Z-order variants as viable alternatives. Purely random serializations are discouraged outside ablation, and overly similar curves may reduce the benefit of dual-view training (Guo et al., 5 May 2026).

The defaults $s_1$7, $s_1$8, and $s_1$9 are reported as robust across broad ranges, with performance peaking around those values. The text warns against extremely large $s_2$0, which may induce feature collapse. It also states that applying consistency at earlier layers increases memory and complexity without clear gains, making the final encoder layer the preferred application point.

Several failure modes are noted. If the two serializations are too similar, the regularizer becomes weak; if they are too dissimilar or random, alignment becomes harder and convergence may slow. DSCD also adds compute because two branches must be processed. Reproducibility details include public code, default hyperparameters, and the note that specific file paths for DSCD configurations are not explicitly listed in the paper, so the repository’s configuration files and training scripts must be consulted.

A separate source of confusion is terminological. In CD4LM, the acronym DSCD refers to Discrete-Space Consistency Distillation, a method for diffusion LLMs operating on masked token sequences with an absorbing mask token. That work explicitly states that there is no notion of “dual-serialization” in its method, and its DSCD trains a trajectory-invariant, time-agnostic student in discrete token space rather than regularizing alternative point-cloud serializations (Liang et al., 5 Jan 2026). The shared acronym therefore names two distinct mechanisms in different domains; in the context of Mantis, DSCD unambiguously denotes Dual-Serialization Consistency Distillation.