Dual-wing Adaptive Dynamic Mixer (DADM)

• DADM is a CNN-based module that adaptively fuses multi-scale temporal convolutions via a dual-wing channel split, enhancing both local detail capture and global context aggregation.
• Its adaptive mechanism computes input-dependent scalar weights to blend receptive fields of various sizes, balancing sensitivity to fine-grained motion and long-range dependencies.
• Integrated within the IONext backbone, DADM significantly improves inertial odometry performance while reducing computational complexity compared to Transformer-based methods.

Searching arXiv for the specified papers and closely related work to ground the article. Dual-wing Adaptive Dynamic Mixer (DADM) is a CNN-based module for inertial odometry introduced within the IONext backbone as a Transformer-inspired replacement for self-attention in hierarchical sequence modeling (Zhang et al., 23 Jul 2025). It is designed to address a specific tension in IMU-based localization: pure Transformers model long-range dependencies effectively but have weak inductive biases and limited sensitivity to local, fine-grained motion variations, whereas conventional CNNs preserve local detail but have a restricted receptive field and static kernels (Zhang et al., 23 Jul 2025). DADM resolves this by splitting channels into two parallel “wings,” applying multi-scale depthwise temporal convolutions in each wing, and using input-dependent scalar weights to adaptively fuse the scales before recombination. In IONext, DADM serves as the principal spatial or spatio-channel mixer inside the Adaptive Dynamic Encoder (ADE), while the Spatio-Temporal Gating Unit (STGU) assumes the role of temporal gating (Zhang et al., 23 Jul 2025). The design is conceptually related to TransXNet’s Dual Dynamic Token Mixer, which also uses an evenly split dual-branch architecture to combine dynamic global and local processing, though DADM specializes this pattern for 1D IMU sequences rather than 2D vision features (Lou et al., 2023).

1. Origin and architectural role

DADM was proposed in "IONext: Unlocking the Next Era of Inertial Odometry" as the core spatial mixer of a purely convolutional inertial odometry backbone (Zhang et al., 23 Jul 2025). The underlying motivation is explicit. Transformer-based inertial odometry models are described as strong at long-range or global dependency modeling, but limited by weak inductive biases such as locality and translation equivariance, reduced sensitivity to local, fine-grained motion variations, and substantial computational cost on long sequences (Zhang et al., 23 Jul 2025). Standard CNNs exhibit the opposite profile: they preserve high-frequency local detail through small kernels but require very deep stacks or very large kernels to expand receptive field, and their convolution kernels remain static rather than input-adaptive (Zhang et al., 23 Jul 2025).

Within IONext, DADM is embedded in the ADE block, where it replaces the self-attention sublayer of a Transformer encoder. The block equations are given as

$$\begin{aligned} X_i' &= X_i + \mathrm{DADM}(\mathrm{BN}(X_i)), \ X_{i+1} &= X_i' + \mathrm{STGU}(\mathrm{BN}(X_i')), \end{aligned}$$

with batch normalization applied before each mixer (Zhang et al., 23 Jul 2025). In this arrangement, DADM performs the main spatial or spatio-channel mixing, while STGU replaces the MLP and carries out temporal gating (Zhang et al., 23 Jul 2025).

IONext is a hierarchical CNN backbone described as conceptually similar to Swin-Transformer but purely convolutional (Zhang et al., 23 Jul 2025). Its four stages contain $N_i=[2,2,6,2]$ ADE blocks with channel sizes $[96,192,384,768]$, so DADM appears in 12 encoder blocks across the network (Zhang et al., 23 Jul 2025). This repeated use is central to the model’s strategy for accumulating long-range temporal context via multi-scale convolutions and stage-wise downsampling rather than explicit self-attention.

2. Internal structure of the dual-wing mixer

The defining property of DADM is its “dual-wing” channel split. For an ADE input $X_i \in \mathbb{R}^{C \times T}$, batch normalization produces $\tilde X_i = \mathrm{BN}(X_i)$, after which channels are evenly divided into two parallel branches

$$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$

(Zhang et al., 23 Jul 2025). Each wing applies an identical multi-scale depthwise convolutional module followed by adaptive fusion, producing outputs $F_0$ and $F_1$, which are concatenated and linearly remixed (Zhang et al., 23 Jul 2025).

The authors motivate the split by citing prior work such as InceptionNext, noting that important information is not uniformly distributed over channels and that naive random partitioning in depthwise structures can be harmful (Zhang et al., 23 Jul 2025). The even split is therefore intended to ensure full channel utilization while reducing compute and parameter cost relative to running full multi-scale stacks over all channels (Zhang et al., 23 Jul 2025). The paper further describes the two wings as analogous to multiple heads in attention, but implemented with convolutions instead of pairwise token interactions (Zhang et al., 23 Jul 2025).

Inside each wing, DADM applies three parallel 1D depthwise convolutions along time: $$Y_{i,j} = \operatorname{DWConv}_i(\mathrm{BN}(X_j)), \quad i \in \{0,1,2\}$$ with kernel sizes $1$, $N_i=[2,2,6,2]$0, and $N_i=[2,2,6,2]$1 (Zhang et al., 23 Jul 2025). In the concrete IONext configuration, ADE blocks use the settings

$N_i=[2,2,6,2]$2

corresponding to $N_i=[2,2,6,2]$3 or $N_i=[2,2,6,2]$4 across stages (Zhang et al., 23 Jul 2025). The $N_i=[2,2,6,2]$5 branch acts as a purely local or per-time-step transform, the medium branch captures short-term motion segments, and the large branch expands temporal receptive field enough to approximate global phrase-like motion patterns over second-scale windows when stacked hierarchically (Zhang et al., 23 Jul 2025).

After the per-wing fusion step, the two outputs are concatenated: $N_i=[2,2,6,2]$6 and passed through a final $N_i=[2,2,6,2]$7 convolution

$N_i=[2,2,6,2]$8

for cross-channel mixing and projection back to $N_i=[2,2,6,2]$9 channels (Zhang et al., 23 Jul 2025). The result is injected through a residual connection,

$[96,192,384,768]$0

which preserves identity information and eases optimization (Zhang et al., 23 Jul 2025).

3. Adaptive dynamic mixing mechanism

DADM’s adaptivity resides in its scale-selection mechanism rather than in full token-token attention. For each wing $[96,192,384,768]$1, the outputs of the three depthwise branches $[96,192,384,768]$2 share the same shape $[96,192,384,768]$3, and the model computes input-dependent scalar weights $[96,192,384,768]$4 over these scales (Zhang et al., 23 Jul 2025).

The weight-generation process begins with adaptive global average pooling over time on $[96,192,384,768]$5, yielding a pooled descriptor $[96,192,384,768]$6 (Zhang et al., 23 Jul 2025). This descriptor is passed through a 1D convolution with kernel size 1, represented as $[96,192,384,768]$7, to produce three logits, one for each scale (Zhang et al., 23 Jul 2025). A softmax then normalizes them: $[96,192,384,768]$8 or equivalently

$[96,192,384,768]$9

(Zhang et al., 23 Jul 2025). These $X_i \in \mathbb{R}^{C \times T}$0 are scalar weights broadcast along channels and time, so the adaptivity is per wing and per sequence rather than per channel or per timestamp (Zhang et al., 23 Jul 2025).

Fusion within a wing is then defined by

$X_i \in \mathbb{R}^{C \times T}$1

(Zhang et al., 23 Jul 2025). This mechanism makes DADM input-adaptive in a restricted but efficient sense. Rather than learning arbitrary pairwise affinities as in self-attention, it dynamically selects among receptive fields of sizes $X_i \in \mathbb{R}^{C \times T}$2 according to the current motion pattern (Zhang et al., 23 Jul 2025).

The paper explicitly compares this behavior to squeeze-and-excitation and dynamic convolution. Squeeze-and-excitation reweights channels using pooled global context, whereas DADM reweights scales using pooled global context (Zhang et al., 23 Jul 2025). The interpretation offered is that high-frequency sequences can induce upweighting of smaller kernels, while smoother motion can favor larger kernels (Zhang et al., 23 Jul 2025). Although the distribution of $X_i \in \mathbb{R}^{C \times T}$3 is not plotted, the gains reported across heterogeneous scenarios such as pocket, handheld, cart, and indoor or outdoor motion suggest that the effective receptive field is being modulated according to motion regime and noise pattern (Zhang et al., 23 Jul 2025). This suggests that DADM functions as a structured low-dimensional alternative to attention: adaptive, but constrained to scale fusion rather than unconstrained token interaction.

4. Local detail, global context, and inductive bias

A central claim for DADM is that it jointly captures local fine-grained motion features and global motion patterns (Zhang et al., 23 Jul 2025). The $X_i \in \mathbb{R}^{C \times T}$4 depthwise branch preserves the highest temporal resolution and is described as maximally sensitive to instantaneous changes such as sudden rotational spikes or quick accelerations (Zhang et al., 23 Jul 2025). The medium branch with kernel size 3 or 5 captures short-term temporal patterns such as short turns or segments of gait cycles (Zhang et al., 23 Jul 2025). These two branches together provide high-frequency modeling relevant to instantaneous velocity and heading estimation (Zhang et al., 23 Jul 2025).

The large branch with kernel size 11 or 17 supplies expanded temporal context (Zhang et al., 23 Jul 2025). The paper notes that with IMU rates around 100–200 Hz and a 1 second window, a kernel length of 11–17 covers approximately $X_i \in \mathbb{R}^{C \times T}$5 seconds, and when these kernels are stacked across 12 ADE blocks with downsampling between stages, the effective receptive field extends over the entire 1 second window and beyond in deeper stages (Zhang et al., 23 Jul 2025). The deeper blocks operate at coarser temporal resolution because each stage halves temporal length through stride-2 convolution, so their large kernels capture long-range dependencies over the entire motion snippet (Zhang et al., 23 Jul 2025). The intended result is Transformer-like global context without explicit attention.

This design introduces several inductive biases that the paper contrasts with pure Transformers: locality and translation equivariance through convolution, multi-scale temporal aggregation reminiscent of Inception or ResNet-style pyramids, and dynamic scale selection that is restricted across scales rather than across arbitrary token pairs (Zhang et al., 23 Jul 2025). The authors argue that these properties make DADM more robust to noisy IMU signals and limited data, while also avoiding the $X_i \in \mathbb{R}^{C \times T}$6 complexity and parameterization associated with multi-head self-attention (Zhang et al., 23 Jul 2025).

A plausible implication is that DADM’s improvement is not merely due to larger receptive fields, but to the particular combination of structured temporal filtering and modest input adaptivity. In the paper’s framing, self-attention must learn useful temporal filters indirectly through similarity structure, whereas DADM imposes a prior over motion-relevant temporal filters and learns how to interpolate between them on a per-sequence basis (Zhang et al., 23 Jul 2025).

5. Relationship to ADE, STGU, and related dual-dynamic mixers

DADM is not a standalone module in IONext; it is paired with the Spatio-Temporal Gating Unit inside ADE. The order is fixed: $X_i \in \mathbb{R}^{C \times T}$7 DADM therefore acts first, computing dynamic multi-scale features, while STGU follows by assigning time-step-specific weights to emphasize representative and task-relevant temporal segments (Zhang et al., 23 Jul 2025).

STGU itself consists of a gating branch and a value branch. The gating branch computes

$X_i \in \mathbb{R}^{C \times T}$8

while the value branch uses a depthwise convolution on $X_i \in \mathbb{R}^{C \times T}$9, and the output is

$\tilde X_i = \mathrm{BN}(X_i)$0

(Zhang et al., 23 Jul 2025). The key distinction is that DADM adapts at the level of scale selection per sequence and per wing, whereas STGU performs temporal gating over time indices (Zhang et al., 23 Jul 2025). The paper summarizes this complementarity as DADM determining what to compute at each temporal scale and STGU determining when those features matter most (Zhang et al., 23 Jul 2025).

The notion of a dual dynamic mixer has a clear precedent in TransXNet’s Dual Dynamic Token Mixer (Lou et al., 2023). There, channels are evenly split between a global dynamics branch based on Overlapping Spatial Reduction Attention (OSRA) and a local dynamics branch based on input-dependent depthwise convolution (IDConv), after which the results are concatenated and refined (Lou et al., 2023). The TransXNet paper explicitly frames this as simultaneous learning of global and local dynamics through input-dependent aggregation weights (Lou et al., 2023). DADM shares the channel-split dual-wing principle and the emphasis on dynamic local processing, but replaces the vision-oriented global attention wing with a convolutional multi-scale mixer specialized for 1D temporal IMU signals (Zhang et al., 23 Jul 2025, Lou et al., 2023).

The IONext paper directly notes analogies to multiple heads in attention and cites InceptionNext for channel partitioning intuition (Zhang et al., 23 Jul 2025). It also situates DADM alongside large-kernel CNNs such as RepLKNet and SLaK, Inception-style architectures, ConvNeXt, SE blocks, MetaFormer-type token mixers, and TransXNet (Zhang et al., 23 Jul 2025). In this positioning, DADM is best understood not as a generic attention surrogate, but as a specialized dual dynamic temporal mixer that “attends across scales” using input-conditioned weights (Zhang et al., 23 Jul 2025).

6. Empirical findings, implementation profile, and limitations

The empirical evidence for DADM is reported through the performance of IONext and through ablations on ADE and related module variants. On six public datasets, IONext is reported to consistently outperform state-of-the-art Transformer- and CNN-based methods (Zhang et al., 23 Jul 2025). On the RNIN dataset, the abstract states that IONext reduces average ATE by 10% and average RTE by 12% compared to iMOT (Zhang et al., 23 Jul 2025). In the detailed results section, Table 2 attributes larger reductions on RNIN relative to iMOT, namely $\tilde X_i = \mathrm{BN}(X_i)$1 by 45.5%, $\tilde X_i = \mathrm{BN}(X_i)$2 by 46.8%, and $\tilde X_i = \mathrm{BN}(X_i)$3 by 16.8% (Zhang et al., 23 Jul 2025). Because these aggregate gains arise from the full IONext design, the paper uses ablation to isolate DADM’s role.

Those ablations indicate that replacing RoNIN-ResNet residual blocks with ADE, deepening the network to $\tilde X_i = \mathrm{BN}(X_i)$4, widening channels to $\tilde X_i = \mathrm{BN}(X_i)$5, and modifying the stem each improve performance, with ADE identified as a major contributor (Zhang et al., 23 Jul 2025). Additional comparisons show that RoNIN-ResNet + DADM already shifts the CDF curves of ATE and RTE favorably on RNIN, and that removing STGU while keeping DADM still produces significant gains over RoNIN-ResNet (Zhang et al., 23 Jul 2025). Radar plots over six datasets further show RoNIN-ResNet being dominated by IONext without STGU, which the paper interprets as evidence of DADM’s impact (Zhang et al., 23 Jul 2025).

From an implementation standpoint, DADM is part of a model that operates on 1 second windows of IMU data with $\tilde X_i = \mathrm{BN}(X_i)$6 input channels corresponding to a 3D accelerometer and 3D gyroscope, $\tilde X_i = \mathrm{BN}(X_i)$7, where $\tilde X_i = \mathrm{BN}(X_i)$8 depends on the sampling rate, such as 100 Hz or 200 Hz (Zhang et al., 23 Jul 2025). IONext begins with a 1D convolutional stem using kernel 4 and stride 4 to create tokens without explicit positional encoding (Zhang et al., 23 Jul 2025). Within each DADM, the depthwise branches have stride 1 and padding that preserves temporal length, and the final projection $\tilde X_i = \mathrm{BN}(X_i)$9 is a $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$0 convolution (Zhang et al., 23 Jul 2025). Downsampling between stages uses 1D non-overlapping convolution with kernel 2 and stride 2, and BatchNorm is reported to outperform LayerNorm in this setting (Zhang et al., 23 Jul 2025).

The training objective does not include a DADM-specific auxiliary loss. The network is optimized end-to-end using mean squared error on predicted window-averaged velocity: $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$1 (Zhang et al., 23 Jul 2025). Training uses Adam with batch size 512, maximum 100 epochs, early stopping when the learning rate falls below $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$2, and initial learning rate $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$3 on RTX 3090 hardware (Zhang et al., 23 Jul 2025).

Efficiency is a recurring theme. IONext with DADM and STGU is reported at approximately $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$4 FLOPs and $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$5 parameters, compared with a Swin-Transformer baseline at $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$6 FLOPs and $$X_j \in \mathbb{R}^{\frac{C}{2} \times T}, \quad j \in \{0,1\}$$7 parameters (Zhang et al., 23 Jul 2025). This supports the paper’s claim that DADM contributes to a significantly more efficient alternative to attention-based inertial odometry backbones (Zhang et al., 23 Jul 2025).

The paper also notes limitations. DADM itself does not explicitly handle device orientation changes, and the overall IONext model still struggles with random device rotations (Zhang et al., 23 Jul 2025). Suggested future directions include rotation-aware mechanisms such as equivariant convolutions or orientation-invariant encoding, as well as richer forms of adaptivity such as per-channel or per-time-step dynamic convolution or combinations with lightweight self-attention or state-space models (Zhang et al., 23 Jul 2025). This suggests that DADM’s current formulation is deliberately conservative: dynamic enough to recover some of attention’s context sensitivity, but structured enough to retain CNN priors and efficiency.