Variable-Rate Spatial Event Mamba

• The paper introduces a causal, window-free architecture that eliminates fixed event accumulation, significantly reducing latency in event-based detection.
• It employs a lightweight causal spatial encoder and a Mamba state-space temporal model with linear complexity to efficiently capture local geometry and time dynamics.
• Empirical results on UAV event streams demonstrate state-of-the-art detection performance with reduced latency and minimal computational overhead.

Searching arXiv for the specified paper to ground the article in the cited source. Variable-Rate Spatial Event Mamba is the core architectural component introduced in CETUS for direct event-stream processing in event-camera perception. It is designed to remove two bottlenecks that dominate event-based detection pipelines: window latency introduced by fixed event accumulation and inference latency introduced by computationally heavy point-, voxel-, or grid-based models. Rather than converting asynchronous events into intermediate representations, it operates on raw events, applies a lightweight causal spatial neighborhood encoder to capture local geometry, uses a Mamba-based state-space backbone for temporal modeling with linear complexity, and employs an adaptive-speed inference controller that changes processing speed according to the event rate. In CETUS, this combination is framed as a way to preserve the stream-native character of event cameras while making real-time detection practical (Liang et al., 17 Sep 2025).

1. Problem formulation and latency model

The motivation for Variable-Rate Spatial Event Mamba begins from the observation that event cameras capture asynchronous pixel-level brightness changes with microsecond temporal resolution, but many existing methods first convert those streams into frames, voxel grids, or point clouds. CETUS argues that such conversions inevitably require predefined time windows and therefore introduce window latency before inference can even begin. The paper states that most prior methods accumulate events into windows of 20–50 ms or more, and gives the example that a 50 ms window implies at least 50 ms of perception lag, which is described as unacceptable for UAVs moving at 40–80 km/h (Liang et al., 17 Sep 2025).

CETUS formalizes total delay as

$$\mathcal{L} = \mathcal{L}_{e} + \mathcal{L}_{s} + \mathcal{L}_{i},$$

where $\mathcal{L}_{e}$ is event latency, $\mathcal{L}_{s}$ is sampling or window latency, and $\mathcal{L}_{i}$ is inference latency. The paper states that $\mathcal{L}_e$ is below 1 ms and negligible, so the central systems problem is the trade-off between $\mathcal{L}_{s}$ and $\mathcal{L}_{i}$. Fixed-window methods reduce computational frequency at the cost of large sampling delay, whereas pointwise methods reduce buffering but can become too expensive because they model many events individually. Variable-Rate Spatial Event Mamba is explicitly positioned as a response to that trade-off: it keeps the stream window-free at the representation level, while scheduling computation at an adaptive pace rather than at a fixed rate.

This framing also distinguishes CETUS from a common simplification in event-based vision: the assumption that lowering the window size is sufficient to reduce latency. CETUS reports that when the window length of fixed-window methods is reduced below 20 ms, detection performance collapses. This suggests that the issue is not only the duration of accumulation, but the use of fixed accumulation itself under highly variable event rates.

2. Event representation and causal spatial encoding

The input to the model is an asynchronous event stream

$\mathcal{E}=\{e_i\}_{i=1}^{N},$

where each event is

$e_i=(x_i,y_i,t_i,p_i),$

with pixel location, timestamp, and polarity. CETUS also uses an event-rate feature $\mathcal{R}$, on the grounds that event rate is informative both for perception and for scheduling (Liang et al., 17 Sep 2025).

The spatial encoder works directly on raw events and never converts them into frames, voxels, or point clouds. For each event $\mathcal{L}_{e}$0, it gathers a small fixed number $\mathcal{L}_{e}$1 of causal neighbors drawn only from earlier events:

$\mathcal{L}_{e}$2

The causality constraint is central: each event can attend only to the past, never the future. CETUS presents this as a requirement for streamable and online inference. If fewer than $\mathcal{L}_{e}$3 valid neighbors exist, padding masks mark invalid entries:

$\mathcal{L}_{e}$4

The center-event feature explicitly includes event rate. For each event, the local rate over horizon $\mathcal{L}_{e}$5 is

$\mathcal{L}_{e}$6

The raw center input concatenates position, time, rate, and polarity, and is then projected into a compact feature space. For neighbor events, CETUS computes relative offsets

$\mathcal{L}_{e}$7

together with spatial and temporal distances,

$\mathcal{L}_{e}$8

and a weighted combined distance $\mathcal{L}_{e}$9. The paper notes that the notation is slightly inconsistent at this point, but states that the intent is to combine spatial and temporal separation into one weighted distance. The vector

$\mathcal{L}_{s}$0

is fed into a two-layer MLP positional encoder

$\mathcal{L}_{s}$1

The neighbor feature is then position-enhanced as

$\mathcal{L}_{s}$2

Local aggregation is performed through single-query multi-head attention over the causal neighborhood. The center event serves as query, and the neighborhood features serve as keys and values:

$\mathcal{L}_{s}$3

Attention weights are computed with masking, aggregated into $\mathcal{L}_{s}$4, and stabilized by residual connection and layer normalization:

$\mathcal{L}_{s}$5

The resulting sequence $\mathcal{L}_{s}$6 is the spatially enriched event sequence passed to the temporal backbone.

The paper emphasizes that this local design captures spatial structure at cost approximately $\mathcal{L}_{s}$7 per event, rather than quadratic in the number of events. A plausible implication is that the architecture treats locality as the principal mechanism for geometric encoding, reserving global sequence modeling for the temporal backbone rather than for the spatial stage.

3. Mamba-based temporal modeling

Temporal modeling in CETUS is handled by a stack of Mamba state-space blocks. The model uses $\mathcal{L}_{s}$8 stacked blocks with residual updates:

$\mathcal{L}_{s}$9

with $\mathcal{L}_{i}$0 and final output $\mathcal{L}_{i}$1 (Liang et al., 17 Sep 2025).

The key property attributed to Mamba in CETUS is that it supports both parallel training and sequential streaming inference. In streaming mode, chunks are processed one by one while each layer maintains its own causal state:

$\mathcal{L}_{i}$2

$\mathcal{L}_{i}$3

$\mathcal{L}_{i}$4

The paper states that temporal continuity is therefore preserved across chunks, and that the amortized cost is close to $\mathcal{L}_{i}$5 per event.

For classification, CETUS applies a lightweight MLP head after layer normalization of the temporal output:

$\mathcal{L}_{i}$6

followed by dropout and a final projection to per-event logits

$\mathcal{L}_{i}$7

During training, when historical context is used, historical labels are padded with dummy logits and masked out in the loss so that alignment is preserved without penalizing past context.

Within CETUS, Mamba is not presented merely as a substitute sequence model. It functions as the temporal efficiency mechanism that makes a stream-native design computationally viable. The ablations reinforce this interpretation: replacing Mamba with LSTM or GRU leaves accuracy largely unchanged but increases latency to about 55–56 ms, indicating that the temporal backbone is the main determinant of real-time behavior rather than of static detection quality alone.

4. Unified variable-rate scheduling

The most distinctive systems component in CETUS is the unified variable-rate scheduling strategy. The paper states that event rates can vary from $\mathcal{L}_{i}$8 to over $\mathcal{L}_{i}$9 events/s. Under such variation, processing each event individually minimizes sampling delay but can exceed the sustainable computational budget. CETUS therefore introduces a controller that adaptively modulates the number of events processed per advancement, denoted $\mathcal{L}_e$0 (Liang et al., 17 Sep 2025).

Under a local Poisson-like assumption, sampling-window latency is approximated by

$\mathcal{L}_e$1

The system sets a window-latency budget $\mathcal{L}_e$2 and an inference-latency budget $\mathcal{L}_e$3. Inference cost is estimated online with an affine model,

$\mathcal{L}_e$4

A conservative base step is then chosen from the intersection of the latency constraints:

$\mathcal{L}_e$5

A PID controller adjusts the step size using the error

$\mathcal{L}_e$6

and the update

$\mathcal{L}_e$7

The updated step is then blended with the base step:

$\mathcal{L}_e$8

The paper explains the operational effect directly: when event rate rises, the controller can reduce the processing step to avoid excessive latency; when event rate falls, it can increase the step so the model does not waste computation on tiny bursts.

The history length used by the spatial encoder is also co-adapted:

$\mathcal{L}_e$9

Faster progression therefore uses shorter neighbor history, reducing overhead. CETUS characterizes this as trading some flexibility in spatial context for a better latency/throughput balance.

This scheduler makes event rate a dual-purpose variable. It is part of the perceptual input through $\mathcal{L}_{s}$0, and it is also the principal systems signal for pacing inference. This suggests a tight coupling between sensing statistics and compute allocation, rather than a separation between perception and scheduling.

5. Training setup, metrics, and empirical results

CETUS evaluates Variable-Rate Spatial Event Mamba on the EV-UAV dataset, described as containing UAV-mounted event streams with pixel-level foreground/background annotations and large event-rate variation (Liang et al., 17 Sep 2025). The implementation uses hidden dimension 128, state dimension 32, $\mathcal{L}_{s}$1 causal neighbors, spatial radius 0.2, and dropout 0.1. Training uses AdamW with learning rate $\mathcal{L}_{s}$2, weight decay $\mathcal{L}_{s}$3, batch size 8, focal loss with $\mathcal{L}_{s}$4 and $\mathcal{L}_{s}$5, gradient clipping at 1.0, and early stopping with patience 5. Inference is causal and event-rate adaptive.

The evaluation covers both point-level and window-level metrics. Point-level metrics include detection probability

$\mathcal{L}_{s}$6

false-alarm rate

$\mathcal{L}_{s}$7

and positive-class IoU

$\mathcal{L}_{s}$8

Window-level evaluation rasterizes positive events into windows and counts a ground-truth object as detected if predicted coverage exceeds a threshold:

$\mathcal{L}_{s}$9

False-alarm density is normalized by number of bins and image area.

Quantitatively, CETUS reports the best results across all key measures in Table 1. The reported values are:

Measure	Value
Window-level Pd	80.57%
Window-level Fa	0.13
Point-level Pd	91.82%
Point-level Fa	6.44
Point-level IoU	86.40%
Point-level ACC	92.29%
Parameters	0.21M

The parameter count is highlighted against several baselines named in the paper: RVT has 10.0M parameters, COSeg has 23.4M, and EV-SpSegNet has 4.0M. On latency, CETUS reports approximately

$\mathcal{L}_{i}$0

The paper describes this as an order-of-magnitude reduction in end-to-end delay relative to the best fixed-window baselines, many of which still require a fixed 50 ms accumulation window and have total delays in the 50–80 ms range.

6. Ablations, limitations, and research significance

The ablation studies reported in CETUS are used to isolate the contribution of the spatial encoder, temporal backbone, and scheduling-related design choices (Liang et al., 17 Sep 2025). Removing spatial KNN causes a substantial drop in detection performance: Pd falls from 91.82% to 73.47%, and IoU and false alarms also worsen. CETUS interprets this as evidence that local geometry is crucial. Replacing the spatial encoder with grid or voxel variants keeps parameters similar but drastically increases latency, with voxel encoding reaching approximately 21.73 ms total. Sensitivity tests identify $\mathcal{L}_{i}$1 as a good balance; $\mathcal{L}_{i}$2 and $\mathcal{L}_{i}$3 slightly worsen performance or latency. Together, these results support the paper’s claim that local causal neighborhoods provide a favorable trade-off between geometric fidelity and computational cost.

The paper also makes a narrower but important point about what does and does not solve low-latency event perception. A common misconception is that direct pointwise processing is sufficient once fixed windows are removed. CETUS argues instead that pointwise approaches often become too computationally expensive because they must model many events individually. Conversely, another misconception is that fixed-window pipelines can be made adequate simply by shortening the window; CETUS reports that performance collapses below 20 ms. The proposed architecture is therefore defined by a joint design: window-free representation, lightweight local spatial aggregation, linear-time temporal modeling, and adaptive scheduling.

The practical scope stated in the paper centers on UAV target detection, robotics, and surveillance. Its main assumptions are that event streams can be treated causally, that event rate is a meaningful signal for adaptive scheduling, and that there is a reasonably stable mapping between step size and inference cost that can be estimated online with a simple affine model. The paper also states a limitation: evaluation is focused on EV-UAV and on a specific detection/segmentation setting, so broader validation on other event tasks and hardware deployments would be needed to establish generality. Another caveat is that the controller introduces additional scheduling logic, though CETUS describes it as lightweight compared with dense frame-based or voxel-based processing.

Within the terminology of CETUS, Variable-Rate Spatial Event Mamba is significant because it is causal, stream-native, rate-aware, and latency-balanced. Its spatial encoder captures fine event geometry without dense intermediate representations, its Mamba backbone supplies scalable temporal modeling with linear complexity, and its PID-based scheduler dynamically adjusts processing speed to incoming event rate. In CETUS, these elements collectively define an event-camera model that attempts to preserve temporal fidelity while keeping end-to-end delay in the few-millisecond regime.