AxisQ: Depth-Adaptive Channel--Frequency Quantization for Camouflaged Object Detection

What it claims

AxisQ is a post-training quantization (PTQ) method for hierarchical camouflaged object detection (COD) models. It picks a different bit-allocation axis by encoder stage: per-channel bits in stages 1–2 and per-DCT-band bits in stages 3–4. At W2A2, it reports mean weighted F-measure gains over the best competing method, averaged across four benchmarks, of 6.6% on CFRN and 21.5% on CamoFormer-P. The paper is under review for ICLR 2027 and was posted to arXiv on 27 October 2026. Code is at https://github.com/chi558/AxisQ.

How it works

Weights use a fixed precision. Each activation layer is split into units (channels or frequency bands), and each unit gets a bit tier. The constraint is that the layer's average equals the target budget exactly. The stage split is fixed before calibration. Where both branches apply, frequency allocation wins.

flowchart TD
  A[Layer activation] --> S{Encoder stage}
  S -->|Stages 1-2| C[Empirical-Fisher channel cost]
  S -->|Stages 3-4| F[Block-DCT band cost: SSE + COD-GGN]
  C --> W[Reverse water filling + exact budget fix]
  F --> L[Lagrangian per-band choice + exact budget fix]
  W --> R[Frozen bits, blockwise reconstruction]
  L --> R
  R --> H[Optional boundary-aware Hessian weights]

Channel branch. The cost is a per-channel empirical-Fisher distortion. It uses the supervised BCE gradient times the quantization error, summed within a channel and then squared. It needs only first derivatives and 64 ground-truth masks. Initial bits are set as the budget plus γ times the channel's log-sensitivity relative to the layer mean. These are rounded to the allowed tiers and then adjusted greedily until the layer average hits the budget exactly.

Frequency branch. Deep activations are split into local blocks, and each block gets an orthonormal 2-D DCT. Coefficients at the same within-block position form a band that shares one bit width. Bands can receive zero bits. The cost blends two normalized terms, weighted by β:

• a per-band reconstruction SSE, minimized over candidate clipping ranges;
• a task term, COD-GGN.

COD-GGN weights the output by foreground/background balance, multi-scale boundary variation and prediction uncertainty, all taken from the full-precision teacher. It maps that weighting back to the layer with one Rademacher-probe vector–Jacobian product per layer and calibration batch. Setting β=0 gives a reconstruction-only allocator.

Reconstruction. Blockwise reconstruction reuses the LS-ViT Hessian objective, AdaRound and QDrop. Matched baselines share this same pipeline. The optional boundary-aware extension reweights the gradient and error statistics by local variation in the teacher probability map. The task costs are discarded after calibration. The authors state this adds no COD-specific computation at inference.

Evidence

• Baselines: BRECQ, AdaRound+QDrop, FIMA-Q and APHQ-ViT.
• Single-benchmark figure: on CAMO at W2A2, relative weighted F-measure gains are 12.7% for CFRN and 33.3% for CamoFormer-P.
• Qualitative examples: Figure 1 shows four selected NC4K images at W2A2. AxisQ's IoU is 0.903–0.935. The best competing method scores 0.470–0.842 on the same images.
• Motivating analysis: this uses a single selected image. In stage S2, 17 DCT bands hold 80% of sensitivity, against 2 bands in S4. Excess concentration peaks at 10.6 pp across channels in S2 and 50.5 pp across frequency bands in S4.

Limits

The fetched text stops partway through the method section. No results tables, ablations, benchmark list beyond CAMO and NC4K, runtime figures or licence are visible.

• Thin motivation: the depth-dependent axis choice rests on one illustrative image in Figure 2.
• Ignored interactions: the channel cost ignores cross-channel interactions.
• Labels required: calibration needs paired ground-truth masks.
• Fixed stage split: the stage-to-domain mapping is fixed by hand per architecture.
• Auxiliary component: the boundary-aware Hessian is evaluated separately from the core allocation.
• Model coverage: results are shown only for CFRN and CamoFormer-P.