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REVIEW 4 major objections 6 minor 31 references

HAMP-LIC: Hessian-Aware Mixed-Precision Post-Training Quantization for Learned Image Compression

T0 review · 4 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A Hessian-aware mixed-precision post-training quantization converts pretrained learned image compression models into roughly 4.85x smaller integer models with under 1% rate-distortion loss and zero cross-platform decode errors.

desk verdict Abstract overclaims 'consistently outperforms' against the paper's own Table I; underneath that, a coherent and potentially useful PTQ framework for LIC. read the letter →

arxiv 2608.12239 v1 pith:YMPHRRUQ submitted 2026-08-12 cs.CV cs.AIcs.MM

Yuefeng Zhang This is my paper · ORCID
classification cs.CVcs.AIcs.MM
keywords learnedimagecompressionpost-trainingquantizationmixed-precisionHessiantracerate-distortionoptimizationsensitivityanalysismodelinteger-onlyinference
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

Learned image compression models are accurate but heavy, and their full-precision arithmetic behaves differently on CPU and GPU, causing decode failures. HAMP-LIC claims that a pretrained model can be converted to a mixed-precision integer model, roughly five times smaller in weight memory, with almost no loss in compression quality. It does so by measuring how sensitive each block is to quantization, combining the curvature of the loss (Hessian trace) with the actual rate–distortion loss when that block is quantized, and then allocating more bits to sensitive blocks and fewer to the rest under a size budget. The allocation is found by a search whose space collapses from about $10^{23}$ to roughly 1,300 candidates, after which small per-block refinements clean up residual error. If the claims hold, on-device deployment becomes practical and encoders and decoders become numerically deterministic across hardware.

What carries the argument

The load-bearing object is the task-aware block sensitivity $\Omega_l(b_l) = \operatorname{Tr}(H_l) \cdot |L_{qp}(b_l)-L_{int8}|/|L_{int8}|$, where $\operatorname{Tr}(H_l)$ is the Hessian trace of the rate–distortion loss with respect to block $l$'s weights (estimated by randomized Hessian-vector products) and the ratio measures the task-loss degradation of quantizing that block alone to $b_l$ bits relative to an 8-bit reference. This score feeds a constrained integer optimization: minimize $\sum_l \Omega_l(b_l)$ subject to the average bit-width budget $\frac{1}{8L}\sum_l b_l \le \epsilon$. The search over the sensitivity-sorted block list is restricted to monotone contiguous partitions, which cuts the space from $k^L$ to $\sum_j \binom{k}{j}\binom{L-1}{j-1}$ (1326 candidates for $L=50$, $k=3$). A final block-wise reconstruction step optimizes quantization scales and adaptive rounding variables against a combined task and quantization loss.

What would settle it

Run HAMP-LIC on a small model with, say, $L=10$ quantizable blocks and candidate bit widths $\{2,4,8\}$, then exhaustively evaluate all $3^{10}=59049$ assignments under the same budget; if any non-monotone assignment achieves lower total sensitivity or better BD-rate than the monotone-contiguous one, the core search restriction is lossy. A second check: vary the 12-image calibration set (e.g., different content) and observe whether the claimed 0.59% BD-rate loss and the zero-error cross-platform result persist.

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Extended reading notes

Core claim

The central claim is that a four-stage post-training pipeline can compress a pretrained learned image compression network by up to 4.85x (weights from 32-bit float to an average of 6.6 bits) while losing at most 0.59% BD-rate on Kodak for the Cheng2020 model, and can do so without retraining on a small 12-image calibration set. The same framework reduces cross-platform encoding–decoding failures from nearly total (24 out of 24 Kodak images for the full-precision model) to zero by producing integer-only arithmetic. Uniform fixed-precision quantization and existing mixed-precision methods for LIC are reported to lose more quality at the same compression (for example, the strongest baseline shows 0.89% BD-rate on Kodak at a 3.99x ratio), so the paper concludes that sensitivity-guided assignment is the correct route to low-bit deployment.

Load-bearing premise

The search for the best bit assignment only considers patterns where every more-sensitive block receives at least as many bits as every less-sensitive block, arranged in contiguous groups; the paper does not test whether a non-monotone assignment could be better.

Editorial extensions

If this is right

  • Pretrained LIC models can be shrunk to about a fifth of their weight memory without retraining, opening the door to on-device image compression at near full-precision quality.
  • Integer-only inference removes the CPU/GPU arithmetic discrepancies that make full-precision LIC models fail to decode, so mixed-platform encoding and decoding become reliable.
  • Bit-operations drop by roughly 94% versus FP32 and 5–9% versus uniform 8-bit weights, because hyperprior path layers are assigned 4 bits while the main path keeps 6–8 bits.
  • The method is demonstrated on two hyperprior-based backbones (Minnen2018 and Cheng2020) across several benchmark datasets, showing consistent gains over fixed- and mixed-precision baselines.

Reading between the lines

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

  • If the monotone-contiguous partition assumption holds, the same Pareto-frontier search reduces exponential bit-allocation to polynomial for any block-structured network, not just learned image codecs; that is a testable transfer to other tasks.
  • The sensitivity list is built by quantizing each block in isolation, so it ignores interactions among blocks; Step 4's sequential reconstruction compensates only partially, and a joint sensitivity estimator might find allocations the current search cannot.
  • The zero cross-platform error result should be read as applying to the fully integer configuration (weights 6.6-bit, activations 8-bit); with floating-point activations, non-determinism could resurface, so deployment should scope the claim accordingly.
  • Because calibration uses only 12 images from one dataset, the reported BD-rate figures may depend on calibration-content similarity; testing with a broader or content-matched calibration set would gauge that sensitivity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper proposes HAMP-LIC, a four-stage post-training quantization framework for learned image compression. Stage 1 computes per-block Hessian-trace sensitivity using Hutchinson's method; Stage 2 combines this with the relative rate-distortion loss degradation of quantizing each block to form a task-aware sensitivity; Stage 3 allocates bit-widths from {2,4,8} under an average-bit-width budget by enumerating monotone contiguous partitions of the sensitivity-sorted block list; Stage 4 performs block-wise scale and rounding optimization. The method is evaluated on Minnen2018 and Cheng2020 using the Kodak, Tecnick, and CLIC datasets, reporting up to 4.85x weight compression with 0.59% BD-rate loss on Cheng2020 (Kodak) and zero decoding errors in cross-platform CPU/GPU experiments.

Significance. If the reported results are reliable, HAMP-LIC would be a practical contribution: it offers a sensitivity-based allocation with a tractable search, and it addresses the real problem of numerical mismatch across hardware platforms. The paper includes a clear algorithm, an ablation of the sensitivity metric (Hessian vs Fisher), a bit-allocation comparison, and a BOPS analysis. However, the empirical support is weakened by single-run results without variance, the lack of code/data, the unvalidated monotone-contiguous search assumption, and the mismatch between the abstract's 'consistently outperforms' claim and Table I on Minnen2018. The cross-platform robustness result is interesting but only demonstrated for Cheng2020.

major comments (4)
  1. [IV-B2, Table I] Table I shows that on Minnen2018, HAMP-LIC (w=6.6, a=32) has BD-rate loss of 1.23% on Kodak and 3.75% on Tecnick, whereas FMPQ achieves 1.20% and 2.64% at 3.97x weight compression; the abstract's claim that HAMP-LIC 'consistently outperforms existing fixed- and mixed-precision PTQ methods across multiple datasets' is therefore not established by the paper's own results. Because the two methods are compared at different average bit-widths, a matched-size comparison or a BD-rate-vs-compression-ratio Pareto plot is needed to support the claimed dominance.
  2. [III-D, Eq. (7)] The reduction to 1326 candidates rests on the assumption that the optimal allocation lies among monotone contiguous partitions of the sensitivity-sorted block list. This assumption is unvalidated and load-bearing, since Step 3 determines every downstream result. Please compare against exhaustive search on a smaller network (e.g., L=10) or provide a bound on the suboptimality introduced by the monotone-contiguous restriction.
  3. [III-D] The text states that only the j=3 terms of Eq. (7) are enumerated, despite the reduced space containing 3 + 147 + 1176 = 1326 candidates covering j=1,2,3. Allocations with one or two distinct bit-widths (e.g., 8-bit and 4-bit blocks with an average of 6.6 bits) are feasible under the budget and could be optimal, so the search is incomplete as described. The paper should either enumerate the full reduced space or justify the restriction.
  4. [IV-A2, Table I] The results are single-run and no code or data are released; the calibration set is selected randomly without a reported seed, and the Hessian-trace estimation uses randomized Hutchinson probes. Without variance estimates or repeated trials, it is impossible to judge whether the reported margins (e.g., 0.59% vs 0.89% BD-rate loss for Cheng2020) are significant. Report error bars over at least three calibration-set draws or release the code to allow reproduction.
minor comments (6)
  1. [IV-C4] The text in Section IV-C4 refers to 'our FMPQ method' in the first sentence; this appears to be a typo for HAMP-LIC and should be corrected.
  2. [III-C, Eq. (4)] The symbol L is used both for the number of quantizable blocks and for the loss function in Eq. (3), which is confusing; please use separate notation (e.g., N_blocks).
  3. [III-D] The notation |B| is used for both the cardinality of the bit-width set and the size of the search space; clarify by using e.g., N_alloc for the latter.
  4. [Table II] Table II states 'Proposed HAMP-LIC' without specifying the weight/activation configuration; from Section IV-B2 this is presumably (w=6.6, a=8), and the caption should state this explicitly.
  5. [Fig. 2] The curves in Fig. 2 for 'Cheng2020 (MPP-LIC)' and 'Minnen2018 (MPP-LIC)' appear to be from the previous DCC paper, while the new method is called HAMP-LIC; the legend should be updated to reflect the proposed method's name.
  6. [Fig. 1] The caption of Fig. 1 contains stray symbols ('⋯Step1: acquire sensitivity list') that appear to be a rendering artifact; please check the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the method is a calibration-set model-selection pipeline evaluated on held-out datasets, with no prediction that reduces by construction to its inputs.

full rationale

HAMP-LIC's derivation chain is self-contained. Step 2 builds task-aware sensitivities from Hessian traces and R-D losses measured on a 12-image calibration set, Step 3 solves a constrained integer allocation over those calibration-defined sensitivities, and Step 4 refines scales and rounding on the same calibration set. The reported BD-rate numbers are measured on held-out Kodak, Tecnick, and CLIC sets, so the headline compression-quality result is not constructed from the evaluation data. The appearance of the R-D loss both inside the sensitivity objective and as the final evaluation metric is standard model selection rather than circularity: no parameter is fitted to the test data, and no claimed result is algebraically identical to an input by construction (no Eq. X reduces to Eq. Y). The self-citation to the authors' DCC paper (MPP-LIC [8]) is a provenance statement and is not load-bearing; the method is fully described and evaluated in the present paper. The monotone-partition restriction in Eq. (7) and the Table I comparison against FMPQ on Minnen2018 are correctness/robustness concerns, not circularity, because they concern whether the solution is globally optimal and whether the headline claim is fully supported, not whether the output is equivalent to the input.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central results depend on several hand-set hyperparameters and heuristic assumptions. The framework restates standard PTQ machinery; the ledger records the choices and assumptions that are not derived from first principles.

free parameters (4)
  • epsilon size budget = 0.75 (with 10% tolerance, effective average bit-width 6.6)
    Sets the allowed average bit-width in Eq. (6); the 4.85x compression ratio follows from the 6.6-bit average.
  • lambda_t task/reconstruction balance = 1.0
    Balancing hyperparameter in Eq. (11) between task loss and block-wise quantization loss; set without sensitivity study.
  • bit-width candidate set B = {2, 4, 8}
    Restricts allowed precisions and fixes k=3 in the search-space formula of Eq. (7).
  • calibration set size = 12 images from CLIC
    All sensitivity estimates and bit allocations depend on this small calibration set; transfer to Kodak, Tecnick, and CLIC test sets is assumed.
assumptions (5)
  • domain assumption The optimal bit allocation lies among monotone non-increasing bit-widths over the sensitivity ranking.
    Eq. (7) reduces the search to contiguous monotone partitions; the paper gives no proof that the constrained optimum belongs to this subset.
  • domain assumption Summing per-block task-aware sensitivities is an adequate proxy for total R-D loss under simultaneous multi-block quantization.
    Eq. (6) minimizes sum of Omega_l; interactions between simultaneously quantized blocks are ignored in the objective.
  • domain assumption A 12-image calibration set from CLIC is representative of Kodak, Tecnick, and CLIC test distributions.
    Hessian traces, loss degradation terms, and block-wise reconstruction are all optimized on this small set in Section IV-A2.
  • domain assumption Integer quantization eliminates cross-platform encoding-decoding mismatches caused by floating-point non-determinism.
    Table II shows zero errors only for CPU vs GPU and for the fully quantized a=8 configuration; other platforms and the a=32 configuration are not tested.
  • standard math Hutchinson's method gives a sufficiently accurate estimate of the Hessian trace.
    Standard randomized probing from [23]; the paper uses 5 Rademacher vectors per block without error analysis.

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Cite this review

Pith. "Pith review of HAMP-LIC: Hessian-Aware Mixed-Precision Post-Training Quantization for Learned Image Compression." pith.science (2026). https://pith.science/paper/YMPHRRUQ

@misc{pith2026260812239,
  author       = {Pith},
  title        = {Pith review of: HAMP-LIC: Hessian-Aware Mixed-Precision Post-Training Quantization for Learned Image Compression},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YMPHRRUQ}},
  note         = {Machine review of arXiv:2608.12239}
}
read the original abstract

Use this plain-text version for the arXiv abstract field: Learned image compression (LIC) models achieve strong rate-distortion performance but are hindered by high computational complexity and encoding-decoding mismatches across heterogeneous hardware platforms. Uniform fixed-precision quantization alleviates these issues but suffers severe quality degradation at low bit widths because it ignores differences in the quantization sensitivities of individual layers. To enable efficient and accurate low-bit deployment of pretrained LIC models, we propose HAMP-LIC, a Hessian-aware mixed-precision post-training quantization (PTQ) framework with a four-stage optimization strategy. First, block-wise sensitivity is estimated from the Hessian trace to capture second-order importance. Second, a task-aware refinement module adjusts these sensitivities by jointly considering quantization distortion and rate-distortion performance. Third, guided by the refined sensitivity profile, bit widths are allocated under a global model-size constraint to balance efficiency and reconstruction quality. Finally, block-wise reconstruction using a small calibration set further suppresses quantization error. Experiments on representative LIC models, including Minnen2018 and Cheng2020, demonstrate that HAMP-LIC achieves up to 4.85x model compression with as little as 0.59% BD-rate loss. It consistently outperforms existing fixed- and mixed-precision PTQ methods across multiple datasets while completely eliminating cross-platform encoding-decoding errors.

Figures

Figures reproduced from arXiv: 2608.12239 by the authors.

Figure 1
Figure 1. The overview of the proposed quantization framework HAMP-LIC [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Compression performance evaluation on the Kodak dataset (left) and the CLIC dataset (right). Traditional codecs and unquantized LIC models are [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Visual comparison of the proposed HAMP-LIC method across different quality levels (Q6 to Q3) on CLIC, Kodak, and Tecnick datasets. PSNR (dB), [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Comparison of Hessian trace with Fisher matrix as the sensitivity [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Comparison of rate distortion performance between the proposed method ( [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Bit-width distribution across the Cheng2020 model layers for four different quality levels. TABLE III BOPS COMPARISON ACROSS QUALITY LEVELS (INPUT RESOLUTION 512 × 768, b a = 8). Quality λ MACs (G) BOPS-Mixed (G) BOPS-FP32 (G) vs. W8A8 Q3 0.0067 34.3 2007.5 35138.5 ↓8.…

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