{"id":"5d75375b-5383-4abb-85c5-de81898cba1f","arxiv_id":"2608.12239","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A Hessian-aware mixed-precision post-training quantization framework for learned image compression reports 4.85x weight compression with BD-rate losses around 0.59 to 1.79 percent on standard test sets.","lead":"Learned image compression models are powerful but expensive to run and can fail when encoding and decoding happen on different hardware. This paper proposes a four-step recipe that assigns different numerical precisions to different parts of the network, cutting model size roughly fivefold while keeping compression quality nearly unchanged.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract's 'consistently outperforms ... across multiple datasets' is contradicted by Table I: on Minnen2018, HAMP-LIC (w=6.6, a=32) has worse BD-rate loss than FMPQ on both Kodak and Tecnick, at a higher compression ratio, leaving the comparison confounded by unequal model-size budgets.","rationale":"The reader's weakest_assumption (monotone contiguous partitions in Eq. 7) is a legitimate concern about optimality, but it is a heuristic issue: even if a non-monotone allocation existed, the reported 4.85x/0.59% results could still be valid as achieved numbers. The contradiction in Table I is more direct: it bears on the exact wording of the central claim. The paper's own table shows that on Minnen2018 the proposed method has higher BD-rate loss than FMPQ on both Kodak (1.23% vs 1.20%) and Tecnick (3.75% vs 2.64%) while compressing weights more (4.85x vs 3.97x). Since the two runs are at different model sizes, the comparison is confounded and the word 'consistently' is unsupported. I also considered the reader's zero-error/0.59% configuration issue and the monotone-partition assumption; both are worth mentioning, but the Minnen/FMPQ table row is the most load-bearing because it is an internal contradiction with the Abstract's strongest claim. My recommended verdict remains conditional: the method may be sound, but the abstract and comparison protocol need revision before acceptance.","tokens_in":14220,"tokens_out":12366,"duration_ms":110851,"concrete_test":"Run HAMP-LIC on Minnen2018 with the model-size budget set to FMPQ's compression ratio (e.g., choose epsilon so the average weight bit-width matches FMPQ's reported ~8 bits, not 6.6) and compare BD-rate on Kodak and Tecnick; if HAMP-LIC still does not beat FMPQ at matched budget, the 'consistently outperforms' claim is unsupported. Alternatively, compute a Pareto frontier of BD-rate loss vs compression ratio for both methods over epsilon in {0.5, 0.65, 0.75, 0.85, 1.0} and check whether HAMP-LIC dominates FMPQ.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"In Table I, the mixed-precision baseline FMPQ on Minnen2018 achieves 1.20% BD-rate loss on Kodak and 2.64% on Tecnick at 3.97x weight compression. The proposed HAMP-LIC (w=6.6, a=32) achieves 1.23% and 3.75% at 4.85x. Thus on this model HAMP-LIC is worse on both datasets, not better, despite having a more aggressive compression ratio; Section IV-B2 itself only claims it 'remains competitive' on Minnen2018. Because the two methods are compared at different average bit-widths (FMPQ ~8 bits, HAMP-LIC 6.6 bits), the headline 'consistently outperforms existing fixed- and mixed-precision PTQ methods across multiple datasets' is not established by the paper's own results. To support it, HAMP-LIC would need to dominate FMPQ on a BD-rate-vs-compression-ratio Pareto frontier, or at least at a matched model-size budget. This is load-bearing because it directly concerns the central empirical claim, not a peripheral detail.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14472,"tokens_out":10032,"duration_ms":82776,"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":[{"comment":"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.","section":"IV-B2, Table I"},{"comment":"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.","section":"III-D, Eq. (7)"},{"comment":"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.","section":"III-D"},{"comment":"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.","section":"IV-A2, Table I"}],"minor_comments":[{"comment":"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.","section":"IV-C4"},{"comment":"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).","section":"III-C, Eq. (4)"},{"comment":"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.","section":"III-D"},{"comment":"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.","section":"Table II"},{"comment":"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.","section":"Fig. 2"},{"comment":"The caption of Fig. 1 contains stray symbols ('⋯Step1: acquire sensitivity list') that appear to be a rendering artifact; please check the final version.","section":"Fig. 1"}],"recommendation":"major_revision","confidential_remarks":"The abstract overstates the empirical claims relative to Table I; this is likely to trigger immediate rejection if not revised. I would also encourage the editor to request code release or at least detailed per-image results, since the margins over FMPQ are small. The relationship to the authors' DCC 2026 paper (MPP-LIC) should be clarified: Fig. 2 shows 'MPP-LIC' curves yet the method here is named HAMP-LIC."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe thing to know about this paper is that the abstract and the data disagree. The abstract says HAMP-LIC 'consistently outperforms' all fixed- and mixed-precision PTQ methods across datasets. But in the paper's own Table I, on Minnen2018, HAMP-LIC (w=6.6, a=32) loses to FMPQ on both Kodak (1.23% vs 1.20% BD-rate) and Tecnick (3.75% vs 2.64%), while being more aggressive (4.85x vs 3.97x compression). The paper's own text wisely says it 'remains competitive' there. So the headline claim is not established; the comparison is also confounded by unequal model-size budgets. That is a real overclaim, not a quibble.\n\nWhat is genuinely new: the integration of Hessian-trace block sensitivity with a rate-distortion task weight and a constrained allocation via monotone contiguous partitions. This combination is not in HAWQ, BRECQ, RDO-PTQ, FMPQ, or the author's own MPP-LIC. The four-stage pipeline is coherent, and the ablation comparing Hessian to Fisher as the sensitivity metric and the bit-allocation optimizer to a simple threshold baseline do provide some evidence for the design choices. On Cheng2020 the reported number is strong: 0.59% BD-rate loss on Kodak at 4.85x compression. The cross-platform zero-error result for the fully quantized (a=8) config, if reproducible, is a useful practical property for edge deployment.\n\nSoft spots, in order of importance. First, the overclaim mentioned above; it should be fixed by either clipping the abstract or adding a Pareto-frontier comparison at matched size budgets. Second, no code or data is released, and all numbers are single-run, so there is no variance to speak of; the calibration set is only 12 images, so overfitting to it is unquantified. Third, the monotone-partition assumption in Eq. (7) is a heuristic that reduces the search to 1326 candidates; there is no validation against a full search or a lower bound. The ablation against a threshold baseline is some support, but it does not establish that the constrained optimum lies in that reduced space. Minor: the BOPS section calls the method 'FMPQ' when it means HAMP-LIC.\n\nWho should read it: anyone doing PTQ for learned codecs, especially for deployment on heterogeneous hardware. It deserves a serious referee, but the referee should push for code, variance estimates, and a fair comparison at matched model sizes.\n\nMy recommendation: send it to review, but expect revision.","headline":"Abstract overclaims 'consistently outperforms' against the paper's own Table I; underneath that, a coherent and potentially useful PTQ framework for LIC.","tokens_in":15018,"tokens_out":4727,"would_cite":false,"duration_ms":35809,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["learned image compression","post-training quantization","mixed-precision quantization","Hessian trace","rate-distortion optimization","sensitivity analysis","model compression","integer-only inference"],"falsifier":"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.","tokens_in":13998,"feed_emoji":"🖼️","tokens_out":10304,"duration_ms":84314,"temperature":0.7,"pith_summary":"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.","feed_headline":"5x smaller learned image codecs, ~0.6% quality loss","feed_subtitle":"Per-layer bit allocation keeps compression quality while killing cross-platform decode failures.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"establishes that LIC models are numerically sensitive across platforms and motivates cross-platform-consistent quantization","marker":"[1]"},{"why":"shows integer-only LIC networks give deterministic, hardware-friendly inference, the property HAMP-LIC aims to preserve","marker":"[2]"},{"why":"first applies post-training quantization to pretrained LIC networks and supplies a baseline that HAMP-LIC extends","marker":"[4]"},{"why":"provides the rate-distortion-aware block-wise reconstruction baseline (RDO-PTQ) that HAMP-LIC compares against and refines","marker":"[5]"},{"why":"defines the existing mixed-precision PTQ baseline (FMPQ) whose 8-bit average limit HAMP-LIC pushes past","marker":"[6]"},{"why":"contributes the Hessian-trace sensitivity metric that underpins the bit-allocation score","marker":"[7]"},{"why":"supplies the adaptive rounding procedure used in block-wise refinement","marker":"[13]"},{"why":"contributes block-wise reconstruction, the template for the final de-quantization-error step","marker":"[14]"},{"why":"defines the Minnen2018 hyperprior backbone used as one test model","marker":"[24]"},{"why":"defines the Cheng2020 backbone, the test model with the headline 0.59% BD-rate result","marker":"[25]"}],"fun_headline_variants":["HAMP-LIC: 4.85x smaller codecs, 0.59% quality loss","Hessian-aware PTQ shrinks LIC models 4.85x, near-zero loss","Mixed-precision PTQ cuts LIC size 4.85x, no cross-platform errors","HAMP-LIC: 4.85x compression, 0.59% BD-rate hit, zero decode errors","Hessian-guided bits: 4.85x smaller LIC, ~0.6% loss"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["HAMP-LIC: 4.85x smaller codecs, 0.59% quality loss","Hessian-aware PTQ shrinks LIC models 4.85x, near-zero loss","Mixed-precision PTQ cuts LIC size 4.85x, no cross-platform errors","HAMP-LIC: 4.85x compression, 0.59% BD-rate hit, zero decode errors","Hessian-guided bits: 4.85x smaller LIC, ~0.6% loss"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001168,"raw_usage":{"total_tokens":4846,"prompt_tokens":971,"completion_tokens":3875,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":587,"completion_tokens_details":{"reasoning_tokens":3744}},"tokens_in":587,"tokens_out":3875,"duration_ms":24031,"temperature":1.0,"reasoning_tokens":3744,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:11:41.446819+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Joint autoregressive and hi- erarchical priors for learned image compression,","cited_arxiv_id":null,"evidence_quote":"defines the Minnen2018 hyperprior backbone used as one test model"},{"cited_title":"Learned image com- pression with discretized gaussian mixture likelihoods and attention modules,","cited_arxiv_id":null,"evidence_quote":"defines the Cheng2020 backbone, the test model with the headline 0.59% BD-rate result"},{"cited_title":"Integer networks for data compression with latent-variable models,","cited_arxiv_id":null,"evidence_quote":"shows integer-only LIC networks give deterministic, hardware-friendly inference, the property HAMP-LIC aims to preserve"},{"cited_title":"Rate-distortion optimized post-training quantization for learned image compression,","cited_arxiv_id":null,"evidence_quote":"provides the rate-distortion-aware block-wise reconstruction baseline (RDO-PTQ) that HAMP-LIC compares against and refines"},{"cited_title":"Flexible mixed precision quantization for learned image compression,","cited_arxiv_id":null,"evidence_quote":"defines the existing mixed-precision PTQ baseline (FMPQ) whose 8-bit average limit HAMP-LIC pushes past"},{"cited_title":"HAWQ: hessian aware quantization of neural networks with mixed-precision,","cited_arxiv_id":null,"evidence_quote":"contributes the Hessian-trace sensitivity metric that underpins the bit-allocation score"},{"cited_title":"Up or down? adaptive rounding for post-training quantization,","cited_arxiv_id":null,"evidence_quote":"supplies the adaptive rounding procedure used in block-wise refinement"},{"cited_title":"BRECQ: pushing the limit of post-training quantization by block reconstruction,","cited_arxiv_id":null,"evidence_quote":"contributes block-wise reconstruction, the template for the final de-quantization-error step"}],"review_version":1}