{"id":"a12cd406-271f-4618-b4cb-3c6992f52912","arxiv_id":"2502.01199","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Double Rounding derives lower-bit neural network weights from a stored 8-bit integer model, achieving accuracy comparable to state-of-the-art multi-precision quantization on ImageNet.","lead":"The paper introduces a quantization method that stores a model once at 8-bit integer precision and switches it to 4, 6, or 2-bit at runtime by applying a second rounding step. This could reduce storage and training time for deploying AI models on devices with different computational limits.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (6) as written yields negative learning rates for every precision, so the described ALRS cannot be the update that produced the reported results.","rationale":"The reader's weakest_assumption (one shared power-of-two scale is near-optimal for all lower precisions) is a real limitation, and the paper's own MobileNetV2 2-bit numbers (50.43 vs 71.14 FP) show the 'nearly lossless' wording is too strong. But that is a risk about how well the method generalizes, not an internal contradiction: the experiments could still support the claim for the settings where it is tested. Eq. (6) is different in kind. As printed, it produces a negative learning rate for every precision because λ=5e−4 is smaller than the [0, 1] correction term. This is not a matter of tuning; the stated algorithm cannot be what generated the figures and tables. Since ALRS is one of the paper's two central contributions and is credited for the 2-bit gains in Table 6, the multi-precision results are unreproducible from the text. I still would not move the verdict to REJECT because the authors release code and the ALRS mechanism may simply be mis-transcribed; a corrected formula and a completed gradient derivation would resolve the issue. That is exactly the CONDITIONAL stance the reader took. I therefore leave the verdict unchanged. Agreement is partial: the reader flagged Eq. (6) in their rationale, but their stated weakest assumption is the scale-sharing question, which is not the concern I consider most load-bearing.","tokens_in":26488,"tokens_out":6578,"duration_ms":67975,"concrete_test":"Download the released code at github.com/haiduo/Double-Rounding, run the ResNet18 ImageNet multi-precision configuration with the stated hyperparameters (λ=5e−4, Adam, batch size 256), and insert a print of λ_b inside the ALRS update at the first training batch. If any λ_b is negative, Eq. (6) is not the implemented rule; compare the code's actual formula to Eq. (6). Additionally, hand-differentiate ∂cW_l/∂s_h through Eq. (2) using STE and check whether it matches any code path in the repository; if the code uses a different ALRS formula or a different low-bit scale gradient, the paper must be revised before it can be evaluated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The single most load-bearing problem is the ALRS update rule, Eq. (6). With L layers, the term (1/L) Σ_i min(max_abs(clip_grad(∇s_i^b, 1.0)), 1.0) is a number in [0, 1] by construction, since max_abs(·) of a clipped gradient is at most 1 and the inner min also caps at 1. Eq. (6) then computes η_b · (λ − [0, 1]). The paper's Section 4.1 sets the initial Adam learning rate to λ = 5e−4. Hence λ_b is negative for every precision and every iteration; scaling by η_b (1, 0.1, 0.01 for 8/6/4-bit) does not change the sign. A negative learning rate applied to quantization scales would systematically move scales in the direction opposite to the gradient, which cannot produce the convergence shown in Fig. 3(d) or the accuracies in Tables 1–2. Algorithm A.2 in the appendix calls this formula, so the method is internally inconsistent as written. The appendix's gradient equations (13)–(14) are also only the standard LSQ single-step gradient; they do not differentiate through the second rounding in Eq. (2), so the exact training objective for low-bit paths remains unspecified. Together these make the central multi-precision claim non-reproducible from the text alone.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a one-shot multi-precision and mixed-precision quantization framework. It introduces Double Rounding, which quantizes weights by first rounding to a high bit-width and then rounding again to lower bit-widths through a power-of-two scale relation, allowing a single stored integer-weight model to be switched among precisions at inference. It also proposes Adaptive Learning Rate Scaling (ALRS) to stabilize joint training across precisions, and a Hessian-Aware Stochastic Bit-switching (HASB) strategy for mixed-precision SuperNets, with an ILP-based search that avoids retraining. Experiments cover ImageNet-1K classification on ResNet and MobileNetV2, COCO detection/segmentation, and TinyLlama language-model tasks. The central claims are that Double Rounding gives nearly lossless bit-switching while storing only the highest integer precision, and that ALRS and HASB improve over prior one-shot multi-precision and mixed-precision methods.","tokens_in":26860,"tokens_out":5428,"duration_ms":58468,"significance":"If the results hold, the storage-saving property (8-bit instead of FP32 storage with runtime bit-switching) and the low-cost mixed-precision search would be practically useful contributions. The paper includes several strengths: results over multiple architectures and tasks, an ablation showing ALRS helps even when applied to prior methods (Table 7), a Pareto-frontier analysis of HASB, and a public code release. However, the significance is currently limited by a load-bearing technical inconsistency in the ALRS update rule and by the fact that the paper's own low-bit accuracy numbers do not support the 'nearly lossless' phrasing. These issues need to be resolved before the contribution can be evaluated on its merits.","major_comments":[{"comment":"The ALRS learning-rate formula as written is not a valid update rule. With the training setup's initial Adam learning rate lambda = 5e-4 (Section 4.1), and with the averaged term (1/L) sum_i min(max_abs(clip_grad(nabla s_i^b, 1.0)), 1.0) lying in [0,1] by construction, Eq. (6) gives lambda_b = eta_b (lambda - [0,1]) < 0 for every precision and every iteration. A negative learning rate applied to the scale optimizer would move the quantization scales in the direction opposite to the gradient, which cannot produce the convergence shown in Figure 3(d) or the accuracies in Tables 1-2. Since Algorithm A.2 explicitly calls this formula, the method as described is internally inconsistent and non-reproducible. The authors need to correct the formula, e.g., by making the gradient statistic a multiplier or a relative adjustment of lambda, and state precisely what clip_grad(., 1.0) means (e.g., clip_grad_value_ versus clip_grad_norm_).","section":"Section 3.2, Eq. (6) and Algorithm A.2"},{"comment":"The headline claim 'nearly lossless bit-switching' is contradicted by the paper's own results. In Table 1, the {8,6,4,2}-bit MobileNetV2 model loses 20.71 points at w2a2 without KD (50.43 vs. 71.14 FP) and 18.08 points with KD (53.06 vs. 71.14 FP); ResNet18 loses about 3.4 points at w2a2 (66.35/66.84 vs. 69.76 FP), and ResNet50 loses about 3.8 points at w2a2 (72.31/73.78 vs. 76.13 FP). These are substantial accuracy drops, especially for the compact model. The term 'nearly lossless' should either be replaced by a more precise claim (e.g., 'improved accuracy compared to prior multi-precision methods at the same storage budget') or be supported by an explicit accuracy-loss tolerance that these numbers satisfy.","section":"Section 3.1 and Abstract"},{"comment":"The gradient derivation does not cover the Double Rounding path. Equations (13)-(14) are the standard LSQ single-rounding gradients for the dequantized value (fW - z)*s or (round((Y - zh)/sh)*sh + zh); they do not differentiate through the second rounding in Eq. (2), i.e., through fW_l = clip(round(fW_h / 2^Delta), ...) and its dequantization cW_l = fW_l * sh * 2^Delta + zh in Eq. (3). The chain rule through the two rounding operations and through the factor 2^Delta is absent, so the exact training objective for the low-bit weight path is unspecified. This is load-bearing because the claimed contribution is precisely the two-step quantization; without the full gradient, the low-bit training procedure cannot be reproduced from the text.","section":"Appendix A.4, Eqs. (13)-(14)"},{"comment":"The HASB threshold sigma is introduced but never fully specified. Algorithm A.3 lists 'the threshold of bit-switching: sigma' in the Require block and then updates it as sigma = sigma * (epoch+1)/total_epochs (line 3), but the initial value of sigma is never given. If sigma starts at 0 the update keeps it at 0; if it starts at a positive value the formula is ambiguous about ordering and can push sigma above 1. Since the bit-selection behavior in Algorithm 1 is only invoked when r < sigma, the stochastic schedule is not well defined. The authors should provide the initial value and the intended schedule explicitly.","section":"Section 3.3 and Algorithm A.3"}],"minor_comments":[{"comment":"The mapping from Eq. (7) to the values stated in the text (eta_b = 1, 0.1, 0.01 for 8/6/4-bit) should be written out; currently the reader must decode the even/odd cases to verify that 8-bit uses Delta=0 (eta=1), 6-bit uses Delta=2 (eta=0.1), and 4-bit uses Delta=4 (eta=0.01).","section":"Section 3.2, Eq. (7)"},{"comment":"The MobileNetV2 rows mix two different bit-list settings ({8,6,4}-bit and {8,6,4,2}-bit) in the same block; adding a horizontal separator or a column entry spelling out the bit list for every row would make the table easier to read and would avoid the appearance that the w8a8 numbers are directly comparable.","section":"Section 4.1.1 and Table 1"},{"comment":"The notation in Eq. (2) uses the floor-symbol glyph (which is actually the rounding symbol) inconsistently with the text; it should be stated once that round(.) is used in all three equations and that fW_h is an integer tensor before the division by 2^Delta.","section":"Section 3.1, Eqs. (1)-(3)"},{"comment":"The LLM experiments in Table 5 show w4a4 and w2a2 accuracies close to chance level for TinyLlama 1.1B (e.g., 36.08/38.46 average vs. 52.99 FP); this should be acknowledged in the main text when claiming that the method 'applies to more recent and complex models', otherwise the reader may over-read the generality claim.","section":"Section 4.3"},{"comment":"The note in Algorithm 1 defines n and L only in the caption note rather than in the Require block; moving these definitions into the algorithm would improve clarity.","section":"Algorithm 1 and its note"}],"recommendation":"major_revision","confidential_remarks":"The negative-learning-rate issue in Eq. (6) is the most serious problem; it may be a typographical or sign error rather than a fundamental flaw, but as written it makes the central ALRS contribution non-reproducible. I would ask the authors to correct the formula, provide the exact update used in the released code, and reword the 'nearly lossless' claim before the paper is reconsidered. The Hessian-grad error in Appendix A.4 should also be fixed because it concerns the core Double Rounding objective."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this paper. First, Double Rounding is a concrete, sensible new mechanism: keep the highest-bit integer weights, and obtain lower-bit weights by a second rounding with a power-of-two scale relationship. That is a real difference from Bit-Mixer and AdaBits, and it lets you serve multiple precisions from one 8-bit checkpoint. Second, the ALRS update rule in Eq. (6) is, as written, algebraically wrong: with the stated lambda = 5e-4 and the average of values in [0,1], the learning rate is negative for every precision and every step. That cannot be the update that produced the convergence curves and tables. This is load-bearing, because the paper credits ALRS for the gains, especially at 2-bit.\n\nWhat the paper does well: the experiments are broad—ImageNet classification on ResNet18/50 and MobileNetV2, COCO detection/segmentation, and TinyLlama. The gains over prior multi-precision and mixed-precision methods are consistent, if modest. The appendix contains training algorithms and the source code is promised. The Hessian-aware bit-switching idea is a reasonable extension, though it is less novel than Double Rounding.\n\nThe soft spots: first and foremost, Eq. (6). If it is a typo, the authors need to state the correct formula and show that the reported results are reproducible. The appendix gradient equations (13)-(14) are the standard LSQ gradients for a single rounding; they do not differentiate through the second rounding in Eq. (2), so the training objective for low-bit paths is under-specified. Second, the headline claim of 'nearly lossless' is contradicted by the paper's own numbers: MobileNetV2 at 2-bit drops to 50.43 from 71.14, and even ResNet18 at 2-bit loses about 3.4 points. The claim should be moderated to something like 'small, consistent gaps at 4-bit and above.'\n\nThe idea is worth serious refereeing, but only after the ALRS formula is corrected and the gradient flow through the second rounding is derived or explicitly handled. As it stands, the method as described is not reproducible from the text alone. I'd send it to review, but the authors need to make those fixes before acceptance. If the code is available and reproduces the tables, that would resolve most of my concern.","headline":"Double Rounding is a genuinely new way to store one integer checkpoint for multiple precisions, but the ALRS update as written cannot be what produced the results.","tokens_in":27331,"tokens_out":2903,"would_cite":false,"duration_ms":26428,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single integer-weight model stored at the highest bit-width can switch to any lower precision at inference with nearly lossless accuracy: Double Rounding makes each lower bit a sub-representation of the stored integer.","keywords":["double rounding","adaptive bit-width switching","multi-precision quantization","mixed-precision quantization","one-shot joint training","quantization-aware training","Hessian-aware stochastic bit-switching","learned step size"],"falsifier":"Train MobileNetV2 twice under the {8,6,4,2}-bit schedule, once with the shared high-bit scale and once with an independently learned 2-bit scale, and compare 2-bit top-1 after the same epoch count; if the independent scale recovers a large share of the reported 20-point gap (50.43 vs. 71.14 full precision), then the fixed power-of-two scale, not training competition, is what caps low-bit accuracy on compact models, and the near-lossless claim fails for exactly the architectures where deployment savings matter most.","tokens_in":26177,"feed_emoji":"🔀","tokens_out":20551,"duration_ms":179030,"temperature":0.7,"pith_summary":"This paper tries to establish that a single quantized network, stored as one integer-weight model at the highest bit-width (typically 8-bit), can be switched to any lower bit-width — 6, 4, or 2 bits — at inference time with accuracy almost equal to training each precision separately, removing the need to keep a full-precision model. The load-bearing mechanism is Double Rounding: quantize to the highest bit first, then round a second time to reach the lower bit, so every low-bit weight is a sub-representation of the stored 8-bit integer and one learned scale serves all precisions. To make one-shot joint training stable, the paper adds Adaptive Learning Rate Scaling (ALRS), which rescales each precision's quantization-scale learning rate and closes most of the convergence gap between high and low precisions. For mixed precision, Hessian-Aware Stochastic Bit-switching (HASB) biases bit-width assignment by per-layer Hessian trace and lets sub-networks be extracted by Integer Linear Programming without retraining. If the claims hold, adaptive precision becomes a deployment-time choice instead of a retraining project, and the artifact that travels to the device is four to eight times smaller than today's float-storing baselines.","feed_headline":"Train once, store one 8-bit model, switch bit-width at will","feed_subtitle":"Switching down to 2 bits from one stored 8-bit model matches or beats baselines that keep a full float copy.","key_machinery":"Double Rounding (Eqs. 1–3) carries the storage claim: weights are quantized once to the highest bit-width $h$ with one learned scale $s_h$ (symmetric quantization, so the zero point is zero), and any lower bit-width $l$ is obtained by rounding the stored integer a second time, $\\tilde{W}_l = \\text{clip}(\\lfloor \\tilde{W}_h / 2^{\\Delta} \\rceil, -2^{l-1}, 2^{l-1}-1)$ with $\\Delta = h-l$, so that the low-bit integer is contained in the high-bit integer and the dequantized value is $\\hat{W}_l = \\tilde{W}_l \\cdot s_h \\cdot 2^{\\Delta}$. Because the scale relation is a power of two, the division and multiplication are hardware shifts, so switching precision costs almost nothing at runtime. Adaptive Learning Rate Scaling (ALRS, Eqs. 6–7) carries the stabilization claim: it scales the quantization-scale learning rate of each precision by a power of ten fixed by the bit gap (1 for 8-bit, 0.1 for 6-bit, 0.01 for 4-bit), countering the empirically observed order-of-magnitude divergence of low-bit scale gradients during joint training. Hessian-Aware Stochastic Bit-switching (HASB, Algorithm 1) carries the mixed-precision claim: the Hessian matrix trace of each layer sets the probability that the Roulette sampler assigns a high bit-width to that layer, and Integer Linear Programming (Algorithm 2) extracts the Pareto-optimal sub-networks without retraining.","core_discovery":"The paper's central claim, stated in Section 3.1, is that rounding twice makes bit-switching nearly lossless while letting the model be stored as the highest-bit integer weight instead of a full-precision weight. Prior methods either kept an FP32 master model with separate quantization parameters per bit-width, or replaced rounding with floor so a single integer model could be shared, accepting accuracy loss at low bits. Double Rounding instead re-rounds the stored high-bit integer $\\tilde{W}_h$ down to $\\tilde{W}_l$ with a power-of-two scale coupling $s_l = s_h \\cdot 2^{\\Delta}$, so every low-precision network is literally a sub-representation of one stored integer model; on ImageNet-1K the paper reports accuracy that matches or exceeds prior one-shot multi-precision and mixed-precision methods that store 32-bit models, while storing only 8-bit (or 4-bit) weights. The paper additionally claims to have located the reason joint multi-precision training is unstable — quantization-scale gradients differ across precisions by an order of magnitude, with 2-bit gradients largest — and shows that rescaling per-precision scale learning rates (ALRS) narrows the convergence gap. For mixed precision, it claims that Hessian-trace sensitivity, used to bias stochastic bit-width sampling, plus a direct ILP search, removes the retraining stage and yields a Pareto frontier of bit allocations.","pith_inferences":["My reading of the paper's own Table 1 is that the 'nearly lossless' claim is strained where deployment matters most: MobileNetV2 drops to 50.43 top-1 at 2 bits from 71.14 full precision after joint training, which suggests the shared high-bit scale fits depthwise-heavy compact models poorly; the authors flag this themselves and point to per-layer or per-channel learning-rate scaling as future work","An operational consequence the paper motivates but does not measure is that precision becomes a runtime knob on integer hardware: because all lower precisions are shift-and-rounds of the stored integers, a device could drop from 8-bit to 4-bit on the fly to save bandwidth or energy without re-instantiating any weights.","Because activations keep per-precision learned scales (Eqs. 4–5), an integer-only deployment still carries several activation-scale tables; extending double rounding to activations with a single stored scale is an open direction the paper leaves implicit.","HASB is a quantization-specific way to spend a capacity budget by layer sensitivity, so the same Hessian-trace-biased sampling could plausibly be ported to other once-for-all sub-network choices such as pruning ratios or layer widths, a connection the paper does not draw."],"forward_implications":["Deployment becomes bit-switchable from one artifact: a model stored as 8-bit integers can be served at 6, 4, or 2 bits without reloading weights, because each lower precision is derived from the stored integers by a shift-and-round.","Storage drops to a quarter of the FP32 baseline for the 8-bit configuration and to an eighth for the {4,3,2}-bit configuration, with ImageNet-1K accuracy matching or exceeding one-shot baselines that store 32-bit models.","Joint multi-precision training costs stay roughly constant as the candidate list grows — ResNet50 on ImageNet costs about 40.8 GPU-hours for four precisions versus 51.6 for training them separately — so more precisions no longer multiply the training budget.","The mixed-precision pipeline drops the final retraining or fine-tuning stage: ILP search returns each sub-network in under two minutes from the trained SuperNet, and the searched configurations form a Pareto frontier across bit budgets.","The single-model switching transfers beyond classification: COCO detection and instance segmentation with Mask-RCNN backbones, and TinyLlama zero-shot tasks, retain most of their accuracy across the 8/6/4/2-bit settings."],"supporting_citations":[{"why":"LSQ supplies the learned step-size quantization whose scale-gradient behavior motivates ALRS, and provides the separate-precision baseline in Table 9.","marker":"[2]"},{"why":"AdaBits introduced adaptive bit-width switching from a stored 8-bit model and is the main baseline for the {8,6,4,2}-bit and MobileNetV2 comparisons.","marker":"[3]"},{"why":"MultiQuant is the knowledge-distillation multi-precision baseline (storing 32-bit weights) that the paper's 8-bit storage claim must match or beat.","marker":"[4]"},{"why":"Any-Precision is a 32-bit-storing multi-precision baseline with and without knowledge distillation used throughout Table 1.","marker":"[6]"},{"why":"The quantizable-DNN method (cited as CoQuant in Table 1 and Q-DNNs in Table 2) is a prior approach that stores an 8-bit model for bit-switching.","marker":"[7]"},{"why":"Bit-Mixer is the closest competitor in both multi-precision and mixed precision; its floor-instead-of-rounding trick is what Double Rounding is designed to fix, and it supplies the TBN mechanism for mixed precision.","marker":"[9]"},{"why":"HAWQ-V2 provides the Hessian matrix trace used as the layer-sensitivity metric that drives HASB's bit-switching probabilities.","marker":"[11]"},{"why":"LARS is the layer-wise adaptive rate scaling concept that inspires the ALRS per-precision learning-rate rule.","marker":"[27]"},{"why":"OMPQ supplies the Integer Linear Programming formulation used to search Pareto-optimal mixed-precision sub-networks.","marker":"[31]"}],"fun_headline_variants":["Double rounding: one integer model, all precisions","Store 8-bit, switch to 2-bit with minimal loss","Bit-switching without FP32: double rounding","Train once, store integer, switch to any bit-width","Nearly lossless bit-switching from a single stored model"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a single quantization scale and zero point, fit to the highest bit-width, stays near-optimal for every lower bit-width through the fixed power-of-two relation $s_l = s_h \\cdot 2^{\\Delta}$, so that when the high-bit scale does not match the low-bit weight distribution, the low-bit model begins training with a step size it cannot escape.","fun_headline_variants_meta":{"raw":{"variants":["Double rounding: one integer model, all precisions","Store 8-bit, switch to 2-bit with minimal loss","Bit-switching without FP32: double rounding","Train once, store integer, switch to any bit-width","Nearly lossless bit-switching from a single stored model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001303,"raw_usage":{"total_tokens":5408,"prompt_tokens":1132,"completion_tokens":4276,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":748,"completion_tokens_details":{"reasoning_tokens":4196}},"tokens_in":748,"tokens_out":4276,"duration_ms":30227,"temperature":1.0,"reasoning_tokens":4196,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T16:14:56.939380+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train MobileNetV2 twice under the {8,6,4,2}-bit schedule, once with the shared high-bit scale and once with an independently learned 2-bit scale, and compare 2-bit top-1 after the same epoch count; if the independent scale recovers a large share of the reported 20-point gap (50.43 vs. 71.14 full precision), then the fixed power-of-two scale, not training competition, is what caps low-bit accuracy on compact models, and the near-lossless claim fails for exactly the architectures where deployment savings matter most.","supporting_citations":[{"cited_title":"Adabits: Neural network quantization with adaptive bit-widths,","cited_arxiv_id":null,"evidence_quote":"AdaBits introduced adaptive bit-width switching from a stored 8-bit model and is the main baseline for the {8,6,4,2}-bit and MobileNetV2 comparisons."},{"cited_title":"Any-precision deep neural networks,","cited_arxiv_id":null,"evidence_quote":"Any-Precision is a 32-bit-storing multi-precision baseline with and without knowledge distillation used throughout Table 1."},{"cited_title":"Bit-mixer: Mixed-precision networks with runtime bit-width selection,","cited_arxiv_id":null,"evidence_quote":"Bit-Mixer is the closest competitor in both multi-precision and mixed precision; its floor-instead-of-rounding trick is what Double Rounding is designed to fix, and it supplies the TBN mechanism for mixed precision."},{"cited_title":"Hawq-v2: Hessian aware trace-weighted quantization of neural networks,","cited_arxiv_id":null,"evidence_quote":"HAWQ-V2 provides the Hessian matrix trace used as the layer-sensitivity metric that drives HASB's bit-switching probabilities."},{"cited_title":"Ompq: Orthogonal mixed precision quantization,","cited_arxiv_id":null,"evidence_quote":"OMPQ supplies the Integer Linear Programming formulation used to search Pareto-optimal mixed-precision sub-networks."}],"review_version":1}