Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization

arXiv:2610.09877 · cs.LG · Submitted 2026-10-07 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: Today's paper: "Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization".

Jane: The gist:

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So, we're looking at this paper today, "Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization." The big idea here is tackling the two main headaches in mixed-precision post-training quantization: figuring out which layers get which bits under a memory budget, and making sure that process doesn't break when the calibration data gets a little messy.

Jane: It sounds like they are saying that because trying to figure out all those possible assignments is combinatorially hard, and because real-world sensor data can be corrupted, we need something much smarter than just guessing.

Lu: Exactly. The authors propose a layerwise probabilistic analysis of the quantization error. They separate the error that gets carried over from previous layers from the new local noise introduced at a specific layer. That separation is key to building a score that works without needing some kind of external solver, which is something they say is really important for speed and robustness.

Meng: But what does this mean for deployment? If we can get around the combinatorial explosion by using these local terms, it means we can find a fast way to allocate bits layer by layer. I need to know if this allocation method is actually fast enough to run during design exploration or when we have a tight schedule.

Lalam: From my perspective, the paper claims that this approach has robustness because it uses a quantile instead of just worst-case errors, which lets it handle outliers in the calibration dataset better. They show that their method matches or improves state-of-the-art baselines under clean calibration, and more importantly, they are more robust to corrupted calibration data with PSNR gains of up to seven point five dB under the tested corruptions <ref:2610.09877#pg2>.

Tom: Seven point five dB gain is significant when you’re dealing with noisy real data. I'm interested in how they handle those corruptions specifically because that’s where most quantization methods start failing in practice.

Jane: And they show some impressive speedups too, which is a big deal for any production pipeline. The experiments show bit-allocation speed-ups from twenty-eight times to two thousand five hundred seventy times over the studied baselines in matched timing comparisons, which shows how much faster this allocation method is compared to what’s out there now.

Paper summary: Lu: I see the core mechanism is decomposing the quantization error at depth l into two parts: propagated error from previous layers and local quantization error introduced at the current layer, which they capture using random variables X and Y that are bounded by properties of the weight matrices. That layerwise bound is what formalizes how those terms interact.

Meng: So, if we look at the practical part, how does this probabilistic analysis translate into a concrete decision for assigning bit-widths to layers? I need to know how they actually build that separable score from these local error terms before they make a final choice.

Tom: They use this local term to build a separable score for a simple allocation algorithm that requires no external solver. It seems they group layers into allocation blocks, g in G, where all layers in a block share one bit-width b g in B g. For a block quantized at bit-width b, the approximated local quantization error is defined as P g,b(x):= X in g (W - Q b(W)) S-one(x) squared.

Jane: That formula looks complicated, but the point is that they summarize these scores by their mean and standard deviation on the calibration set D cal. So instead of looking at every single configuration, they get summary statistics for each block and bit-width combination.

Lu: And the probabilistic nature of this whole approach provides a bound on the output error, where epsilon is defined by the sum of local and propagated error terms across all layers, which is what keeps things epsilon-probabilistic. This analysis keeps the source of each quantization error visible and generalizes previous deterministic analyses.

Meng: So they are trading worst-case guarantees for a probabilistic guarantee that allows for speed, which makes sense when dealing with noisy data where worst-case bounds can be overly pessimistic or simply too slow to compute. What happens if we apply this to something like diffusion models, which we see mentioned in the results?

Tom: The results show that on denoising tasks with DRUNet, they get those PSNR gains of up to seven point five dB under the tested corruptions, and for quantized diffusion models, a direct application of their framework also improves the state-of-the-art <ref:2610.09877#pg2>.

Jane: That’s really interesting because it shows that this isn't just some niche trick; it works across different model types like DRUNet and even diffusion models. It suggests the layerwise attribution is a general way to look at where errors are coming from in quantization.

Paper summary: Lu: The experiments on DRUNet show that their method's mean bit-width under corrupted calibration yields a PSNR of thirty-four point four zero one dB, which is better than CLADO's performance under the same corruption, and the allocation diagnostics show that their method changes fewer block bit-widths than CLADO and better preserves their ordering under both calibration corruptions <ref:2610.09877#pg2>.

Meng: When I think about deployment costs at scale, seeing a two thousand five hundred seventy times speedup over baselines is fantastic for design exploration because it means we can test more configurations quickly without waiting for long allocation times. But what about the runtime of the quantized model itself? Is there any trade-off in inference speed when we use these different bit-widths?

Tom: The paper focuses heavily on the allocation part being fast, and they keep the quantizer fixed when choosing the bit-width, so it addresses that specific constraint. However, as Lu mentioned, we still need to consider how many bits are actually used per layer—the budget is still there.

Jane: And looking at the overall performance comparisons on CelebA-HQ, they found this mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison, which sounds like a very solid overall result for image quality metrics.

Lu: The main thing I see is that this layerwise analysis successfully tracks what's carried from previous layers versus what's introduced locally, and their practical algorithm turns that local perturbation into a reusable table of scores for each block and bit-width, which then meets the budget with a simple greedy algorithm without an external solver.

Meng: So to summarize for production: we get speed, we get robustness to corrupted data from the probabilistic bounds, and we keep quality competitive or better than other methods under noise. That seems like a very practical combination for shipping models today.

Tom: I agree. The focus on making the allocation fast and robust when calibration data is corrupted is exactly what you need when moving from research prototypes to actual deployed AI systems that run on real-world sensors.

Jane: So, this paper, "Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization," gives us a way to systematically analyze error propagation layer by layer, leading to a fast allocation strategy that performs well even when the calibration set is imperfect.

Conclusion: Tom: So, to wrap up this paper, "Layerwise Error Attribution for Fast and Robust Mixed-Precision Post-Training Quantization," we’re looking at how they figured out a fast way to decide which layers get which bit-widths without needing some super slow solver.

Jane: It boils down to this idea of tracing the error. They do this by splitting the total quantization error into what carried over from previous layers and what happened right there in the current layer.

Lu: Exactly. That separation lets them build a score for allocating bits that doesn't rely on guessing every single combination, because they use these local terms to create a separable score.

Meng: From my side, it means we can actually do this allocation quickly during design exploration or when we’re iterating on model structures. Speed is key for us when shipping models at scale.

Tom: And the results show that this method works really well for denoising tasks like DRUNet, matching or improving state-of-the-art baselines, even when the calibration data gets corrupted by noise.

Jane: That robustness is what’s interesting here. It uses a probabilistic view instead of just looking at the absolute worst case error, which makes it handle messy real data better.

Lu: The practical part is they group layers into blocks and summarize the local error scores for each block and bit-width combination, which lets them use a simple greedy rule to pick the best configuration.

Meng: I’m curious about how much faster this allocation process actually is compared to what we have right now in production pipelines.

Tom: They show speedups from twenty-eight times up to two thousand five hundred times over the baselines, which is a huge jump for our design workflow.

Jane: So, it’s like they gave us a reliable map that shows where the errors are coming from, so we don't have to check every single path blindly.

Lu: This paper suggests that by tracking the origin of each quantization error layer by layer, you can meet those two major needs: being fast and being robust to bad calibration data.

Meng: It seems like they’ve managed to make a method that balances high quality under clean conditions with stability under messy real-world conditions.

Tom: And for diffusion models too, applying this framework directly improved the state-of-the-art performance we saw before.

Jane: The implication is that understanding the error structure at the layer level gives us a much more controlled way to compress models reliably across different tasks.

Lu: We’re looking at how tracking propagated versus local error allows for a cleaner, more systematic approach to bit allocation than what we have currently tried.

Samy Houache, Yann Traonmilin, Jean-François Aujol

University of Bordeaux · Thales AVS

cs.LG

Submitted: 2026-10-07

Updated: 2026-10-07

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 80/100

The gist: The gist: A probabilistic layerwise analysis of quantization error allows for a fast and robust mixed-precision post-training quantization algorithm that matches or improves state-of-the-art

Key concepts

Layerwise Probabilistic Analysis: This technique decomposes the total quantization error at any layer into two parts: error carried over from previous layers (propagated) and new error introduced by the current layer (local perturbation). This mathematical separation is key to understanding how errors accumulate during the quantization process.
Separable Score: The analysis uses this local term to build a 'separable score' for a simple allocation algorithm. This means the decision of which bit-width to assign to a layer can be calculated independently based on its local error contribution, rather than needing complex, slow global optimization.
Robustness via Quantile Estimation: Instead of relying on worst-case deterministic errors, the method uses a probabilistic approach involving quantiles. This allows the algorithm to be more tolerant of outliers or corrupted data in the calibration set, leading to better performance when the training or calibration data is imperfect.

Terminology

Quantization — 1× in this paper · explained in 13 episodes

Summary

The gist: A probabilistic layerwise analysis of quantization error allows for a fast and robust mixed-precision post-training quantization algorithm that matches or improves state-of-the-art baselines while being more robust to corrupted calibration data.

How it works

The core idea involves deriving a layerwise probabilistic analysis of the quantization error that separates propagated error from the local perturbation introduced at a given layer The paper proposes this analysis to build a separable score for a simple allocation algorithm that requires no external solver This approach provides robustness to corrupted data because it uses the local term to build a separable score for an allocation algorithm that requires no external solver.

The analysis is formalized through a layerwise bound, where the error at depth l is decomposed into propagated error from previous layers and local quantization error introduced at the current layer This decomposition is captured by Equation (1), which states that the difference between full-precision and quantized forward passes, i.e., the quantization error, at depth l is ∆l:= Sl − S′l. The random variables Xl and Yl measure how much the propagated and local terms are amplified on the current input These ratios satisfy 0 ≤ Xl ≤∥Wl∥op, 0 ≤ Yl ≤∥Wl − W′ l∥op.

The Allocation Algorithm

The proposed algorithm is a fast and robust mixed-precision PTQ algorithm that computes separable local scores from one full-precision pass per calibration image, then assigns bit-widths with a simple greedy rule and no external solver. To estimate the local influence of each layer, the algorithm retains the local quantization error identified by Theorem 1 and evaluates it before choosing a complete configuration.

The practical algorithm groups layers into allocation blocks g ∈ G, which reduces the number of decisions and matches block partitions used in comparisons All layers l ∈ g in a given block share one bit-width bg ∈ Bg. For a block g quantized at bit-width b, the approximated local quantization error is defined as Pg,b(x):= Xl∈g (Wl − Qb(Wl)) Sl−1(x) 2. The scores are summarized by their mean and standard deviation on the calibration set Dcal.

Robustness and Performance

The probabilistic nature of the approach brings robustness to corrupted data because it uses a quantile instead of worst-case errors, permitting increased robustness to outliers in available datasets. The layerwise bound Theorem 1 provides an ε-probabilistic upper bound for the output error, where ε is defined by the sum of local and propagated error terms across all layers This probabilistic analysis keeps the source of each quantization error visible and generalizes previous worst-case deterministic analysis.

Experiments on denoising tasks with DRUNet show that our method matches or improves state-of-the-art mixed-precision baselines under clean calibration, and is more robust to corrupted calibration, with PSNR gains of up to 7.5 dB under the tested corruptions The bit-allocation speed-ups are substantial, showing improvements from 28× to 2,570× over the studied baselines in matched timing comparisons.

Experimental Results

On DRUNet with a target budget of 4 bits per weight, our method achieves PSNR gains of up to 7.5 dB under the tested corruptions. For quantized diffusion models, direct application of our framework also improves the state-of-the-art.

In comparisons on DRUNet, Table 1 shows that our method's mean bit-width under corrupted calibration yields a PSNR of 34.401 dB, which is better than CLADO's performance under the same corruption. The allocation diagnostics show that our method changes fewer block bit-widths than CLADO and better preserves their ordering under both calibration corruptions.

The measured selection time for DRUNet on one A100 is 24.32 seconds, which is 28× faster than AIMET AMP and 30× faster than OMPQ-ORM with a fixed β. For latent diffusion models, our method obtains a FID of 20.853, compared to 22.626 for Q-Diffusion

Conclusion

The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. The practical algorithm turns the local perturbation into a reusable table of scores for each block and bit-width, and then meets the budget with a simple greedy algorithm and no external solver. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison. The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison. The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison. The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison. The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison. The layerwise analysis keeps track of the origin of the quantization error by separating what is carried from previous layers from what is introduced locally. This addresses the two practical requirements set out in the introduction: fast allocation and robustness to corrupted calibration data. On DRUNet, our method combines competitive quality under clean calibration with gains of up to 7.5 dB under the tested corruptions and bit-width allocation speed-ups from 28× to 2,570×. On CelebA-HQ, our mixed-precision model combines competitive FID with the highest mean PSNR to FP32 in the paired comparison.

Improvements for AI systems

Bold allocation speed-ups from 28× to 2,570× over studied baselines: This enables extremely fast model design exploration, allowing researchers to test a vastly larger configuration space when designing mixed-precision PTQ pipelines without incurring prohibitive computational costs.
Robustness to corrupted calibration data: The probabilistic layerwise analysis separates the error propagated from earlier layers from the local perturbation introduced at a given layer, which allows for robustness to corrupted data and enables the method to preserve the relative ordering of blocks by assigned bit-width even when calibration inputs are degraded.
High-quality model compression with minimal quality loss: The method achieves PSNR gains of up to 7.5 dB under the tested corruptions and matches or improves state-of-the-art mixed-precision baselines, such as achieving highest mean PSNR to FP32 in latent diffusion experiments.
Solver-free allocation algorithm: The framework proposes a method that computes separable local scores from one full-precision pass per calibration image, then assigns bit-widths with a simple greedy rule and no external solver, eliminating the need for slow iterative optimization or complex integer programming solvers during the allocation phase.

Sources

Benchmarking the Reliability of Post-training Quantization: a Particular Focus on Worst-case Performance