WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

arXiv:2610.22232 · cs.CV · Submitted 2026-10-15 · Read on arXiv

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

Tom: We're looking at the paper: "WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression".

Jane: The gist The proposed WaveLLM framework introduces a wavelet-domain LLM entropy model for lossless image compression, demonstrating superior performance across three benchmarks compared to existing methods.

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

Paper summary: Jane: So to wrap up this talk on WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression, the core message is that you need a structured input for an LLM entropy model to perform well. They proved that by using wavelet decomposition, you turn one hard problem into several simpler ones.

Tom: And they showed that this structured approach works because it allows the same shared LLM backbone to adapt its statistical understanding to different parts of the image based on task prompts. The performance numbers—two point five one, two point two four, and two point two seven bpsp on Kodak, CLIC.pro, and DIV2K—show it’s a competitive method for lossless coding rates right now compared to other LLM approaches > Page three — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al <ref:2610.22232#pg1>.

Lu: The authors confirm that wavelet subbands provide a more suitable representation for LLM-based probability modeling than the flat pixel and residual sequences they tested > Page two — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al <ref:2610.22232#pg1>.

Meng: From what I’ve seen so far, the main hurdle for deployment is making sure that this task-adaptive prompting strategy doesn't introduce too much overhead when running continuously on live traffic.

Tom: The authors also point out that they plan to look at distillation and quantization in future work to address that practical side of things > Page three — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al <ref:2610.22232#pg1>.

Jane: It sounds like this paper shows a path forward by combining a numerical interface for the LLM and task prompts to handle the complexity of image signals in a way that actually improves prediction accuracy > Page one — WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression <ref:2610.22232#pg1,WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression>

Conclusion: Tom: So, WaveLLM is about using wavelet decomposition to make large language models better at lossless image compression > Page one — WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

Jane: It’s basically taking an image, breaking it down into wavelet pieces, and feeding those pieces into an LLM instead of just feeding the raw pixels one by one. But why that specific math structure?

Lu: The core idea is that a single sequence of pixels is really messy, with all these different statistical patterns tangled up in there > Page five — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Meng: So the paper claims that this decomposition turns one huge prediction problem into a bunch of smaller ones that are easier for an autoregressive model to handle > Page four — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Tom: Exactly. They’re not just throwing more parameters at the LLM; they’re changing the input format so the model doesn't have to learn an impossible amount of noise simultaneously > Page five — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Jane: And how do they actually connect those wavelet coefficients—which are just numbers—to the LLM’s language-like tokens? That seems like a huge engineering hurdle > Page six — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Lu: They introduced a numerical interface that maps those coefficients into local value IDs and gives them embeddings so the LLM treats them like text > Page seven — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Meng: That mapping is what lets the model learn something new about the structure of the image data rather than just memorizing pixel sequences > Page seven — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Tom: The results are pretty concrete too. they’re showing rates of two point five one bpsp on Kodak and other benchmarks > Page three — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Jane: That's good to see. So what does this mean for someone who just listens to the show? It means that in the world of lossless compression right now, using a structured representation like wavelets is actually giving LLMs an edge over just looking at raw pixel data > Page one — WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

Lu: It suggests that for complex signals, reorganizing the input structure to be more statistically regular really helps the probability estimation part of the AI model work better > Page two — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Meng: The authors also mentioned they're still working on making sure this thing runs smoothly when you try to deploy it in a real production environment > Page three — WaveLLM MM ’twenty-six November ten–fourteen two thousand twenty-six Rio de Janeiro, Brazil Yue Yu et al.

Tom: Right. So we've seen the mechanics and the numbers behind WaveLLM. next up we're going to look at what this means for real-world image compression systems and where they might go next > Page one — WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression

Yue Yu, Bowei Kang, Changsheng Gao, Dong Liu, Xiaoyan Sun

University of Science and Technology of China · Nanyang Technological University Singapore

cs.CV

Submitted: 2026-10-15

Updated: 2026-10-16

Comments: Accepted at ACM Multimedia 2026 (MM '26). 10 pages, 6 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 82/100

The gist: The gist The proposed WaveLLM framework introduces a wavelet-domain LLM entropy model for lossless image compression, demonstrating superior performance across three benchmarks compared to existing

Key concepts

Wavelet-Domain Decomposition: The image is broken down into multiple wavelet subbands using a fixed transform. This converts the complex, mixed signal of an image into several simpler, more statistically consistent prediction problems. Coding proceeds by predicting the deepest band first and using its result to reconstruct the next shallower band.
Numerical Interface: This component connects the continuous wavelet coefficients to the LLM's text-based token space. It maps integer wavelet values into a local symbol space, adds trainable embeddings, and uses a prediction head to estimate these values. This ensures that numerical data is processed alongside language semantics effectively.
Task-Adaptive Prompting: Instead of training separate models for every subband, WaveLLM uses one shared LLM. A specific text prompt describes the current subband's statistical properties and context, allowing the single model to adapt its probability estimation strategy optimally for that specific band.

Summary

The gist The proposed WaveLLM framework introduces a wavelet-domain LLM entropy model for lossless image compression, demonstrating superior performance across three benchmarks compared to existing methods.

Motivation and Core Argument

Lossless image compression fundamentally relies on accurate entropy modeling, driving a recent shift toward large language model (LLM)-based methods in this paper<ref:2610.22232#pg2> However, existing approaches mainly emphasize the modeling capacity of LLMs while directly serializing images into pixel or residual sequences, leaving heterogeneous signal patterns entangled within a single prediction stream<ref:2610.22232#pg5> In this paper, we argue that effective entropy modeling depends not only on model capacity, but also on the predictability of the input representation When heterogeneous signal patterns are entangled within a single sequence, the entropy model must continuously adapt to sharply different statistical regimes, which makes accurate probability estimation intrinsically more difficult By contrast, when the input is reorganized into simpler components with clearer statistical regularity, the same model can solve a substantially easier prediction problem

Wavelet-Domain Decomposition

The paper proposes to perform probability prediction and entropy coding in the wavelet domain By decomposing an image into multi-level wavelet subbands, WaveLLM converts a heterogeneous prediction problem into a set of more structured and statistically homogeneous subproblems that are more amenable to autoregressive probability estimation The decomposition involves:

Decomposing an 8-bit RGB image into YCoCg and decomposing it by a four-level fixed 5/3 integer wavelet transform, producing 13 subbands including the deepest low-frequency band LL4 and three directional high-frequency bands (HLl, LHl, HHl) at each of four levels
The coding order follows the lossless wavelet factorization: LL4 is coded first, followed by the three high-frequency bands at each level from the deepest level to the shallowest
The inverse wavelet transform synthesizes the next shallower low-frequency band for use as decoded context

Bridging Wavelets and LLMs

A key technical challenge addressed is bridging the gap between wavelet coefficients and the LLM’s native text token space To bridge this gap, a dedicated interface is introduced that maps wavelet coefficients into a compact local symbol space, equips them with trainable value embeddings, and predicts valid coefficient values through a dedicated value prediction head Specifically, the integer wavelet coefficients are remapped to local value IDs using the mapping z = v + o, where o = 512 is a fixed offset that shifts the observed coefficient range into the valid local range of K = 2048 This design ensures that text semantics and coefficient numerics are processed through independent embedding pathways, avoiding vocabulary mismatch

Adaptive Modeling Strategy

To handle the distinct statistical characteristics of different wavelet subbands, WaveLLM employs a task-adaptive prompting strategy Rather than training an independent model for each subband, one shared entropy model is reused across different subbands through task prompts The LLM input for each subband is organized as a task prompt with two components: a text prompt that identifies the subband type and describes the available context, and a value sequence containing the serialized integer values of the decoded context and target bands This task-specific natural-language string serves as the primary mechanism through which the shared backbone activates different statistical priors for different subbands

Performance and Analysis

WaveLLM was built on Llama-3.2-3B with LoRA adaptation, achieving 2.51, 2.24, and 2.27 bpsp on Kodak, CLIC.pro, and DIV2K benchmarks respectively WaveLLM outperforms the PixelCNN-based codec using the same wavelet transform by 0.43, 0.36, and 0.46 bpsp on Kodak, CLIC.pro, and DIV2K respectively The wavelet-domain formulation is consistently the strongest among tested variants when compared to pixel-domain and residual-based alternatives Analysis shows that the LLM yields a positive local gain over iWave for every subband, indicating more accurate probability prediction throughout the hierarchy Ablation studies confirm that removing text prompts causes the largest single-component degradation, supporting the effectiveness of the proposed task prompt The final results suggest that wavelet subbands provide a more suitable representation for LLM-based probability modeling than tested flat pixel and residual sequences

Conclusion

WaveLLM achieves competitive rates with strong learned lossless codecs while remaining competitive with recent LLM-based lossless compressors on all three benchmarks Future work will consider distillation, quantization, and near-lossless coding The proposed framework combines a coding-oriented numerical interface, task prompts, and same-level decoded context within a LoRA-adapted Llama-3.2-3B backbone WaveLLM achieves 2.51, 2.24, and 2.27 bpsp on Kodak, CLIC.pro, and DIV2K respectively The results suggest that wavelet subbands provide a more suitable representation for LLM-based probability modeling than the tested flat pixel and residual sequences The paper is licensed under a Creative Commons Attribution 4.0 International License This work is licensed under a Creative Commons Attribution 4.0 International License The paper is also available on arXiv as arXiv:2610.22232v1 [cs.CV] 15 Oct 2026 The paper is also available on arXiv as arXiv:2610.3>

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WaveLLM MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil Yue Yu, Bowei Kang, Changsheng Gao, Dong Liu & Xiaoyan Sun This work was in part supported by the National Natural Science Foundation of China under grants 62472399 and Open Fund of APKL of BIIP, IAI, Hefei Comprehensive National Science Center under grants 24YGXT003

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WaveLLM MM ’26, November 10–14, 2026, Rio de Janeiro, Brazil Yue Yu et al. The paper is also available on arXiv as arXiv:2610.3> The paper is also available on arXiv as arXiv:2610.3>

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