Channel Simulation and Distributed Compression with Ensemble Rejection Sampling

Thank you for your review and encouraging comments. We're glad you appreciated the theoretical advancements of our ERS and RS-based coding scheme and the empirical benefits of ERS in both synthetic and real-data experiments. Please find your concerns answered below.

(1) Extra Experiments and Comparison to other Compression Method We conduct experiments on the CIFAR-10 dataset, comparing our ERS approach against the quantization baseline [A1], the implicit neural representation method [A2] (which is one of the recent state-of-the-art image compression method), and the Importance Matching Lemma (IML) [33]. We use Mean Squared Error (MSE) as the distortion metric across all schemes, where lower values indicate better performance. By effectively leveraging side information in the encoding process, ERS consistently achieve lower distortion across all settings.

(2) Technical Contributions

The core technical contribution of our work is the development of new encoding schemes within the RS/ERS framework, which offer several key advantages over existing methods:

• Compared to the Importance Matching Lemma (IML): ERS produces exact output samples rather than approximate ones, resulting in better performance, particularly in low-distortion regimes (see Section 6).

• Compared to Greedy Rejection Sampling (GRS): ERS achieves substantially higher distributed matching probabilities.

• Compared to the original Poisson Matching Lemma (PML): Our ERS-based framework, integrated with neural networks, overcomes the decoder-side termination issue that remains a challenge in the original PML design for high-dimensional data.

Besides the development of new coding schemes, our contribution also includes substantial technical novelty in the analysis, with each core proof spanning over 10 pages. In particular, the achievability proof for channel simulation with ERS at an arbitrary batch size $N$ involves bounding a complex probabilistic integral arising from self-normalized importance sampling, without assuming any specific form for the target or proposal distributions [A3]. This derivation notably relies on a symmetry-based argument, rather than standard concentration tools such as Hoeffding’s or log-Sobolev inequalities, allowing us to establish an upper bound that holds uniformly over all values of $N$. The challenges of handling self-normalized importance sampling terms also arise in our analysis of the matching lemmas. Specifically, proving the bounds in Propositions 5.4 and 5.6 requires substantial analytical effort, involving intricate combinations of probabilistic reasoning as well as set-theoretic arguments.

(3) Limitations and Impact We will include a more detailed discussion of the limitations and potential impact of our work in the main paper. Channel simulation techniques are commonly used in privacy-preserving applications, such as secure data sharing and communication, which contributes positively to societal impact.

Let us know if you have additional concerns and we will address them.

References

[A1] Ballé, Johannes, et al. "Variational image compression with a scale hyperprior." International Conference on Learning Representations. 2018.

[A2] He, Jiajun, et al. "RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations." The Twelfth International Conference on Learning Representations.

[A3] Agapiou, Sergios, et al. "Importance sampling: Intrinsic dimension and computational cost." Statistical Science (2017): 405-431.

Thank you for your thoughtful and detailed review. We appreciate your recognition of our theoretical contributions—including the new RS and ERS coding schemes and the distributed matching lemma—as well as the practical value of ERS in distributed compression tasks. Please find your concerns addressed below.

(1) Dependence on Global Bounding Constant/Computational Complexity

Your observation is indeed correct for the current scheme based on standard rejection sampling, where both parties must share knowledge of $\omega$. In practice, the encoder can transmit this information prior to sending the actual samples, allowing the coding cost of $\mathcal{O}(\log(\omega))$ to be amortized over time.

Moreover, ERS provides several benefits compared to existing methods:

• Compared to the Importance Matching Lemma, ERS delivers exact output samples, resulting in improved performance in low-distortion scenarios for distributed compression, as shown in Section 6.
• Compared to the Greedy Rejection Sampling scheme, ERS also achieves better distributed matching probabilities, where GRS falls short.
• Compared to the original PML scheme for distributed compression with high-dimensional data, our ERS-based coding scheme with neural networks effectively addresses the decoder-side termination issue, which the original PML scheme does not fully resolve (also see the answer for Question 1 below).

We further note that, in the context of distributed compression using ERS, choosing the batch size as $N = 2^{\mathbb{E}[D_{\mathrm{KL}}(p_{Y|X}(\cdot|x) \,\|\, q_Y(\cdot))] + 4}$ is sufficient to ensure a low coding cost for the batch index. Empirically, the algorithm tends to terminate within 2 to 4 batches. This leads to a constant $\mathcal{O}(1)$ coding cost, allowing the batch index to be efficiently encoded via unary coding. This is practically more efficient than using the global constant $\omega$ described in Proposition 5.6, which serves as a conservative bound for the general achievability result. Importantly, the validity of the output samples is maintained regardless of the specific value of $N$.

(2) Looser Rate Bounds

Our experiments in Figures 2 and 3, conducted with actual distributions, indicate that the coding cost bounds stated in Proposition 4.1 and Proposition 5.1 tend to overestimate the cost observed in practice. This suggests that the theoretical bounds—particularly the one for ERS—can likely be tightened and the higher constants could be the consequences of our bounding techniques.

(3) Practicality of PML: Compute Local Constant On The Fly

In our scheme using ERS, the encoder requires an upper bound $\omega_x$, which depends on the target distribution $p_{Y|X}$ and the proposal $q_Y$, to guarantee termination. Importantly, this constant is local to the encoder, and the scheme does not rely on $\omega_{x'}$, the corresponding constant on the decoder’s side. In contrast, PML requires the decoder to compute $\omega_{x'}$ to ensure termination, which demands further assumptions on $p_{Y|X'}$ and can degrade performance. This asymmetry highlights a key practical advantage of ERS over PML.

In our experiment, the decoder uses a neural contrastive estimator to directly estimate the likelihood ratio $\frac{p_{Y'|X'}(y'|x')}{q_{Y'}(y')}$ without assuming a specific form---such as Gaussian---for the posterior $p_{Y'|X'}$. Consequently, computing the local constant $\omega_{B,x'}$ needed for PML becomes intractable. If we instead assume a Gaussian form, $\mathcal{N}(\mu(x'), \sigma(x'))$, PML becomes feasible; however, our experimental results show that this assumption introduces a mismatch that worsens the rate-distortion tradeoff. See the table below for further details, note that we are presenting MSE distortion for different schemes  and lower is better. Embedding MSE refers to the error measured with respect to the encoder's neural network output, while pixel MSE captures the distortion at the image level.

(4) Implicit Information in the choice of group size and PML

We understand you are referring to the batch size $N$, chosen such that $N > \omega$, where $\omega$ denotes the global upper bound of the encoder’s density ratio. Please let us know if this interpretation is incorrect. Since $\omega$ serves as a global constant for the encoder’s target distributions, we are not aware of any existing methods for inferring the decoder’s local constant $\omega_{B,x’}$ based solely on $\omega$. This is because $\omega_{B,x’}$ requires an explicit knowledge of $p_{Y|X’}$, which is complex/intractable in general. We will clarify this difference and add the presented experimental results above to clarify the advantage of our scheme over PML.

(5) Computational Cost of the Sorting-Based Coding

A key challenge is that the decoder does not know the value of $x$, and therefore the group size $\omega_x$ is also unknown. As a result, encoding the sample using its runtime complexity $\omega_x$ remains an open problem. While explicitly transmitting $\omega_x$ would incur a high communication cost, exploring strategies where the sampling complexity adapts to $\omega_x$ is a promising direction for future work, which we will highlight in the paper.

(6) Downside of making groups larger than $\omega$

In the proposed protocol, where each sample has an acceptance probability of $\frac{1}{\omega}$, the group size is set to $\omega$ (or its floor value). If the group size exceeds $\omega$, for instance, approaching infinity, the coding cost for $\hat{K}$ will increase since there will be more uniform random variables whose value is smaller than the one selected by the rejection sampler (in terms of expectation). Technically, this is evident in equations (82-84) of the proof in the appendix, where replacing $\lfloor \omega \rfloor$ (the group size) with extreme values will show the effect.

(7) Minor Suggestions for Presentation

Thank you for your comment. We will incorporate these in the revised version.

We hope this clarify your concerns. Let us know if you have further questions.

We thank the reviewer for the question and would like to provide some clarification. We first note that in channel simulation, the output sample generated by ERS is guaranteed to be unbiased. Our scheme ---alongside Poisson Monte Carlo (PMC) and Greedy Rejection Sampling (GRS)--- satisfies this property.

In contrast, for distributed matching with communication (please see Section 3.2.2) --- the setting that applies to distributed compression — the scenario is a bit different. Note that the encoder and decoder use two different target distributions. The encoder uses a target distribution $P^A(y)$ while the decoder with side information $Z$ uses a target distribution $P^B_{Y|Z}(y|z)$. As we have noted in our paper, while the sample $Y_A$ generated at the encoder remains unbiased i.e., $Y_A$ follows the target distribution $P^A(y)$ this is not the case with the sample $Y_B$ generated at the decoder i.e., $Y_B$ may not follow the target distribution $P^B_{Y|Z}(y|z)$ even if the density ratios $P^B_{Y|Z}(y|z)/Q_Y(y)$ is perfectly estimated. We kindly refer you to Section 3.2.2 ( lines 132-138 on page 4) for further clarification of this issue. The reason for this is that side information $Z$ in general can be dependent on the common randomness $W$ as it is only required to satisfy the Markov chain $Z - (X, Y_A) - W$ (see Section~3.2.2). We note that this has also been clarified in the [1] (see discussion after Lemma 2) which considers a similar setting using the Poission Monte Carlo sampling method and is not a limitation of our proposed method.

We would like to however emphasize that our proposed scheme does guarantee that the samples generated the encoder are unbiased and follow the target distribution at the encoder. Indeed any reference to unbiasedness in our experimental section refers solely to the encoder’s sample quality. This property enables our scheme to outperform the Importance Matching Lemma baseline, where even the encoder's outputs are biased.

We also note that if the density ratio is incorrectly estimated at the decoder, it could decrease the matching probability and in turn introduce more errors at the decoder. We will add a clarification on this in the paper if it is accepted.

[1] Li, Cheuk Ting, and Venkat Anantharam. "A unified framework for one shot achievability via the Poisson matching lemma." IEEE Transactions on Information Theory 67.5 (2021): 2624-2651.

Thank you for your thoughtful review and for highlighting the novelty and rigor of our RS and ERS coding techniques, as well as the strength of our theoretical analysis. Please find the answer to your questions below.

(1) Sample Quality for Truncated $\omega$

When the constant $\omega$ is truncated, we believe it is possible to characterize the quality of the generated samples. In particular, it suffices to consider inputs $x$ where the local constant $\omega_x = \max_y P_{Y|X}(y|x)/Q_Y(y)\geq \omega$, as sample quality remains unaffected otherwise. To the best of our knowledge, the effect of truncating the upper bound $\omega$ has been studied in the contexts of rejection sampling (RS) and importance sampling (IS), but not for PMC. For $N = 1$, which corresponds to standard RS, existing early stopping techniques [A6] can be applied to derive bounds on sample quality. When $N > 1$, ERS incorporates an IS step, allowing similar analyses from [6,39] to be adapted for bounding the sample quality under ERS. We note that PMC remains the primary competitor for generating unbiased samples with high matching probability and this point showcase another advantage of our scheme over PMC that we will put a discussion in the revision.

Finally, in terms of terminating condition in the distributed compression application there is an important practical advantage that ERS has over PMC as discussed in reponse to Question 1 for Reviewer MpW9 (answered in points (3) and (4) in our rebuttal to their).

(2) Benefits of ERS over prior methods and RS The motivation for developing ERS is to improve the matching probability of RS and its greedy variant, i.e. Greedy Rejection Sampling (GRS), which alone are not competitive, also demonstrated in the examples of Figure 4 and Appendix D.2. To address this, ERS integrates RS with IS—an approach known for achieving high matching probabilities, albeit with biased output samples. In this sense, ERS combines the best of both worlds: high matching probability and unbiased output samples. We highlight several advantages of the ERS scheme over existing approaches:

• Compared to the Importance Matching Lemma [33], ERS generates exact output samples, leading to improved performance in low-distortion regimes for distributed compression, as shown in Section 6.
• Compared to GRS and standard RS scheme [12], ERS consistently achieves higher distributed matching probabilities.
• Compared to the PML scheme for distributed compression with high-dimensional data, our ERS-based coding scheme with neural networks effectively addresses the decoder-side termination issue, which the original PML scheme does not fully resolve.

In channel simulation, ERS has the potential to offer additional advantages over standard RS. There exists a substantial body of research aimed at improving the sample efficiency of IS, such as multiple IS and quasi-Monte Carlo. As ERS incorporates an IS within its procedure, we believe these advances could be effectively integrated to further enhance the efficiency of the ERS framework.

(3) The choice of $N$

For the distributed compression, the choice of $N$ is crucial for the performance. If $N=1$, we will have a low matching probability. On the other hand, setting $N$ very large will lead to high computational overheads. For any $N$, the scheme is feasible and the right choice of $N$ is to obtain the balance between matching probability and computational complexity. Our experiments suggest that setting the batch size as $N=2^{\mathbb{E}[D_{\mathrm{KL}}(p_{Y|X}(\cdot|x) \,\|\, q_Y(\cdot))]+4}$ is sufficient to achieve low coding costs for the batch index. This choice is not arbitrary—it aligns with the number of samples typically required to ensure low bias in IS [6]. With this, ERS usually terminates within just 2--4 batches. Thanks to this $\mathcal{O}(1)$ coding cost, the batch index can be efficiently encoded using unary coding and is more practical than relying on the global constant $\omega$ introduced in the theoretical analysis of Proposition 5.6, which primarily serves to make the rate analysis tractable. Importantly, the correctness of the generated samples is maintained for any choice of $N$.

(4) Gumbel-Max trick and Matching Lemmas

In [39], the technique known as Ordered Random Coding utilizes the Gumbel-max trick to address termination time. However, this method inherently produces biased samples due to its reliance on IS (see Corollary 3.2 in [39]). In contrast PFRL is an exact sampling scheme that generates unbiased samples (unlike the approach in [39]). An extension of this approach to matching scenarios as you described was introduced by Phan et al. [33], known as the Importance Matching Lemma (IML), which also produces biased samples. Our work directly extends the work by Phan et al. [33], which serves as a baseline we compared against in Section 6. The primary distinction of our approach compared to those in [33, 39] lies in our method of generating unbiased samples by combining IS with RS, and achieving better empirical performance in the Section 6. In particular, the results in Section 6 demonstrate that ERS outperforms IML in distributed compression scenarios.

(5) Definitions of $\mu$ Thank you for pointing this out. We will revise and adjust this.

(6) Verification of Matching Probability and Implication in Lossy Compression. We verify of the general matching probability in Proposition 5.4 with empirical comparisons of different methods presented in Figure 4. For Proposition 5.6, we report empirical matching probabilities under joint compression of multiple samples in Figure 9 (Appendix), which also illustrates the phenomenon described in Remark 5.7. We note that the matching probability is a central quantity in distributed compression, directly influencing the rate-distortion tradeoff. Our experiments involving distributed compression are designed to validate the performance gains attributed to improved matching probabilities. Schemes that fail to achieve high matching probability—despite being efficient for channel simulation such as RS and GRS—do not yield competitive rate-distortion performance in the distributed setting.

Finally, result in Proposition 5.6 can be translated into related quantities, such as the probability of excess distortion, as discussed in [25]. This can be used to derive bounds on the expected distortion for bounded inputs, which we will incorporate in the revision. Since matching probability is a central quantity in the distributed compression setting, we characterize it in Proposition 5.6. This is consistent with the IML/PML baseline and Proposition 5.6 serves as a counterpart result within our framework.

(7) Scaling Channel Simulation-Based Approaches

Channel simulation is increasingly applied to high-dimensional datasets. In image compression, [A1, A2] use it within diffusion models to achieve competitive performance on 512×512 images with < 10 second encoding, outperforming traditional quantization in perceptual quality. It is also effectively combined with implicit neural representations, which have shown superior results over quantization-based methods [A8].

Furthermore, the application of channel simulation extends beyond lossy image compression. It has been explored in areas such as differential privacy [A3] and quantum communication [A9]. Recent works [A4, A5] also apply similar distributed-matching techniques to accelerate inference in large language models, showcasing the growing interest of using such techniques for machine learning problems.

Regarding the scaling of the neural contrastive estimator to higher dimensional data, a practical workaround is to partition the input into smaller chunks and train a separate neural contrastive estimator on each subset. Furthermore, state-of-the-art methods for density estimation are still rapidly evolving, as demonstrated by recent advances in multimedia generative models. Nonetheless, in applications such as vertical federated learning—where feature dimensionality does not increase as quickly as in image-based tasks—channel simulation-based approaches remain both practical and directly applicable. Overall, scaling channel simulation to high-dimensional data is an active and promising research direction (see [37], [A7]).

We hope the reviewer is convinced about the strength of our scheme over prior methods.

References

[A1] Vonderfecht, J., & Liu, F. Lossy Compression with Pretrained Diffusion Models. ICLR 2025.

[A2] Yang, Yibo, et al. "Progressive Compression with Universally Quantized Diffusion Models.". ICLR 2025

[A3] Liu, Yanxiao, et al. "Universal exact compression of differentially private mechanisms.". NeurIPS 2024

[A4] Kobus, Szymon, and Deniz Gündüz. "Speculative sampling via exponential races." arXiv preprint arXiv:2504.15475 (2025).

[A5] Rowan, Joseph, Buu Phan, and Ashish Khisti. "List-Level Distribution Coupling with Applications to Speculative Decoding and Lossy Compression." arXiv preprint arXiv:2506.05632 (2025).

[A6] Block, Adam, and Yury Polyanskiy. "The sample complexity of approximate rejection sampling with applications to smoothed online learning." PMLR, 2023.

[A7] Jiajun He, et al. "Accelerating relative entropy coding with space partitioning." NeurIPS 2024

[A8] He, Jiajun, et al. "RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations." ICLR 2024

[A9] Steiner, Michael. "Towards quantifying non-local information transfer: finite-bit non-locality." Physics Letters 2000.

Thank you for your question. In our work, rather than estimating the mutual information $I(X’;Y)$, we focus on estimating the density ratio $P_{Y|X’}(y|x’)/Q(y)$ using the scheme in [1] (see Appendix C) --- an approach that is well-established and widely used in the literature. In high dimensional settings more advanced schemes developed in [2] can also be used. In our experiments, since we project the input images (MNIST/CIFAR) into an embedding vector of size 3 and perform distributed compression in this lower dimensional space it turns out that vanilla estimator sufficiently gives stable and acceptable performance.

We demonstrate this through the following experiment. In Table 1, we revisit the 4D Gaussian setup by replacing the closed-form log-density ratio with a neural network scheme in [1]. We evaluate both approaches at four target distortion levels—corresponding to the encoder's ideal distortion tradeoffs, similar to the setting in Figure 5 (middle). For each distortion level, we fix the same rate as in the experiment in the paper and measure the actual distortion at the decoder’s output. The results show that the neural network scheme closely matches the performance of the closed-form expression across all settings.

Table 1. Distortion (in dB) achieved at various target rates using closed-form vs. NCE-based estimation (repeat with 5 seeds).

To illustrate the stability of our approach in the MNIST setting, we train three neural networks with different random seeds to estimate the likelihood ratio. We then evaluate the agreement rate---defined as the percentage of times the decoders select the same output given the same setup (i.e., the same input $X$, common randomness $W$, and side information $X'$), but using different neural network estimators. We conduct experiments across four different target distortion level (or equivalently the $\beta-VAE$ hyperparameter described in Appendix K). We observe consistently high agreement scores across all settings (>97%), indicating that the proposed approach is stable with respect to variations in the neural network estimator. The results is in Table 2.

Table.2 Agreement rate across different target distortion levels (measured by \beta).

We would like to add that in the distributed compression the density ratio is used as an intermediate quantity that is used to compute a score function to guide sample selection at the decoder. Small inaccuracies in this score can be considered as small perturbations in the ranked code points and consequently will not affect the decoding. We sincerely hope that the reviewer is convinced about the technical soundness of our approach of computing the density ratio using neural networks and are happy to provide any further clarifications.

[1] Hermans, Joeri, Volodimir Begy, and Gilles Louppe. "Likelihood-free mcmc with amortized approximate ratio estimators." International conference on machine learning. PMLR, 2020.

[2] Choi, Kristy, et al. "Density ratio estimation via infinitesimal classification." International Conference on Artificial Intelligence and Statistics. PMLR, 2022.

Thank you for your thoughtful review and positive feedback. We appreciate your recognition of the theoretical justification, well-structured proofs, and clear presentation of our contributions. You can find your questions addressed below.

(1) Additional Experiment on CIFAR-10 Dataset We conduct the experiments on the CIFAR-10 dataset and compare our method with the implicit neural representations [A3] , quantization approach [A7] and Importance Matching Lemma (IML). We use Mean Squared Error (MSE) as the distortion metric across all schemes, where lower values indicate better performance. Our approach consistently achieves lower distortion by leveraging side information within the encoding scheme.

(2) Details about Channel Simulation In the context of our work, the main task of channel simulation is compressing a noisy sample $Y \sim P_{Y|X=x}$ of the input $X = x$ from the encoder , which will be then transmitted to the decoder. In the setting we consider, both parties share a source of common randomness $W$, which corresponds to a shared random seed in practice. The encoder employs a sampling algorithm—such as (ensemble) rejection sampling, importance sampling, or Poisson functional representation—to select the sample $Y$ using $W$. Once $Y$ is selected, the goal is to encode the index of $Y$ in $W$ to be close to the theoretical limit $I(X;Y)$ and communicate this message to the decoder. Since the decoder has access to $W$, it can retrieve the value $Y$ after decoding the index from the message.

(3) Details about Distributed Matching Quantity The probability in (2) is of interest because it quantifies how likely both parties are to select the same index, given their respective target distributions $P_A$ and $P_B$. This quantity plays a central role in the distributed compression setting. Since many distributed compression and communication problems can be characterized as specific instances of distributed matching (Figure 1.c), this quantity can be used to derive one-shot achievability results for a range of compression and communication settings [25]. We further note that this setup is related to the coupling problems in statistics and computer science and have found many applications therein.

(4) The choice of batch size N in ERS

In the context of distributed compression using ERS, setting the batch size as $N = 2^{\mathbb{E}[D_{\mathrm{KL}}(p_{Y|X}(\cdot|x) \,\|\, q_Y(\cdot))] + 4}$ is sufficient to ensure a low $\mathcal{O}(1)$ coding cost for the batch index. This choice is motivated by the analysis of the number of samples required in importance sampling [6]. Empirically, the algorithm typically terminates within 2 to 4 batches, resulting in a constant $\mathcal{O}(1)$ coding cost. This enables efficient encoding of the batch index using unary coding. Notably, this choice is more efficient than relying on the global constant $\omega$ from Proposition 5.6, which provides a conservative bound for the general achievability result. Importantly, the validity of the output samples is preserved regardless of the specific value of $N$.

In our experiments, when jointly compressing a 4D Gaussian vector as described in Section 6, this configuration requires approximately $2^{24}$ proposals, which are parallelized and executed on a single A4500 GPU with 20GB of memory. The average encoding time is under one second per sample. Further improvements can be achieved by incorporating techniques such as space partitioning [19]. Since larger values of $N$ reduce the overhead in batch index encoding, it is beneficial in practice to increase $N$ as much as GPU capacity allows, in order to maximize parallelism.

(4) ERS on domains beyond images

There are several existing works showing promise in scaling channel simulation techniques to high-dimensional data, which we believe can benefit ERS. For example, [A1, A2] demonstrate how to compress high-fidelity images using channel simulation methods applied to diffusion models. In particular, [A2] introduces a custom CUDA kernel that exploits parallelism to encode images in under 10 seconds. These methods outperform traditional quantization techniques by better preserving perceptual realism. An additional advantage is their natural compatibility with diffusion models, a leading approach in image generation. Given the strong performance of diffusion models in video generation, we believe similar extensions of channel simulation techniques to video are feasible. Beyond diffusion models, channel simulation has also been applied to implicit neural representation methods for image compression, demonstrating promising results. For example, [A3] applied channel simulation techniques to video compression problems, and such approaches may potentially be extended to other modalities as well.

(5) ERS in privacy-preserving setting

Several existing works have applied channel simulation techniques to differential privacy problems [A4, A5], suggesting that our ERS framework can also be extended in this direction. Moreover, since our scheme is inherently designed for distributed compression with distribution preservation, it opens up the possibility of incorporating differential privacy into distributed compression—an exciting direction for future research, particularly in practical settings such as vertical or clustered federated learning [A6].

We hope that our rebuttal address your concerns. Please let us know if you have any additional questions.

References

[A1] Vonderfecht, J., & Liu, F. Lossy Compression with Pretrained Diffusion Models. In The Thirteenth International Conference on Learning Representations.

[A2] Yang, Yibo, Justus Will, and Stephan Mandt. "Progressive Compression with Universally Quantized Diffusion Models." The Thirteenth International Conference on Learning Representations.

[A3] He, Jiajun, et al. "RECOMBINER: Robust and Enhanced Compression with Bayesian Implicit Neural Representations." The Twelfth International Conference on Learning Representations.

[A4] Shah, Abhin, et al. "Optimal compression of locally differentially private mechanisms." International Conference on Artificial Intelligence and Statistics. PMLR, 2022.

[A5] Liu, Yanxiao, et al. "Universal exact compression of differentially private mechanisms." Advances in Neural Information Processing Systems 37 (2024): 91492-91531.

[A6] Kim, Heasung, Hyeji Kim, and Gustavo De Veciana. "Clustered federated learning via gradient-based partitioning." Forty-first international conference on machine learning. 2024.

[A7] Ballé, Johannes, et al. "Variational image compression with a scale hyperprior." International Conference on Learning Representations. 2018.