The stakes are higher than they might first appear. Privacy regulations such as the European Union’s General Data Protection Regulation grant individuals a Right to be Forgotten, and similar obligations exist under the California Consumer Privacy Act. When a participant in a federated system demands erasure, the operator cannot simply delete the client’s local files; the fingerprints of that data persist in the aggregated global model. Membership inference attacks and gradient reconstruction attacks have demonstrated that such residual traces can leak sensitive information. In security-sensitive settings the problem is even more acute: a single malicious or poisoned client can corrupt a jointly trained fraud detection model, and eliminating its influence becomes essential to restoring the model’s reliability. In both scenarios, the removal must be complete, not approximate.

The gold-standard solution, retraining from scratch with the remaining clients, does achieve exact unlearning, because a model trained only on the surviving data is provably independent of the departed client’s dataset. But the cost is prohibitive. Federated training typically runs for hundreds to a thousand communication rounds, and restarting the process introduces significant deployment delays. Worse, the random initialization that begins a fresh training run can lead to severe performance degradation, particularly when the remaining client population is small or heterogeneous. For time-sensitive applications, from fraud detection to medical imaging, waiting days for a retrained model is simply not an option. This gap between the guarantees of retraining and the practical need for immediacy is precisely where the new work positions itself.

The first of the two proposed algorithms, Bi-Models Training, takes a surprisingly simple approach. During the normal federated training process, each client maintains an isolated local copy of the model that is trained only on its own data, alongside its participation in the shared global training. These local copies are never mixed with anyone else’s data, so their influence sets contain exactly one client each. When a client later requests to be forgotten, the server simply discards every stored state influenced by that client and uses the remaining clients’ isolated local models to provide a strong initialization for the post-unlearning global model. Instead of starting from random weights, the recovered model starts from weights that already encode useful knowledge learned by the surviving participants, dramatically shortening the recovery phase and improving final accuracy.

Bi-Models Training, however, treats each client in isolation, which means it cannot capture how the influence of multiple clients is jointly entangled in the global model. This is where Multi-Models Training, the paper’s centerpiece, departs from convention. Rather than training a single global model, the server orchestrates a carefully constructed set of sub-federated models, each trained on a disjoint subset of clients. Because the subsets do not overlap, no client’s influence spreads across multiple sub-models, and the influence structure of the entire system can be represented as a tree whose leaves are the individual clients. When a client must be removed, the algorithm identifies the most influential models that remain unaffected by that client and aggregates them to reinitialize the global model, guaranteeing that the departed client’s data plays no role in the result.

One of the most striking theoretical contributions of the paper is the connection it draws between the design of these influence trees and a classic result from information theory. The authors prove that the expected number of models that must be aggregated after an unlearning event, a quantity they call the influence-dependent storage cost, is minimized when the tree of sub-models is constructed according to Huffman coding, the same greedy algorithm used to build optimal prefix-free compression codes. In other words, the optimal way to partition clients into disjoint training groups mirrors the optimal way to assign short binary codewords to frequent symbols. This unexpected bridge between compression theory and federated unlearning gives the method a principled foundation rather than a heuristic one, and it allows the system to exploit known probabilities about which clients are likely to request erasure.

The guarantees of exactness are established formally. The authors model training as a composition of deterministic primitives, including initialization, copying, optimizer resets, local training on a dataset, and server aggregation. They define the influence set of any model state as the set of clients whose data could have affected it, and they prove that a model state’s value depends on the training data only through this influence set. The unlearning procedure then discards every stored state whose influence set contains the departing client, aggregates the retained states, and continues training only on the remaining clients’ data. Because the departing client is never reintroduced into any influence set, the final deployed model is provably invariant to any replacement of that client’s dataset, which is precisely the formal definition of exact unlearning. Notably, the framework is compatible with arbitrary federated learning protocols, so it does not require modifying the underlying aggregation rules.

Memory efficiency is another decisive advantage. An earlier exact approach, Exact-Fun, stores auxiliary models for every communication round, and with typical federated training spanning one hundred to one thousand rounds this becomes extremely memory-inefficient, and in the authors’ experiments with Llama-3.2 language models, outright infeasible. By contrast, the storage cost of both Bi-Models Training and Multi-Models Training depends only on the number of clients, making them well suited to cross-silo deployments involving ten to one hundred participants, such as consortia of hospitals or financial institutions. The authors even arranged their evaluation order to disadvantage their own method, ensuring that the global model could not simply be replaced by a single sub-model and had to be reconstructed through aggregation, a choice that strengthens the credibility of their reported gains.

The empirical results span both vision and language tasks. On image classification benchmarks including CIFAR-10, Fashion-MNIST, and datasets evaluated with VGG-style convolutional networks, as well as language tasks including language identification and multilingual sentiment classification drawn from public Hugging Face datasets and experiments fine-tuning Llama-3.2, Bi-Models Training consistently outperformed existing exact unlearning baselines. Multi-Models Training went further, achieving more than a twofold improvement in post-unlearning performance while maintaining the exact unlearning guarantee. The comparison baselines included approaches such as FedEraser, Exact-Fun, and federated unlearning via weight negation, alongside the retraining-from-scratch reference point. The consistent pattern across tasks suggests that the benefit stems from the initialization strategy itself rather than from any quirk of a particular dataset or architecture.

The implications reach well beyond the immediate technical contribution. As federated learning spreads through healthcare, open banking, mobile keyboards, and recommendation systems, the ability to honor erasure requests instantly, and to surgically excise poisoned participants from security-critical models, is becoming a baseline requirement rather than a luxury. The work also highlights a subtle vulnerability: unlearning systems themselves can be targets, with recent research demonstrating data reconstruction attacks specifically aimed at federated unlearning procedures. By making exactness a structural property of the training process rather than a post-hoc repair, the new algorithms close a gap that approximate methods leave open. The research, supported by Singapore’s National Research Foundation and the Singapore-MIT Alliance for Research and Technology, suggests a future in which the right to be forgotten and the demand for high-performing collaborative models are no longer in tension, but are satisfied simultaneously by design.

Subject of Research: Exact federated unlearning algorithms that remove a client's influence from collaboratively trained models while improving post-unlearning performance

Article Title: MMT: Achieving Exact Federated Unlearning with Improved Post-unlearning Performance

Article References: MMT: Achieving Exact Federated Unlearning with Improved Post-unlearning Performance. (n.d.). https://doi.org/10.1007/s10994-026-07117-8

Image Credits: AI Generated

DOI: 10.1007/s10994-026-07117-8

Keywords: federated learning, machine unlearning, exact unlearning, data privacy, GDPR, Huffman coding, model poisoning, Llama-3.2, influence trees, Machine Learning journal, federated protocols, post-unlearning performance

The central idea behind the research is deceptively simple: instead of relying on a single compression algorithm, chain two complementary techniques so that each one exploits the weaknesses left behind by the other. The first stage of both proposed schemes is a technique called Rounding Intensity Followed by Dividing, or RIFD, which was previously introduced by the same author in 2016. RIFD is a lossy operation that reduces the bit depth of an image by rounding pixel intensity values and then dividing them, which collapses many nearly identical gray levels into single representative values. This deliberate quantization shrinks the alphabet of symbols that the subsequent lossless coder has to handle, and it simultaneously reshapes the statistical distribution of those symbols, creating strong redundancies that entropy coders can harvest efficiently.

The two schemes differ in what happens after RIFD has done its work. The first, designated HLL1, feeds the preprocessed image into the Lossless Method of Decomposing Huffman Trees, abbreviated LM-DH, a technique first described by Alkhalayleh and Otair in 2015. Classical Huffman coding, invented by David Huffman in 1952, assigns shorter binary codes to more frequent symbols, but building and storing a single large Huffman tree for an image with many distinct intensity values can itself consume considerable space. LM-DH addresses this by decomposing the Huffman tree into smaller subtrees, which reduces the overhead of transmitting the coding table and improves the overall compression ratio. The second scheme, HLL2, pairs RIFD with the Lempel-Ziv-Welch algorithm, or LZW, the dictionary-based coder that Terry Welch derived from the foundational 1977 work of Jacob Ziv and Abraham Lempel and published in 1984. LZW builds a dictionary of recurring symbol sequences on the fly, so it needs no explicit code table to be sent alongside the compressed data.

To evaluate the two pipelines, the author ran experiments on a dataset of 20 standard test images spanning three common formats: 8-bit grayscale, 16-bit grayscale, and 24-bit RGB color. All processing was performed in MATLAB R2021b, a standard environment for image processing research, and the benchmark images were drawn from widely used public collections, including the CLIC dataset from the Challenge on Learned Image Compression, the USC-SIPI Image Database, the Kodak True Color Image Suite, and the Set11 collection of grayscale images used in reconstruction and compression studies. Using established public benchmarks matters, because it allows other researchers to reproduce the numbers and compare the new schemes directly against both classical baselines and modern learned codecs.

The headline result concerns how much better the hybrid schemes perform than their own lossless components alone. HLL1 produced an average improvement in compression ratio, measured as an ICR value, of 0.20 over the RIFD plus Huffman baseline, meaning that decomposing the Huffman tree into subtrees consistently squeezed out additional savings beyond what conventional Huffman coding could achieve on the same preprocessed data. HLL2 delivered an even more striking figure on the 8-bit grayscale datasets, where pairing RIFD with LZW yielded an average improvement of 73 percent. The author attributes this to the way RIFD’s bit-depth reduction creates long runs of repeated intensity values, precisely the kind of repetitive structure that dictionary-based LZW coding converts into short dictionary references.

Just as important as the size reductions is what the schemes do not cost in quality. Because the second stage of each pipeline is strictly lossless, it introduces no additional distortion whatsoever beyond the RIFD preprocessing step. In other words, once the image has been rounded and divided, every subsequent operation is perfectly reversible, so the decoded image is an exact replica of the preprocessed version. The perceptual integrity of the image is therefore determined entirely by how aggressive the RIFD quantization is, giving practitioners a single, tunable knob for balancing file size against visual fidelity. The study reports that the proposed techniques dramatically shrink file sizes without sacrificing perceptual quality, which makes them candidates for bandwidth-constrained and storage-limited environments where every kilobyte counts.

The work situates itself within a long tradition of hybrid compression research. Earlier studies have combined the discrete wavelet transform with set partitioning techniques and Huffman encoding, and medical imaging researchers have stacked linear predictive coding, wavelet transforms, and Huffman coding to compress clinical scans. More recently, the field has been transformed by learned compression, in which neural networks are trained end to end to transform and entropy-code images, with systems such as variational models with scale hyperpriors, discretized Gaussian mixture likelihoods with attention modules, unevenly grouped space-channel contextual adaptive coding, and latent diffusion approaches for compression all pushing the state of the art. Against this backdrop, the appeal of the new schemes is their computational simplicity: RIFD, Huffman tree decomposition, and LZW all involve elementary arithmetic and table lookups rather than deep network inference, which makes them attractive for hardware with tight power and processing budgets.

The technical logic of why the hybrids work is worth unpacking. Lossless entropy coders are bounded by the entropy of their input: the more skewed and repetitive the symbol distribution, the fewer bits per symbol they need. A raw 8-bit grayscale image often uses most of its 256 possible values with a relatively flat distribution, which limits any lossless coder working alone. RIFD deliberately flattens fine distinctions between neighboring intensities, concentrating probability mass on a smaller set of representative values. For Huffman-style coding, this means shorter average code lengths and, with LM-DH, a smaller tree structure to serialize. For dictionary coding, it means the same intensity values recur in predictable spatial patterns, so the LZW dictionary fills with long, frequently reused phrases. The lossy step thus acts as an amplifier for the lossless stage, and the two designs test two different ways of cashing in that amplification.

The practical implications reach across several domains. Telemedicine systems transmitting diagnostic images over rural networks, remote sensing platforms downlinking satellite imagery, digital archives preserving vast image collections, and consumer services serving billions of photos all face the same trade-off between bandwidth, storage cost, and image fidelity. A method that can be tuned by adjusting a single quantization parameter, that runs quickly on ordinary hardware, and that guarantees no hidden loss beyond the explicitly chosen quantization offers a predictable and auditable alternative to opaque neural codecs. The fact that the study used only public datasets, including CLIC, USC-SIPI, Kodak, and Set11, and performed all experiments in a widely available MATLAB release further lowers the barrier for independent verification and adoption.

There are, of course, boundaries to what the study claims. The reported gains are averages over 20 standard test images in three bit-depth formats, and performance on any particular image class, such as noisy medical scans or highly textured natural photographs, would need separate validation. The comparison baselines are the author’s own RIFD plus Huffman configuration rather than the newest learned codecs, so the schemes should be understood as an efficient classical alternative rather than a replacement for state-of-the-art neural compression at the very highest performance frontier. Nevertheless, the paper demonstrates a clear and reproducible principle: a carefully designed lossy preprocessing step can unlock substantial extra performance from decades-old lossless algorithms, and the choice of the lossless partner, whether a decomposed Huffman tree or an adaptive LZW dictionary, meaningfully shapes where the biggest wins appear. As image volumes continue to explode, such pragmatic hybrids may prove that some of the best new tools for an old problem are clever recombinations of proven ones.

Subject of Research: Hybrid lossy-lossless image compression using RIFD preprocessing with Huffman tree decomposition and LZW coding

Article Title: Hybrid image compression techniques based on RIFD with LM-DH and LZW

Article References: Otair, M. (2026). Hybrid image compression techniques based on RIFD with LM-DH and LZW. Multimedia Tools and Applications, 85(9), Article 741. https://doi.org/10.1007/s11042-026-21902-6

Image Credits: AI Generated

DOI: 10.1007/s11042-026-21902-6

Keywords: image compression, hybrid compression, RIFD, Huffman coding, LM-DH, LZW, lossless coding, lossy compression, entropy coding, MATLAB, grayscale images, Multimedia Tools and Applications