Lethe: Multifaceted Approaches to Erasure

• Lethe is a recurrent label for systems that implement controlled forgetting, deletion, or information erasure across diverse domains such as machine learning, database management, simulation, and astronomy.
• In federated unlearning, Lethe introduces a three-stage Reshape–Rectify–Restore pipeline that minimizes knowledge resurfacing to below 1% by decoupling forgotten and retained information.
• In data systems and simulations, Lethe underpins delete-aware compaction and adaptive load balancing to enhance performance, privacy, and operational efficiency.

to=arxiv_search.search 东臣 საქმე 大发娱乐 શોધ_query code {"query":"Lethe arXiv (Tan et al., 30 Jan 2026) federated unlearning Lethe-DEM (Sarkar et al., 2020, Minaei et al., 2017, Tong et al., 3 Aug 2025, Chen et al., 28 Aug 2025, Sohn et al., 2016)", "max_results": 10} to=arxiv_search.search 天天众արկել code {"query":"ti:Lethe OR abs:Lethe", "max_results": 20} to=arxiv_search.search авази code {"query":"(Tan et al., 30 Jan 2026)", "max_results": 5} to=arxiv_search.search 天天中彩票足彩 code {"query":"(Chakraborty et al., 31 Mar 2026)", "max_results": 5} Lethe denotes several distinct research entities across machine learning, database systems, computational mechanics, and astronomy. In recent arXiv literature, the most prominent usage is a federated unlearning method, “Lethe: Adapter-Augmented Dual-Stream Update for Persistent Knowledge Erasure in Federated Unlearning,” which targets persistent erasure under continued training rather than only immediate post-unlearning behavior (Tan et al., 30 Jan 2026). The same name also identifies a tunable delete-aware LSM engine (Sarkar et al., 2020), a deletion-concealment mechanism for social platforms (Minaei et al., 2017), an open-source CFD/DEM software framework and its DEM module (Golshan et al., 2021, Saavedra et al., 2022), a large-language-model backdoor defense (Chen et al., 28 Aug 2025), a vision-transformer unlearning method (Tong et al., 3 Aug 2025), an online data-poisoning technique called Lethean Attack (Perry, 2020), and a stellar stream measured with the Hubble Space Telescope (Sohn et al., 2016).

1. Research uses of the name

The literature does not treat Lethe as a single concept. Rather, it is a recurrent label attached to technically unrelated systems whose common thread is often forgetting, deletion, erasure, or obscured absence. This suggests a semantic convergence at the level of metaphor rather than methodology.

Usage	Domain	Defining feature
Lethe	Federated unlearning	Persistent knowledge erasure under continued training
Lethe	LSM storage engine	Tunable delete persistence latency and secondary-key range deletes
Lethe	Social-platform privacy	Intermittent withdrawals to conceal true deletions
Lethe / Lethe-DEM	CFD and DEM	Open-source parallel simulation with load balancing
LETHE / LetheViT / Lethean Attack	ML security and unlearning	Backdoor purification, selective forgetting, catastrophic forgetting induction
Lethe stream	Astronomy	Kinematically cold stellar stream candidate population

A further distinction is that some usages are system names anchored in operational mechanisms, such as the LSM engine and the federated-unlearning protocol, whereas others are proper names inherited by an astronomical object or by a software framework that later acquires domain-specific modules (Sarkar et al., 2020, Golshan et al., 2021, Sohn et al., 2016).

2. Persistent federated unlearning

In federated learning, Lethe is a method for persistent knowledge erasure after client-level, class-level, or sample-level removal requests. Its central claim is that most prior federated unlearning methods analyze only the immediate unlearning phase and neglect the case in which federated training continues on the remaining data. The paper identifies the resulting failure mode as knowledge resurfacing: erased influence can reappear because gradients from the remaining data remain positively correlated with the erased-data gradient, formalized in Proposition 4.1 as

$E_t \langle g_u, g_{r,t} \rangle > p > 0$

where $g_u$ is the gradient of the unlearned set and $g_{r,t}$ is the gradient on remaining data at round $t$ (Tan et al., 30 Jan 2026).

Lethe addresses this with a three-stage Reshape–Rectify–Restore pipeline. In Reshape, a temporary lightweight adapter is attached to the server model’s backbone, the backbone is frozen, and the adapter is trained by gradient ascent on the unlearning set $D_u$:

$$\phi^* \leftarrow \phi^* + \nu \nabla_\phi L(w, \phi; D_u).$$

This produces a probe direction encoding what should be forgotten. In Rectify, the frozen adapter is plugged into the model and two update streams are computed: a forget stream producing a reference direction $\Delta u$ on $D_u$, and a retain stream producing $\Delta r$ from the remaining clients. Lethe then performs layer-wise rectification using cosine-similarity gating:

$$\tilde{\Delta}^{(l)} = \begin{cases} \Delta r^{(l)} - \gamma \Delta u^{(l)} & \text{if } \text{sim}^{(l)} > 0 \ -\Delta u^{(l)} & \text{if } \text{sim}^{(l)} < 0 \end{cases}$$

followed by the global update

$g_u$0

In Restore, the adapter is discarded and a short recovery stage is run on the retained data (Tan et al., 30 Jan 2026).

The method’s significance lies in its explicit attempt to de-correlate knowledge to be unlearned from knowledge to be retained. Empirically, the paper reports Resurfacing Rate <1% in most cases, near-zero resurfacing across client-, class-, and sample-level settings, and continued updates that remain near-orthogonal to the rollback vector with cosine similarity below $g_u$1. Ablations reported in the paper state that removing the adapter, rectification, or layer-wise gating increases resurfacing rate or requires many more communication rounds. The authors also report that keeping the adapter after unlearning gives no benefit, arguing against the interpretation that the method merely relocates the forgotten knowledge into an auxiliary module (Tan et al., 30 Jan 2026).

3. Deletion, concealment, and inference control in data systems

In database systems, Lethe names a delete-aware LSM engine designed around the proposition that deletes should be treated as a first-class systems concern. The engine introduces FADE, a family of delete-aware compaction policies, and KiWi, a physical layout that interleaves sort-key and delete-key order. FADE assigns a time-to-live to files containing tombstones using level-dependent thresholds,

$g_u$2

with $g_u$3, so that delete persistence latency is bounded by a user-specified threshold. KiWi introduces delete tiles whose pages are sorted by a secondary delete key, enabling secondary range deletes by dropping entire pages rather than rewriting the full tree. The paper reports higher read throughput of $g_u$4–$g_u$5, lower space amplification of $g_u$6–$g_u$7, and a modest write-amplification increase of $g_u$8–$g_u$9 (Sarkar et al., 2020).

A different Lethe appears in social-platform privacy. There, the mechanism is intermittent withdrawals: non-deleted posts alternate between public UP periods and temporary DOWN periods, while deleted posts enter a permanent DOWN state. UP durations are sampled from a geometric distribution and DOWN durations from a negative binomial distribution. The privacy objective is to make an observer uncertain whether an absent post is truly deleted or merely withdrawn. The paper reports deletion privacy for up to 3 months while maintaining content availability as high as 95% and adversarial precision at 20%, with the adversary overwhelmed by false positives (Minaei et al., 2017).

These systems are explicitly connected by later work on inference-aware deletion. That paper distinguishes logical deletion, physical deletion, and semantic deletion, and frames meaningful deletion as a bound on what remains inferable from the residual visible state $g_{r,t}$0 and the deletion pattern $g_{r,t}$1:

$g_{r,t}$2

Its comparison categorizes Lethe the LSM engine as a physical-layer mechanism addressing timeliness and storage visibility, while emphasizing that dependencies, views, caches, and deletion footprints require broader semantic controls. A plausible implication is that the storage-engine Lethe solves only one layer of a larger deletion stack, whereas semantic deletion requires joint control of both residual-state leakage and pattern leakage (Chakraborty et al., 31 Mar 2026).

4. Lethe as a simulation framework

In computational mechanics, Lethe is an open-source high-order adaptive CFD framework for incompressible flows, and Lethe-DEM is its parallel discrete element module. Lethe-DEM supports two-dimensional and three-dimensional DEM simulations, uses deal.II infrastructure with p4est-based partitioning, and implements dynamic or periodic load balancing based on

$g_{r,t}$3

with $g_{r,t}$4 the local particle count, $g_{r,t}$5 the local cell count, and typically $g_{r,t}$6. The module’s strong and weak scaling studies show that load balancing can increase parallel efficiency by approximately 25–70% depending on the granular simulation, that the best scalability is obtained for $g_{r,t}$7, and that a three-dimensional cylindrical silo with $g_{r,t}$8 was simulated on 320 cores (Golshan et al., 2021).

The broader Lethe framework is also used for implicit large-eddy simulation of turbulent flow over periodic hills. In that setting it solves the incompressible Navier–Stokes equations with stabilized continuous finite elements, equal-order $g_{r,t}$9 interpolation, SUPG/PSPG stabilization, and an implicit BDF2 time integrator. The periodic-hills study at $t$0, $t$1, and $t$2 reports good accuracy for average velocities and Reynolds stresses, fewer degrees of freedom than reference numerical solutions, and reattachment-point predictions that approach the experimental benchmark as the mesh is refined (Saavedra et al., 2022).

A later additive-manufacturing study uses Lethe’s DEM capabilities to reproduce multi-layer powder spreading. That work reports a sudden increase in packing density beyond layers 5 to 10, reproduces the four regimes observed experimentally—first-layer effect, plateau, densification, and decrease in packing density—and attributes densification to the growth and merger of wall-induced static zones. The amplitude and onset layer of densification are reported to correlate with the spacing of the vertical walls delimiting the powder-spreading region (Gaboriault et al., 30 Sep 2025).

5. Forgetting, unlearning, and adversarial manipulation in machine learning

Beyond federated learning, the Lethe name appears in several ML methods centered on forgetting. Lethean Attack is an online data-poisoning technique for test-time training. Its mechanism is to induce catastrophic forgetting by feeding samples for which the gradients of the main loss and the auxiliary self-supervised loss become negatively correlated:

$t$3

In the paper’s CIFAR-10 experiments with a ResNet-18 two-head architecture, rotated training images are used to construct the poisoning sequence, and the reported effect is that test-time training can be driven back to coin-flip accuracy with a short sample sequence (Perry, 2020).

LetheViT addresses selective machine unlearning for vision transformers. The paper’s central observation is that masking high-attention areas preserves recognition capability while weakening memorization ability. It therefore combines attention-guided masking with a contrastive objective in which masked forget samples act as positives and original forget samples as negatives. The reported outcome is state-of-the-art performance in random data forgetting for ViTs, with ablations indicating that masking the top-5% attended patches yields the best trade-off between memorization reduction and recognition preservation (Tong et al., 3 Aug 2025).

A different LETHE targets backdoored LLMs through knowledge dilution. Its internal mechanism trains a clean model on a lightweight clean dataset using LoRA and merges it with the backdoored model, with SLERP as the default merge strategy. Its external mechanism extracts keywords by TextRank and augments prompts with benign, semantically relevant evidence:

$t$4

The paper reports that LETHE outperforms 8 state-of-the-art baselines against 8 backdoor attacks across 5 widely used LLMs and can reduce the attack success rate of advanced backdoor attacks by up to 98% while maintaining model utility (Chen et al., 28 Aug 2025).

Related work that does not use the Lethe name directly but occupies the same technical neighborhood is L2F (Learn to Forget) for meta-learning. L2F introduces task- and layer-wise attenuation of the shared MAML initialization through multiplicative masks $t$5, reporting improvements such as miniImageNet 5-way 5-shot ResNet12 accuracy from 68.26% to 74.68% and tieredImageNet from 71.24% to 77.61%. This suggests that “forgetting” has become a general design principle spanning privacy, adaptation, and robustness, even when the Lethe label itself is absent (Baik et al., 2019).

6. The Lethe stellar stream

In astronomy, Lethe denotes a stellar stream rather than a computational method. Hubble Space Telescope proper-motion measurements in the ORPH-F4 field identified three candidate Lethe stars using combined color–magnitude and proper-motion criteria. The stars are consistent with a 12 Gyr, [Fe/H] = -1.5 isochrone at a distance of approximately 12 kpc, and cluster near $t$6 mas yr$t$7. The measured average proper motion is

$t$8

with intrinsic one-dimensional velocity dispersion

$t$9

After correcting for solar reflex motion, the net motion indicates that Lethe is moving northeast on the sky (Sohn et al., 2016).

The paper interprets the stream as kinematically cold and argues that the low velocity dispersion is consistent with globular cluster debris. It further states that these are the first direct proper motion measurements for Lethe stream stars, providing new orbital constraints and supporting earlier proposals regarding the stream’s progenitor (Sohn et al., 2016).

7. Comparative interpretation

Taken together, the various Lethe systems define a cross-domain vocabulary of removal. In federated learning, the removed object is client-, class-, or sample-level influence; in storage engines, it is key-value state and tombstone persistence; in social-platform privacy, it is the observability of deletion itself; in ViTs and meta-learning, it is sample-specific or initialization-specific information; in LLM security, it is malicious backdoor behavior; and in astronomy, Lethe is simply a named stellar stream.

This distribution suggests two major meanings. First, Lethe often labels mechanisms that attempt to make prior information operationally unavailable without destroying system utility. Second, the same name does not imply methodological continuity: adapter-based rectification in federated unlearning, delete-aware compaction in LSM trees, intermittent withdrawals in social platforms, and knowledge dilution in LLM purification solve different problems at different abstraction layers. A common misconception would therefore be to treat “Lethe” as a single research program. The literature instead supports a narrower conclusion: it is a recurrent naming pattern attached to technically heterogeneous work whose unifying motif is forgetting, deletion, or the suppression of recoverable influence.