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General Machine Learning · Transfer, Multitask and Meta-learning

Kotaro Yoshida, Yuji Naraki, Takafumi Horie, Ryotaro Shimizu, Ioannis Mitliagkas, Hiroki Naganuma

Model merging has emerged as an efficient and flexible paradigm for multi-task learning, with numerous methods being proposed in recent years. However, these state-of-the-art techniques are typically evaluated on benchmark suites that are highly favorable to model merging, and their robustness in more realistic settings remains largely unexplored. In this work, we first investigate the vulnerabilities of model-merging methods and pinpoint the source-model characteristics that critically underlie them. Specifically, we identify two factors that are particularly harmful to the merging process: (1) disparities in task vector norms, and (2) the low confidence of the source models. To address this issue, we propose **DisTaC** (**Dis**tillation for **Ta**sk vector **C**onditioning), a novel method that pre-conditions these problematic task vectors before the merge. DisTaC leverages knowledge distillation to adjust a task vector's norm and increase source-model confidence while preserving its essential task-specific knowledge. Our extensive experiments demonstrate that by pre-conditioning task vectors with DisTaC, state-of-the-art merging techniques can successfully integrate models that exhibit these harmful traits, where they would otherwise fail, and achieve significant performance gains.

General Machine Learning · Transfer, Multitask and Meta-learning

Akash Gupta, Amos Storkey, Mirella Lapata

Large Multimodal Models (LMMs) often rely on in-context learning (ICL) to perform new visual question answering (VQA) tasks with minimal supervision. However, ICL performance, especially in smaller LMMs, does not always improve monotonically when increasing the number of examples. We hypothesize that this happens because the LMM is overwhelmed by extraneous information in the image embeddings that is irrelevant to the downstream task. To address this, we propose a meta-learning approach that induces few-shot capabilities in LMMs through a fixed set of soft prompts distilled from task-relevant visual features, which are adapted at test time using a small number of examples. We facilitate this distillation through an attention-mapper module that can be easily integrated with any LMM architecture and is jointly learned with soft prompts. Evaluation on the VL-ICL Bench shows that our method successfully achieves task adaptation in low-data regimes with just a few gradient steps, outperforming ICL by 21.2%. Comparisons with parameter-efficient finetuning methods demonstrate that meta-learning further enhances this adaptation by 7.7% for various VQA tasks.

General Machine Learning · Transfer, Multitask and Meta-learning

Hengyu Luo, Raúl Vázquez, Timothee Mickus, Filip Ginter, Jörg Tiedemann

Concerns have been raised that knowledge distillation may transfer test-set knowledge from a contaminated teacher to a clean student---a "data laundering" effect that potentially threatens evaluation integrity. In this paper, we assess the severity of this phenomenon. If these concerns regarding data laundering are minor, then distillation could be used to mitigate risks of direct data exposure. Across eight classification benchmarks, we find that substantial laundering is the exception rather than the rule: unlike the large performance gains from direct contamination, any accuracy inflation from laundering is consistently smaller and statistically insignificant in all but two cases. More broadly, using sample-level analysis, we find that the two phenomena are weakly correlated, suggesting that laundering is not simply a diluted form of contamination but a distinct effect that arises primarily when benchmarks exhibit large train–test distribution gaps. Motivated by this, we conduct controlled experiments that systematically enlarge the train–test distance on two benchmarks where laundering was initially negligible, and observe that laundering becomes more significant as the gap widens. Taken together, our results indicate that knowledge distillation, despite rare benchmark-specific residues, can be expected to function as an effective decontamination technique that largely mitigates test-data leakage.

General Machine Learning · Transfer, Multitask and Meta-learning

Divyam Madaan, Sumit Chopra, Kyunghyun Cho

Machine learning (ML) models often struggle to maintain performance under distribution shifts, leading to inaccurate predictions on unseen future data. In this work, we investigate whether and under what conditions models can achieve such a generalization when relying solely on past data. We explore two primary approaches: convex combinations of past model parameters (parameter interpolation) and explicit extrapolation beyond the convex hull of past parameters (parameter extrapolation). We benchmark several methods within these categories on a diverse set of temporal tasks, including language modeling, news summarization, news tag prediction, academic paper categorization, satellite image-based land use classification over time, and historical yearbook photo gender prediction. Our empirical findings show that none of the evaluated methods consistently outperforms the simple baseline of using the latest available model parameters in all scenarios. In the absence of access to future data or robust assumptions about the underlying data-generating process, these results underscore the inherent difficulties of generalizing and extrapolating to future data and warrant caution when evaluating claims of such generalization.

General Machine Learning · Transfer, Multitask and Meta-learning

Chanhyuk Lee, Jiho Choi, Chanryeol Lee, Donggyun Kim, Seunghoon Hong

Model merging has emerged as a promising approach for unifying independently fine-tuned models into an integrated framework, significantly enhancing computational efficiency in multi-task learning. Recently, several SVD-based techniques have been introduced to exploit low-rank structures for enhanced merging, but their reliance on heuristically designed rank selection often leads to inter-task interference and suboptimal performance. In this paper, we propose **AdaRank**, a model merging framework that replaces this heuristic selection by adaptively selecting the beneficial singular components of task vectors to merge multiple models. We first show empirically that **(i)** selecting only the top singular components of task vectors can cause critical interference with other tasks, and **(ii)** assigning fixed ranks does not align with the varying complexity of tasks and layers. AdaRank addresses both issues by adapting per-component masks, indicating the selection of the component, to the unlabeled test data with entropy minimization. Our experimental findings show that AdaRank consistently improves existing merging methods across diverse backbones from different modalities, largely narrowing the performance gap against individually fine-tuned models.

General Machine Learning · Transfer, Multitask and Meta-learning

Fuli Qiao, Mehrdad Mahdavi

Parameter-efficient continual learning has emerged as a promising approach for large language models (LLMs) to mitigate catastrophic forgetting while enabling adaptation to new tasks. Current Low-Rank Adaptation (LoRA) continual learning techniques often retain and freeze previously learned LoRAs or generate data representations to overcome forgetting, typically utilizing these to support new LoRAs learn new tasks. However, these methods not only ignore growing computational memory with tasks and limited storage space but also suffer from potential task interference due to the lack of effective LoRA merging mechanisms. In this paper, we propose a novel continual learning method that orthogonally initializes and sequentially merges LoRAs updates into a single unified LoRA. Our method leverages orthogonal basis extraction from previously learned LoRA to initialize the learning of new tasks, further exploits the intrinsic asymmetry property of LoRA components by using a time-aware scaling mechanism to balance new and old knowledge during continual merging. Our approach maintains constant memory complexity with respect to the number of tasks, minimizes interference between past and new tasks via orthogonal basis initialization, and improves performance over asymmetric LoRA merging via adaptive scaling. We provide theoretical analysis to justify our design and conduct extensive experiments across diverse continual learning benchmarks using various LLMs, demonstrating the effectiveness and efficiency of our method.

General Machine Learning · Transfer, Multitask and Meta-learning

Emily Xiao, Yixiao Zeng, Ada Chen, Chin-Jou Li, Amanda Bertsch, Graham Neubig

A popular method to adapt large language models (LLMs) to new tasks is in-context learning (ICL), which is effective but incurs high inference costs as context length grows. In this paper we propose a method to perform instruction induction, where we take training examples and reduce them to a compact but descriptive prompt that can achieve performance comparable to ICL over the full training set. Specifically, we propose Prompt-MII, a reinforcement learning (RL) based framework to meta-learn an instruction induction model that can generate compact instructions on the fly for an arbitrary new dataset. We train on over 3,000 diverse classification datasets from the HuggingFace hub, and evaluate on 90 unseen tasks. Prompt-MII improves downstream model quality by 4-9 F1 points (10-20\% relative), matching ICL performance while requiring 3-13x fewer tokens.

General Machine Learning · Transfer, Multitask and Meta-learning

Siqi Wang, Aoming Liu, Bryan Plummer

Methods addressing Learning with Noisy Labels (LNL) and multi-source Domain Generalization (DG) use training techniques to improve downstream task performance in the presence of label noise or domain shifts, respectively. Prior work often explores these tasks in isolation, and the limited work that does investigate their intersection, which we refer to as Noise-Aware Generalization (NAG), only benchmarks existing methods without also proposing an approach to reduce its effect. We find that this is likely due, in part, to the new challenges that arise when exploring NAG, which does not appear in LNL or DG alone. For example, we show that the effectiveness of DG methods is compromised in the presence of label noise, making them largely ineffective. Similarly, LNL methods often overfit to easy-to-learn domains as they confuse domain shifts for label noise. Instead, we propose Domain Labels for Noise Detection (DL4ND), the first direct method developed for NAG which uses our observation that noisy samples that may appear indistinguishable within a single domain often show greater variation when compared across domains. We find DL4ND outperforms DG and LNL methods, including their combinations, even when simplifying the NAG challenge by using domain labels to isolate domain shifts from noise. Performance gains up to 12.5% over seven diverse datasets with three noise types demonstrates DL4ND’s ability to generalize to a wide variety of settings.

General Machine Learning · Transfer, Multitask and Meta-learning

Jackson Harmon, Andreas Hochlehnert, Matthias Bethge, Ameya Prabhu

Scaled post‑training now drives many of the largest capability gains in language models (LMs), yet its effect on pretrained knowledge remains poorly understood. Not all forgetting is equal: Forgetting one fact (e.g., a U.S. president or an API call) does not “average out” when recalling another. Hence, we propose a sample-wise paradigm to measure what is forgotten and when backward transfer occurs. Our metric counts 1→0 transitions (correct before post‑training, incorrect after) to quantify forgetting and 0→1 transitions to quantify backward transfer. Traditional task averages conflate these effects and obscure large changes. For multiple‑choice benchmarks, we add chance‑adjusted variants that subtract the expected contribution of random guessing from pre‑ and post‑training accuracies. We apply this framework across post‑training stages, model sizes, and data scales. Our large‑scale analysis across nearly 30 model pairs and 100 sub-benchmarks with up to 32,768 generated tokens per sample shows that: (1) Domain-continual pretraining induces moderate forgetting with low-to-moderate backward transfer; (2) RL/SFT post-training applied to base models and instruction tuning yields moderate-to-large backward transfer on math and logic with overall low-to-moderate forgetting; (3) Applying RL/SFT to instruction‑tuned models is sensitive on data scale: at small scales, both forgetting and backward transfer are small; at larger scales, effects are mixed and warrant further study with better controls; (4) Model merging does not reliably mitigate forgetting. Overall, our framework offers a practical yardstick for mapping how post‑training alters pretrained knowledge at scale -- enabling progress towards generally capable AI systems.

General Machine Learning · Transfer, Multitask and Meta-learning

Philipp Mondorf, Shijia Zhou, Monica Riedler, Barbara Plank

Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their knowledge to novel compositional scenarios, revealing notable limitations in systematic generalization. There has been an ongoing debate about whether neural networks possess the capacity for systematic generalization, with recent studies suggesting that meta-learning approaches designed for compositionality can significantly enhance this ability. However, these insights have largely been confined to linguistic problems, leaving their applicability to other tasks an open question. In this study, we extend meta-learning for compositionality to the domain of abstract spatial reasoning. To this end, we introduce $\textit{Compositional-ARC}\textemdash{}$a dataset designed to evaluate the capacity of models to systematically generalize from known geometric transformations (e.g., translation, rotation) of abstract two-dimensional objects to novel combinations of these transformations (e.g., translation+rotation). Our results show that a small transformer-based encoder-decoder model, trained via meta-learning for compositionality, can systematically generalize to previously unseen transformation compositions. Notably, despite having only 5.7M parameters, this model significantly outperforms state-of-the-art LLMs$\textemdash{}$including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior$\textemdash{}$and performs on par with the winning model of the ARC prize 2024, an 8B-parameter LLM trained via test-time training. Our findings highlight the effectiveness of meta-learning in promoting systematicity beyond linguistic tasks, suggesting a promising direction toward more robust and generalizable models.

General Machine Learning · Transfer, Multitask and Meta-learning

Qingyuan Liu, Jia-Chen Gu, Yunzhi Yao, Hong Wang, Nanyun (Violet) Peng

Large language models (LLMs) require constant updates to remain aligned with evolving real-world knowledge. Model editing offers a lightweight alternative to retraining, but sequential editing that updates the LLM knowledge through multiple successive edits often destabilizes representations and induces catastrophic forgetting. In this work, we seek to better understand and mitigate performance degradation caused by sequential editing. We hypothesize that hyperspherical uniformity, a property that maintains uniform distribution of neuron weights on a hypersphere, helps the model remain stable, retain prior knowledge, while still accommodate new updates. We use Hyperspherical Energy (HE) to quantify neuron uniformity during editing, and examine its correlation with editing performance. Empirical studies across widely used editing methods reveals a strong correlation between HE dynamics and editing performance, with editing failures consistently coinciding with uncontrolled HE fluctuations. We further theoretically prove that HE dynamics impose a lower bound on the degradation of pretrained knowledge, highlighting why HE stability is crucial for knowledge retention. Motivated by these insights, we propose SPHERE (Sparse Projection for Hyperspherical Energy-Regularized Editing), an HE-driven regularization strategy that stabilizes neuron weight distributions, ultimately preserving prior knowledge while enabling reliable sequential updates. Specifically, SPHERE identifies a sparse space complementary to the principal hyperspherical directions of the pretrained weight matrices and projects new knowledge onto it, attenuating perturbations on the principal directions. Extensive experiments on LLaMA3 (8B) and Qwen2.5 (7B) show that SPHERE outperforms the best baseline in editing capability by an average of 16.41%, while most faithfully preserving general model performance, thereby offering a principled path toward reliable large-scale knowledge editing.

General Machine Learning · Transfer, Multitask and Meta-learning

Weiduo Liao, Fei Han, Hisao Ishibuchi, Qingfu Zhang, Ying Wei

Vision learners often struggle with catastrophic forgetting due to their reliance on class recognition by comparison, rather than understanding classes as compositions of representative concepts. This limitation is prevalent even in state-of-the-art continual learners with foundation models and worsens when current tasks contain few classes. Inspired by the recent success of concept-level understanding in mitigating forgetting, we design a universal framework CompSLOT to guide concept learning across diverse continual learners. Leveraging the progress of object-centric learning in parsing semantically meaningful slots from images, we tackle the challenge of learning slot extraction from ImageNet-pretrained vision transformers by analyzing meaningful concept properties. We further introduce a primitive selection and aggregation mechanism to harness concept-level image understanding. Additionally, we propose a method-agnostic self-supervision approach to distill sample-wise concept-based similarity information into the classifier, reducing reliance on incorrect or partial concepts for classification. Experiments show CompSLOT significantly enhances various continual learners and provides a universal concept-level module for the community.

General Machine Learning · Transfer, Multitask and Meta-learning

Alexander Murphy, Michal Danilowski, Soumyajit Chatterjee, Abhirup Ghosh

Test-Time Adaptation (TTA) methods are often computationally expensive, require a large amount of data for effective adaptation, or are brittle to hyperparameters. Based on a theoretical foundation of the geometry of the latent space, we are able to significantly improve the alignment between source and distribution-shifted samples by re-centering target data embeddings at the origin. This insight motivates NEO – a hyperparameter-free fully TTA method, that adds no significant compute compared to vanilla inference. NEO is able to improve the classification accuracy of ViT-Base on ImageNet-C from 55.6\% to 59.2\% after adapting on just one batch of 64 samples. When adapting on 512 samples NEO beats all 7 TTA methods we compare against on ImageNet-C, ImageNet-R and ImageNet-S and beats 6/7 on CIFAR-10-C, while using the least amount of compute. NEO performs well on model calibration metrics and additionally is able to adapt from 1 class to improve accuracy on 999 other classes in ImageNet-C. On Raspberry Pi and Jetson Orin Nano devices, NEO reduces inference time by 63\% and memory usage by 9\% compared to baselines. Our results based on 3 ViT architectures and 4 datasets show that NEO can be used efficiently and effectively for TTA.

General Machine Learning · Transfer, Multitask and Meta-learning

Gregory De Ruyter, Mathias Verbeke, Hans Hallez

Neural Architecture Search (NAS), particularly gradient-based techniques, has proven highly effective in automating the design of neural networks. Recent work has extended NAS to hardware-aware settings, aiming to discover architectures that are both accurate and computationally efficient. Many existing methods integrate hardware metrics into the optimization objective as regularization terms, which introduces differentiability requirements and hyperparameter tuning challenges. This can either result in overly penalizing resource-intensive architectures or architectures failing to meet the hardware constraints of the target device. To address these challenges, we propose ConNAS, a novel gradient-based NAS framework that enforces hardware constraints directly through gradient modification. This approach eliminates the need for differentiable hardware metrics and regularization weights. The novelty in ConNAS lies in modifying gradients with respect to architectural choices, steering the search away from infeasible architectures while ensuring constraint satisfaction. Evaluations on the NATS-Bench benchmark demonstrate that ConNAS consistently discovers architectures that meet the imposed hardware constraints while achieving performance within just 0.14% of the optimal feasible architecture. Additionally, in a practical deployment scenario, ConNAS outperforms handcrafted architectures by up to 1.55% in accuracy under tight hardware budgets. Our code is publicly available at https://gitlab.kuleuven.be/m-group-campus-brugge/distrinet_public/connas.

General Machine Learning · Transfer, Multitask and Meta-learning

Yiyun Zhou, Jingwei Shi, Mingjing Xu, Zhonghua Jiang, Jingyuan Chen

Knowledge Distillation (KD) has emerged as a powerful technique for model compression, enabling lightweight student networks to benefit from the performance of redundant teacher networks. However, the inherent capacity gap often limits the performance of student networks. Inspired by the expressiveness of pretrained teacher networks, a compelling research question arises: is there a type of network that can not only inherit the teacher’s structure but also maximize the inheritance of its knowledge? Furthermore, how does the performance of such an inheriting network compare to that of student networks, all benefiting from the same teacher network? To further explore this question, we propose InherNet, a neural network inheritance method that performs asymmetric low-rank decomposition on the teacher’s weights and reconstructs a lightweight yet expressive network without significant architectural disruption. By leveraging Singular Value Decomposition (SVD) for initialization to ensure the inheritance of principal knowledge, InherNet effectively balances depth, width, and compression efficiency. Experimental results across unimodal and multimodal tasks demonstrate that InherNet achieves higher performance compared to student networks of similar parameter sizes. Our findings reveal a promising direction for future research in efficient model compression beyond traditional distillation.

General Machine Learning · Transfer, Multitask and Meta-learning

Anh Hoang, Van Cuong Pham, Trung Le, Jianfei Cai, Thanh-Toan Do

Diffusion models have shown remarkable performance in image synthesis by progressively estimating a smooth transition from a Gaussian distribution of noise to a real image. Unfortunately, their practical deployment is limited by slow inference speed, high memory usage, and the computational demands of the noise estimation process. Post-training quantization (PTQ) emerges as a promising solution to accelerate sampling and reduce the memory overhead of diffusion models. Existing PTQ methods for diffusion models typically apply uniform weights to calibration samples across timesteps, which is sub-optimal since data at different timesteps may contribute differently to the diffusion process. Additionally, due to varying activation distributions and gradients across timesteps, a uniform quantization approach is sub-optimal. Each timestep requires a different gradient direction for optimal quantization, and treating them equally can lead to conflicting gradients that degrade performance. In this paper, we propose a novel PTQ method that addresses these challenges by assigning appropriate weights to calibration samples. Specifically, our approach learns to assign optimal weights to calibration samples to align the quantized model’s gradients across timesteps, facilitating the quantization process. Extensive experiments on CIFAR-10, LSUN-Bedrooms, and ImageNet datasets demonstrate the superiority of our method compared to other PTQ methods for diffusion models.

General Machine Learning · Transfer, Multitask and Meta-learning

Zhanwang Liu, Yuting Li, Haoyuan Gao, Yexin Li, Linghe Kong, Lichao Sun, Weiran Huang

Catastrophic forgetting, the tendency of neural networks to forget previously learned knowledge when learning new tasks, has been a major challenge in continual learning (CL). To tackle this challenge, CL methods have been proposed and shown to reduce forgetting. Furthermore, CL models deployed in mission-critical settings can benefit from uncertainty awareness by calibrating their predictions to reliably assess their confidences. However, existing uncertainty-aware continual learning methods suffer from high computational overhead and incompatibility with mainstream replay methods. To address this, we propose idempotent experience replay (IDER), a novel approach based on the idempotent property where repeated function applications yield the same output. Specifically, we first adapt the training loss to make model idempotent on current data streams. In addition, we introduce an idempotence distillation loss. We feed the output of the current model back into the old checkpoint and then minimize the distance between this reprocessed output and the original output of the current model. This yields a simple and effective new baseline for building reliable continual learners, which can be seamlessly integrated with other CL approaches. Extensive experiments on different CL benchmarks demonstrate that IDER consistently improves prediction reliability while simultaneously boosting accuracy and reducing forgetting. Our results suggest the potential of idempotence as a promising principle for deploying efficient and trustworthy continual learning systems in real-world applications. Our code is available at https://github.com/YutingLi0606/Idempotent-Continual-Learning.

General Machine Learning · Transfer, Multitask and Meta-learning

Divyat Mahajan

Structural Causal Models (SCMs) offer a principled framework to reason about interventions and support out-of-distribution generalization, which are key goals in scientific discovery. However, the task of learning SCMs from observed data poses formidable challenges, and often requires training a separate model for each dataset. In this work, we propose an amortized inference framework that trains a single model to predict the causal mechanisms of SCMs conditioned on their observational data and causal graph. We first use a transformer-based architecture for amortized learning of dataset embeddings, and then extend the Fixed-Point Approach (FiP) to infer the causal mechanisms conditionally on their dataset embeddings. As a byproduct, our method can generate observational and interventional data from novel SCMs at inference time, without updating parameters. Empirical results show that our amortized procedure performs on par with baselines trained specifically for each dataset on both in and out-of-distribution problems, and also outperforms them in scare data regimes.

General Machine Learning · Transfer, Multitask and Meta-learning

Yehan Zhang, Huaidong Zhang, Xuandi Luo, Shengfeng He

Healthcare insurance fraud detection presents unique machine learning challenges: labeled data are scarce due to delayed verification processes, and fraudulent behaviors evolve rapidly, often manifesting in complex, graph-structured interactions. Existing methods struggle in such settings. Pretraining routines typically overlook structural anomalies under limited supervision, while online models often fail to adapt to changing fraud patterns without labeled updates. To address these issues, we propose the Continual Fiedler Vector Graph model (ConFVG), a fraud detection framework designed for label-scarce and non-stationary environments. The framework comprises two key components. To mitigate label scarcity, we develop a Fiedler Vector-guided graph autoencoder that leverages spectral graph properties to learn structure-aware node representations. The Fiedler Vector, derived from the second smallest eigenvalue of the graph Laplacian, captures global topological signals such as community boundaries and connectivity bottlenecks, which are patterns frequently associated with collusive fraud. This enables the model to identify structurally anomalous nodes without relying on labels. To handle evolving graph streams, we propose a Subgraph Attention Fusion (SAF) module that constructs neighborhood subgraphs and applies attention-based reweighting to emphasize emerging high-risk structures. This design allows the model to adapt to new fraud patterns in real time. A Mean Teacher mechanism further stabilizes online updates and prevents forgetting of previously acquired knowledge. Experiments on real-world medical fraud datasets demonstrate that the Continual Fiedler Vector Graph model outperforms state-of-the-art baselines in both low-label and distribution-shift scenarios, offering a scalable and structure-sensitive solution for real-time fraud detection.

General Machine Learning · Transfer, Multitask and Meta-learning

Yilang Zhang, Abraham Jaeger Mountain, Bingcong Li, Georgios B Giannakis

Meta-learning offers a principled framework leveraging *task-invariant* priors from related tasks, with which *task-specific* models can be fine-tuned on downstream tasks, even with limited data records. Gradient-based meta-learning (GBML) relies on gradient descent (GD) to adapt the prior to a new task. Albeit effective, these methods incur high computational overhead that scales linearly with the number of GD steps. To enhance efficiency and scalability, existing methods approximate the gradient of prior parameters (meta-gradient) via truncated backpropagation, yet suffer large approximation errors. Targeting accurate approximation, this work puts forth binomial GBML (BinomGBML), which relies on a truncated binomial expansion for meta-gradient estimation. This novel expansion endows more information in the meta-gradient estimation via efficient parallel computation. As a running paradigm applied to model-agnostic meta-learning (MAML), the resultant BinomMAML provably enjoys error bounds that not only improve upon existing approaches, but also decay super-exponentially under mild conditions. Numerical tests corroborate the theoretical analysis and showcase boosted performance with slightly increased computational overhead.