NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

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Adjust Pearson's $r$ to Measure Arbitrary Monotone Dependence

Xinbo Ai

展开摘要

Pearson's $r$, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research challenges this notion, suggesting that Pearson's $r$ should not be ruled out a priori for measuring nonlinear monotone relationships. Pearson's $r$ is essentially a scaled covariance, rooted in the renowned Cauchy-Schwarz Inequality. Our findings reveal that different scaling bounds yield coefficients with different capture ranges, and interestingly, tighter bounds actually expand these ranges. We derive a tighter inequality than Cauchy-Schwarz Inequality, leverage it to refine Pearson's $r$, and propose a new correlation coefficient, i.e., rearrangement correlation. This coefficient is able to capture arbitrary monotone relationships, both linear and nonlinear ones. It reverts to Pearson's $r$ in linear scenarios. Simulation experiments and real-life investigations show that the rearrangement correlation is more accurate in measuring nonlinear monotone dependence than the three classical correlation coefficients, and other recently proposed dependence measures.

Poster
Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization

Nicola Bariletto, Nhat Ho

展开摘要

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample performance due to distributional uncertainty. In the spirit of distributionally robust optimization, we propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet process) theory and a recent decision-theoretic model of smooth ambiguity-averse preferences. First, we highlight novel connections with standard regularized empirical risk minimization techniques, among which Ridge and LASSO regressions. Then, we theoretically demonstrate the existence of favorable finite-sample and asymptotic statistical guarantees on the performance of the robust optimization procedure. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet process representations. We also show that the smoothness of the criterion naturally leads to standard gradient-based numerical optimization. Finally, we provide insights into the workings of our method by applying it to a variety of tasks based on simulated and real datasets.

Poster
Stratified Prediction-Powered Inference for Effective Hybrid Evaluation of Language Models

Adam Fisch, Joshua Maynez, R. Alex Hofer, Bhuwan Dhingra, Amir Globerson, William W. Cohen

展开摘要

Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. PPI achieves this by combining small amounts of human-labeled data with larger amounts of data labeled by a reasonably accurate---but potentially biased---automatic system, in a way that results in tighter confidence intervals for certain parameters of interest (e.g., the mean performance of a language model). In this paper, we propose a method called Stratified Prediction-Powered Inference (StratPPI), in which we show that the basic PPI estimates can be considerably improved by employing simple data stratification strategies. Without making any assumptions on the underlying automatic labeling system or data distribution, we derive an algorithm for computing provably valid confidence intervals for parameters of any dimensionality that is based on stratified sampling. In particular, we show both theoretically and empirically that, with appropriate choices of stratification and sample allocation, our approach can provide substantially tighter confidence intervals than unstratified approaches. Specifically, StratPPI is expected to improve in cases where the performance of the autorater varies across different conditional distributions of the target data.

Poster
Unified Insights: Harnessing Multi-modal Data for Phenotype Imputation via View Decoupling

Qiannan Zhang, Weishen Pan, Zilong Bai, Chang Su, Fei Wang

展开摘要

Phenotype imputation plays a crucial role in improving comprehensive and accurate medical evaluation, which in turn can optimize patient treatment and bolster the reliability of clinical research. Despite the adoption of various techniques, multi-modal biological data, which can provide crucial insights into a patient's overall health, is often overlooked. With multi-modal biological data, patient characterization can be enriched from two distinct views: the biological view and the phenotype view. However, the heterogeneity and imprecise nature of the multimodal data still pose challenges in developing an effective method to model from two views. In this paper, we propose a novel framework to incorporate multi-modal biological data via view decoupling. Specifically, we segregate the modeling of biological data from phenotype data in a graph-based learning framework. From the biological view, the latent factors in biological data are discovered to model patient correlation. From the phenotype view, phenotype co-occurrence can be modeled to reveal patterns across patients. Then patients are encoded from these two distinct views. To mitigate the influence of noise and irrelevant information in biological data, we devise a cross-view contrastive knowledge distillation aimed at distilling insights from the biological view to enhance phenotype imputation. We show that phenotype imputation with the proposed model significantly outperforms the state-of-the-art models on the real-world biomedical database.

Poster
On the Expressivity and Sample Complexity of Node-Individualized Graph Neural Networks

Paolo Pellizzoni, Till Hendrik Schulz, Dexiong Chen, Karsten Borgwardt

展开摘要

Graph neural networks (GNNs) employing message passing for graph classification are inherently limited by the expressive power of the Weisfeiler-Leman (WL) test for graph isomorphism. Node individualization schemes, which assign unique identifiers to nodes (e.g., by adding random noise to features), are a common approach for achieving universal expressiveness. However, the ability of GNNs endowed with individualization schemes to generalize beyond the training data is still an open question. To address this question, this paper presents a theoretical analysis of the sample complexity of such GNNs from a statistical learning perspective, employing Vapnik–Chervonenkis (VC) dimension and covering number bounds. We demonstrate that node individualization schemes that are permutation-equivariant result in lower sample complexity, and design novel individualization schemes that exploit these results. As an application of this analysis, we also develop a novel architecture that can perform substructure identification (i.e., subgraph isomorphism) while having a lower VC dimension compared to competing methods. Finally, our theoretical findings are validated experimentally on both synthetic and real-world datasets.

Poster
Offline Behavior Distillation

Shiye Lei, Sen Zhang, Dacheng Tao

展开摘要

Massive reinforcement learning (RL) data are typically collected to train policies offline without the need for interactions, but the large data volume can cause training inefficiencies. To tackle this issue, we formulate offline behavior distillation (OBD), which synthesizes limited expert behavioral data from sub-optimal RL data, enabling rapid policy learning. We propose two naive OBD objectives, DBC and PBC, which measure distillation performance via the decision difference between policies trained on distilled data and either offline data or a near-expert policy. Due to intractable bi-level optimization, the OBD objective is difficult to minimize to small values, which deteriorates PBC by its distillation performance guarantee with quadratic discount complexity $\mathcal{O}(1/(1-\gamma)^2)$. We theoretically establish the equivalence between the policy performance and action-value weighted decision difference, and introduce action-value weighted PBC (Av-PBC) as a more effective OBD objective. By optimizing the weighted decision difference, Av-PBC achieves a superior distillation guarantee with linear discount complexity $\mathcal{O}(1/(1-\gamma))$. Extensive experiments on multiple D4RL datasets reveal that Av-PBC offers significant improvements in OBD performance, fast distillation convergence speed, and robust cross-architecture/optimizer generalization.

Poster
SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion

Lu Han, Xu-Yang Chen, Han-Jia Ye, De-Chuan Zhan

展开摘要

Multivariate time series forecasting plays a crucial role in various fields such as finance, traffic management, energy, and healthcare. Recent studies have highlighted the advantages of channel independence to resist distribution drift but neglect channel correlations, limiting further enhancements. Several methods utilize mechanisms like attention or mixer to address this by capturing channel correlations, but they either introduce excessive complexity or rely too heavily on the correlation to achieve satisfactory results under distribution drifts, particularly with a large number of channels. Addressing this gap, this paper presents an efficient MLP-based model, the Series-cOre Fused Time Series forecaster (SOFTS), which incorporates a novel STar Aggregate-Redistribute (STAR) module. Unlike traditional approaches that manage channel interactions through distributed structures, \textit{e.g.}, attention, STAR employs a centralized strategy to improve efficiency and reduce reliance on the quality of each channel. It aggregates all series to form a global core representation, which is then dispatched and fused with individual series representations to facilitate channel interactions effectively. SOFTS achieves superior performance over existing state-of-the-art methods with only linear complexity. The broad applicability of the STAR module across different forecasting models is also demonstrated empirically. We have made our code publicly available at https://github.com/Secilia-Cxy/SOFTS.

Poster
Make-it-Real: Unleashing Large Multimodal Model for Painting 3D Objects with Realistic Materials

Ye Fang, Zeyi Sun, Tong Wu, Jiaqi Wang, Ziwei Liu, Gordon Wetzstein, Dahua Lin

展开摘要

Physically realistic materials are pivotal in augmenting the realism of 3D assets across various applications and lighting conditions. However, existing 3D assets and generative models often lack authentic material properties. Manual assignment of materials using graphic software is a tedious and time-consuming task. In this paper, we exploit advancements in Multimodal Large Language Models (MLLMs), particularly GPT-4V, to present a novel approach, Make-it-Real: 1) We demonstrate that GPT-4V can effectively recognize and describe materials, allowing the construction of a detailed material library. 2) Utilizing a combination of visual cues and hierarchical text prompts, GPT-4V precisely identifies and aligns materials with the corresponding components of 3D objects. 3) The correctly matched materials are then meticulously applied as reference for the new SVBRDF material generation according to the original albedo map, significantly enhancing their visual authenticity. Make-it-Real offers a streamlined integration into the 3D content creation workflow, showcasing its utility as an essential tool for developers of 3D assets.

Poster
Self-supervised Transformation Learning for Equivariant Representations

Jaemyung Yu, Jaehyun Choi, Dong-Jae Lee, HyeongGwon Hong, Junmo Kim

展开摘要

Unsupervised representation learning has significantly advanced various machine learning tasks. In the computer vision domain, state-of-the-art approaches utilize transformations like random crop and color jitter to achieve invariant representations, embedding semantically the same inputs despite transformations. However, this can degrade performance in tasks requiring precise features, such as localization or flower classification. To address this, recent research incorporates equivariant representation learning, which captures transformation-sensitive information. However, current methods depend on transformation labels and thus struggle with interdependency and complex transformations. We propose Self-supervised Transformation Learning (STL), replacing transformation labels with transformation representations derived from image pairs. The proposed method ensures transformation representation is image-invariant and learns corresponding equivariant transformations, enhancing performance without increased batch complexity. We demonstrate the approach’s effectiveness across diverse classification and detection tasks, outperforming existing methods in 7 out of 11 benchmarks and excelling in detection. By integrating complex transformations like AugMix, unusable by prior equivariant methods, this approach enhances performance across tasks, underscoring its adaptability and resilience. Additionally, its compatibility with various base models highlights its flexibility and broad applicability. The code is available at https://github.com/jaemyung-u/stl.

Poster
Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models

Regev Cohen, Idan Kligvasser, Ehud Rivlin, Daniel Freedman

展开摘要

The pursuit of high perceptual quality in image restoration has driven the development of revolutionary generative models, capable of producing results often visually indistinguishable from real data. However, as their perceptual quality continues to improve, these models also exhibit a growing tendency to generate hallucinations – realistic-looking details that do not exist in the ground truth images. Hallucinations in these models create uncertainty about their reliability, raising major concerns about their practical application. This paper investigates this phenomenon through the lens of information theory, revealing a fundamental tradeoff between uncertainty and perception. We rigorously analyze the relationship between these two factors, proving that the global minimal uncertainty in generative models grows in tandem with perception. In particular, we define the inherent uncertainty of the restoration problem and show that attaining perfect perceptual quality entails at least twice this uncertainty. Additionally, we establish a relation between distortion, uncertainty and perception, through which we prove the aforementioned uncertainly-perception tradeoff induces the well-known perception-distortion tradeoff. We demonstrate our theoretical findings through experiments with super-resolution and inpainting algorithms. This work uncovers fundamental limitations of generative models in achieving both high perceptual quality and reliable predictions for image restoration. Thus, we aim to raise awareness among practitioners about this inherent tradeoff, empowering them to make informed decisions and potentially prioritize safety over perceptual performance.

Poster
Pin-Tuning: Parameter-Efficient In-Context Tuning for Few-Shot Molecular Property Prediction

Liang Wang, Qiang Liu, Shaozhen Liu, Xin Sun, Shu Wu

展开摘要

Molecular property prediction (MPP) is integral to drug discovery and material science, but often faces the challenge of data scarcity in real-world scenarios. Addressing this, few-shot molecular property prediction (FSMPP) has been developed. Unlike other few-shot tasks, FSMPP typically employs a pre-trained molecular encoder and a context-aware classifier, benefiting from molecular pre-training and molecular context information. Despite these advancements, existing methods struggle with the ineffective fine-tuning of pre-trained encoders. We attribute this issue to the imbalance between the abundance of tunable parameters and the scarcity of labeled molecules, and the lack of contextual perceptiveness in the encoders. To overcome this hurdle, we propose a parameter-efficient in-context tuning method, named Pin-Tuning. Specifically, we propose a lightweight adapter for pre-trained message passing layers (MP-Adapter) and Bayesian weight consolidation for pre-trained atom/bond embedding layers (Emb-BWC), to achieve parameter-efficient tuning while preventing over-fitting and catastrophic forgetting. Additionally, we enhance the MP-Adapters with contextual perceptiveness. This innovation allows for in-context tuning of the pre-trained encoder, thereby improving its adaptability for specific FSMPP tasks. When evaluated on public datasets, our method demonstrates superior tuning with fewer trainable parameters, improving few-shot predictive performance.

Poster
Offline Oracle-Efficient Learning for Contextual MDPs via Layerwise Exploration-Exploitation Tradeoff

Jian Qian, Haichen Hu, David Simchi-Levi

展开摘要

Motivated by the recent discovery of a statistical and computational reduction from contextual bandits to offline regression \citep{simchi2020bypassing}, we address the general (stochastic) Contextual Markov Decision Process (CMDP) problem with horizon $H$ (as known as CMDP with $H$ layers). In this paper, we introduce a reduction from CMDPs to offline density estimation under the realizability assumption, i.e., a model class $\mathcal{M}$ containing the true underlying CMDP is provided in advance. We develop an efficient, statistically near-optimal algorithm requiring only $O(H \log T)$ calls to an offline density estimation algorithm (or oracle) across all $T$ rounds. This number can be further reduced to $O(H \log \log T)$ if $T$ is known in advance. Our results mark the first efficient and near-optimal reduction from CMDPs to offline density estimation without imposing any structural assumptions on the model class. A notable feature of our algorithm is the design of a layerwise exploration-exploitation tradeoff tailored to address the layerwise structure of CMDPs. Additionally, our algorithm is versatile and applicable to pure exploration tasks in reward-free reinforcement learning.

Poster
FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learning

Tristan Cinquin, Marvin Pförtner, Vincent Fortuin, Philipp Hennig, Robert Bamler

展开摘要

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of the weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinite-dimensional function spaces, we recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant (as is the case in many scientific inference tasks). At the same time, it stays competitive for black-box supervised learning problems, where neural networks typically excel.

Poster
Learning from Pattern Completion: Self-supervised Controllable Generation

Zhiqiang Chen, Guofan Fan, Jinying Gao, Lei Ma, Bo Lei, Tiejun Huang, Shan Yu

展开摘要

The human brain exhibits a strong ability to spontaneously associate different visual attributes of the same or similar visual scene, such as associating sketches and graffiti with real-world visual objects, usually without supervising information. In contrast, in the field of artificial intelligence, controllable generation methods like ControlNet heavily rely on annotated training datasets such as depth maps, semantic segmentation maps, and poses, which limits the method’s scalability. Inspired by the neural mechanisms that may contribute to the brain’s associative power, specifically the cortical modularization and hippocampal pattern completion, here we propose a self-supervised controllable generation (SCG) framework. Firstly, we introduce an equivariance constraint to promote inter-module independence and intra-module correlation in a modular autoencoder network, thereby achieving functional specialization. Subsequently, based on these specialized modules, we employ a self-supervised pattern completion approach for controllable generation training. Experimental results demonstrate that the proposed modular autoencoder effectively achieves functional specialization, including the modular processing of color, brightness, and edge detection, and exhibits brain-like features including orientation selectivity, color antagonism, and center-surround receptive fields. Through self-supervised training, associative generation capabilities spontaneously emerge in SCG, demonstrating excellent zero-shot generalization ability to various tasks such as superresolution, dehaze and associative or conditional generation on painting, sketches, and ancient graffiti. Compared to the previous representative method ControlNet, our proposed approach not only demonstrates superior robustness in more challenging high-noise scenarios but also possesses more promising scalability potential due to its self-supervised manner. Codes are released on Github and Gitee.

Poster
Rethinking The Training And Evaluation of Rich-Context Layout-to-Image Generation

Jiaxin Cheng, Zixu Zhao, Tong He, Tianjun Xiao, Zheng Zhang, Yicong Zhou

展开摘要

Recent advancements in generative models have significantly enhanced their capacity for image generation, enabling a wide range of applications such as image editing, completion and video editing. A specialized area within generative modeling is layout-to-image (L2I) generation, where predefined layouts of objects guide the generative process. In this study, we introduce a novel regional cross-attention module tailored to enrich layout-to-image generation. This module notably improves the representation of layout regions, particularly in scenarios where existing methods struggle with highly complex and detailed textual descriptions. Moreover, while current open-vocabulary L2I methods are trained in an open-set setting, their evaluations often occur in closed-set environments. To bridge this gap, we propose two metrics to assess L2I performance in open-vocabulary scenarios. Additionally, we conduct a comprehensive user study to validate the consistency of these metrics with human preferences.

Poster
Adversarially Trained Weighted Actor-Critic for Safe Offline Reinforcement Learning

Honghao Wei, Xiyue Peng, Arnob Ghosh, Xin Liu

展开摘要

We propose WSAC (Weighted Safe Actor-Critic), a novel algorithm for Safe Offline Reinforcement Learning (RL) under functional approximation, which can robustly optimize policies to improve upon an arbitrary reference policy with limited data coverage. WSAC is designed as a two-player Stackelberg game to optimize a refined objective function. The actor optimizes the policy against two adversarially trained value critics with small importance-weighted Bellman errors, which focus on scenarios where the actor's performance is inferior to the reference policy. In theory, we demonstrate that when the actor employs a no-regret optimization oracle, WSAC achieves a number of guarantees: $(i)$ For the first time in the safe offline RL setting, we establish that WSAC can produce a policy that outperforms {\bf any} reference policy while maintaining the same level of safety, which is critical to designing a safe algorithm for offline RL. $(ii)$ WSAC achieves the optimal statistical convergence rate of $1/\sqrt{N}$ to the reference policy, where $N$ is the size of the offline dataset. $(iii)$ We theoretically show that WSAC guarantees a safe policy improvement across a broad range of hyperparameters that control the degree of pessimism, indicating its practical robustness. Additionally, we offer a practical version of WSAC and compare it with existing state-of-the-art safe offline RL algorithms in several continuous control environments. WSAC outperforms all baselines across a range of tasks, supporting the theoretical results.

Poster
Identifiability Analysis of Linear ODE Systems with Hidden Confounders

Yuanyuan Wang, Biwei Huang, Wei Huang, Xi Geng, Mingming Gong

展开摘要

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time $t$. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

Poster
Twin-Merging: Dynamic Integration of Modular Expertise in Model Merging

Zhenyi Lu, Chenghao Fan, Wei Wei, Xiaoye Qu, Dangyang Chen, Yu Cheng

展开摘要

In the era of large language models, model merging is a promising way to combine multiple task-specific models into a single multitask model without extra training. However, two challenges remain: (a) interference between different models and (b) heterogeneous data during testing. Traditional model merging methods often show significant performance gaps compared to fine-tuned models due to these issues. Additionally, a one-size-fits-all model lacks flexibility for diverse test data, leading to performance degradation. We show that both shared and exclusive task-specific knowledge are crucial for merging performance, but directly merging exclusive knowledge hinders overall performance. In view of this, we propose Twin-Merging, a method that encompasses two principal stages: (1) modularizing knowledge into shared and exclusive components, with compression to reduce redundancy and enhance efficiency; (2) dynamically merging shared and task-specific knowledge based on the input. This approach narrows the performance gap between merged and fine-tuned models and improves adaptability to heterogeneous data. Extensive experiments on $20$ datasets for both language and vision tasks demonstrate the effectiveness of our method, showing an average improvement of $28.34\%$ in absolute normalized score for discriminative tasks and even surpassing the fine-tuned upper bound on the generative tasks.

Poster
DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models

Hengkang Wang, Xu Zhang, Taihui Li, Yuxiang Wan, Tiancong Chen, Ju Sun

展开摘要

Pretrained diffusion models (DMs) have recently been popularly used in solving inverse problems (IPs). The existing methods mostly interleave iterative steps in the reverse diffusion process and iterative steps to bring the iterates closer to satisfying the measurement constraint. However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility) and fit the measurement (i.e., measurement feasibility), especially for nonlinear IPs. Moreover, their capabilities to deal with noisy IPs with unknown types and levels of measurement noise are unknown. In this paper, we advocate viewing the reverse process in DMs as a function and propose a novel plug-in method for solving IPs using pretrained DMs, dubbed DMPlug. DMPlug addresses the issues of manifold feasibility and measurement feasibility in a principled manner, and also shows great potential for being robust to unknown types and levels of noise. Through extensive experiments across various IP tasks, including two linear and three nonlinear IPs, we demonstrate that DMPlug consistently outperforms state-of-the-art methods, often by large margins especially for nonlinear IPs.

Poster
SwitchHead: Accelerating Transformers with Mixture-of-Experts Attention

Róbert Csordás, Piotr Piękos, Kazuki Irie, Jürgen Schmidhuber

展开摘要

Despite many recent works on Mixture of Experts (MoEs) for resource-efficient Transformer language models, existing methods mostly focus on MoEs for feedforward layers. Previous attempts at extending MoE to the self-attention layer fail to match the performance of the parameter-matched baseline. Our novel SwitchHead is an effective MoE method for the attention layer that successfully reduces both the compute and memory requirements, achieving wall-clock speedup, while matching the language modeling performance of the baseline Transformer. Our novel MoE mechanism allows SwitchHead to compute up to 8 times fewer attention matrices than the standard Transformer. SwitchHead can also be combined with MoE feedforward layers, resulting in fully-MoE "SwitchAll" Transformers. For our 262M parameter model trained on C4, SwitchHead matches the perplexity of standard models with only 44% compute and 27% memory usage. Zero-shot experiments on downstream tasks confirm the performance of SwitchHead, e.g., achieving more than 3.5% absolute improvements on BliMP compared to the baseline with an equal compute resource.

Poster