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Deep Learning · Theory

Quinn Fisher, Haoming Meng, Vardan Papyan

Mixup is a data augmentation strategy that employs convex combinations of training instances and their respective labels to improve the robustness and calibration of deep neural networks. Despite its widespread adoption, the nuanced mechanisms that underpin its success are not entirely understood. The observed phenomenon of Neural Collapse, where the last-layer activations and classifier of deep networks converge to a simplex equiangular tight frame (ETF), provides a compelling motivation to explore whether mixup induces alternative geometric configurations and whether those could explain its success. In this study, we delve into the last-layer activations of training data for deep networks subjected to mixup, aiming to uncover insights into its operational efficacy. Our investigation, spanning various architectures and dataset pairs, reveals that mixup's last-layer activations predominantly converge to a distinctive configuration different than one might expect. In this configuration, activations from mixed-up examples of identical classes align with the classifier, while those from different classes delineate channels along the decision boundary. These findings are unexpected, as mixed-up features are not simple convex combinations of feature class means (as one might get, for example, by training mixup with the mean squared error loss). By analyzing this distinctive geometric configuration, we elucidate the mechanisms by which mixup enhances model calibration. To further validate our empirical observations, we conduct a theoretical analysis under the assumption of an unconstrained features model, utilizing the mixup loss. Through this, we characterize and derive the optimal last-layer features under the assumption that the classifier forms a simplex ETF.

Reinforcement Learning

Philip Amortila, Dylan Foster, Nan Jiang, Ayush Sekhari, Tengyang Xie

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of *density ratio modeling*, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start.In this work we show---perhaps surprisingly---that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as *coverability* (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2023) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

Reinforcement Learning · Batch/Offline

Zhilong Zhang, Yihao Sun, Junyin Ye, Tian-Shuo Liu, Jiaji Zhang, Yang Yu

Offline preference-based reinforcement learning (PbRL) offers an effective solution to overcome the challenges associated with designing rewards and the high costs of online interactions. In offline PbRL, agents are provided with a fixed dataset containing human preferences between pairs of trajectories. Previous studies mainly focus on recovering the rewards from the preferences, followed by policy optimization with an off-the-shelf offline RL algorithm. However, given that preference label in PbRL is inherently trajectory-based, accurately learning transition-wise rewards from such label can be challenging, potentially leading to misguidance during subsequent offline RL training. To address this issue, we introduce our method named $\textit{Flow-to-Better (FTB)}$, which leverages the pairwise preference relationship to guide a generative model in producing preferred trajectories, avoiding Temporal Difference (TD) learning with inaccurate rewards. Conditioning on a low-preference trajectory, $\textit{FTB}$ uses a diffusion model to generate a better one with a higher preference, achieving high-fidelity full-horizon trajectory improvement. During diffusion training, we propose a technique called $\textit{Preference Augmentation}$ to alleviate the problem of insufficient preference data. As a result, we surprisingly find that the model-generated trajectories not only exhibit increased preference and consistency with the real transition but also introduce elements of $\textit{novelty}$ and $\textit{diversity}$, from which we can derive a desirable policy through imitation learning. Experimental results on D4RL benchmarks demonstrate that FTB achieves a remarkable improvement compared to state-of-the-art offline PbRL methods. Furthermore, we show that FTB can also serve as an effective data augmentation method for offline RL.

Applications · Language, Speech and Dialog

Zeyu Liu, Gourav Datta, Anni Li, Peter Beerel

Transformer models have demonstrated high accuracy in numerous applications but have high complexity and lack sequential processing capability making them ill-suited for many streaming applications at the edge where devices are heavily resource-constrained. Thus motivated, many researchers have proposed reformulating the transformer models as RNN modules which modify the self-attention computation with explicit states. However, these approaches often incur significant performance degradation.The ultimate goal is to develop a model that has the following properties: parallel training, streaming and low-cost inference, and state-of-the-art (SOTA) performance. In this paper, we propose a new direction to achieve this goal. We show how architectural modifications to a fully-sequential recurrent model can help push its performance toward Transformer models while retaining its sequential processing capability. Specifically, inspired by the recent success of Legendre Memory Units (LMU) in sequence learning tasks, we propose LMUFormer, which augments the LMU with convolutional patch embedding and convolutional channel mixer. Moreover, we present a spiking version of this architecture, which introduces the benefit of states within the patch embedding and channel mixer modules while simultaneously reducing the computing complexity. We evaluated our architectures on multiple sequence datasets. Of particular note is our performance on the Speech Commands V2 dataset (35 classes). In comparison to SOTA transformer-based models within the ANN domain, our LMUFormer demonstrates comparable performance while necessitating a remarkable $70\times$ reduction in parameters and a substantial $140\times$ decrement in FLOPs. Furthermore, when benchmarked against extant low-complexity SNN variants, our model establishes a new SOTA with an accuracy of 96.12\%. Additionally, owing to our model's proficiency in real-time data processing, we are able to achieve a 32.03\% reduction in sequence length, all while incurring an inconsequential decline in performance.

Theory · Reinforcement Learning and Planning

Raj Ghugare, Matthieu Geist, Glen Berseth, Benjamin Eysenbach

Some reinforcement learning (RL) algorithms have the capability of recombining together pieces of previously seen experience to solve a task never seen before during training. This oft-sought property is one of the few ways in which dynamic programming based RL algorithms are considered different from supervised learning (SL) based RL algorithms. Yet, recent RL methods based on off-the-shelf SL algorithms achieve excellent results without an explicit mechanism for stitching; it remains unclear whether those methods forgo this important stitching property. This paper studies this question in the setting of goal-reaching problems. We show that the desirable stitching property corresponds to a form of generalization: after training on a distribution of (state, goal) pairs, one would like to evaluate on (state, goal) pairs not seen together in the training data. Our analysis shows that this sort of generalization is different from i.i.d. generalization. This connection between stitching and generalization reveals why we should not expect existing RL methods based on SL to perform stitching, even in the limit of large datasets and models. We experimentally validate this result on carefully constructed datasets.This connection suggests a simple remedy, the same remedy for improving generalization in supervised learning: data augmentation. We propose a naive temporal data augmentation approach and demonstrate that adding it to RL methods based on SL enables them to successfully stitch together experience, so that they succeed in navigating between states and goals unseen together during training.

Reinforcement Learning · Batch/Offline

Yihuan Mao, Chengjie Wu, Xi Chen, Hao Hu, Ji Jiang, Tianze Zhou, Tangjie Lv, Changjie Fan, Zhipeng Hu, Yi Wu 等

Previous literature on policy diversity in reinforcement learning (RL) either focuses on the online setting or ignores the policy performance. In contrast, offline RL, which aims to learn high-quality policies from batched data, has yet to fully leverage the intrinsic diversity of the offline dataset. Addressing this dichotomy and aiming to balance quality and diversity poses a significant challenge to extant methodologies. This paper introduces a novel approach, termed Stylized Offline RL (SORL), which is designed to extract high-performing, stylistically diverse policies from a dataset characterized by distinct behavioral patterns. Drawing inspiration from the venerable Expectation-Maximization (EM) algorithm, SORL innovatively alternates between policy learning and trajectory clustering, a mechanism that promotes policy diversification. To further augment policy performance, we introduce advantage-weighted style learning into the SORL framework. Experimental evaluations across multiple environments demonstrate the significant superiority of SORL over previous methods in extracting high-quality policies with diverse behaviors. A case in point is that SORL successfully learns strong policies with markedly distinct playing patterns from a real-world human dataset of a popular basketball video game "Dunk City Dynasty."

Reinforcement Learning · Deep RL

Nicholas Corrado, Josiah Hanna

Recently, data augmentation (DA) has emerged as a method for leveraging domain knowledge to inexpensively generate additional data in reinforcement learning (RL) tasks, often yielding substantial improvements in data efficiency.While prior work has demonstrated the utility of incorporating augmented data directly into model-free RL updates,it is not well-understood when a particular DA strategy will improve data efficiency.In this paper, we seek to identify general aspects of DA responsible for observed learning improvements.Our study focuses on sparse-reward tasks with dynamics-invariant data augmentation functions, serving as an initial step towards a more general understanding of DA and its integration into RL training.Experimentally, we isolate three relevant aspects of DA: state-action coverage, reward density, and the number of augmented transitions generated per update (the augmented replay ratio).From our experiments, we draw two conclusions: (1) increasing state-action coverage often has a much greater impact on data efficiency than increasing reward density, and (2) decreasing the augmented replay ratio substantially improves data efficiency.In fact, certain tasks in our empirical study are solvable only when the replay ratio is sufficiently low.

Deep Learning · Generative Models and Autoencoders

Tianrong Chen, Jiatao Gu, Laurent Dinh, Evangelos Theodorou, Joshua Susskind, Shuangfei Zhai

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in \textbf{phase space dynamics}, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Deep Learning · Generative Models and Autoencoders

Xiang Hu, Qingyang Zhu, Kewei Tu, Wei Wu

We present ReCAT, a recursive composition augmented Transformer that is able to explicitly model hierarchical syntactic structures of raw texts without relying on gold trees during both learning and inference. Existing research along this line restricts data to follow a hierarchical tree structure and thus lacks inter-span communications.To overcome the problem, we propose a novel contextual inside-outside (CIO) layer that learns contextualized representations of spans through bottom-up and top-down passes, where a bottom-up pass forms representations of high-level spans by composing low-level spans, while a top-down pass combines information inside and outside a span. By stacking several CIO layers between the embedding layer and the attention layers in Transformer, the ReCAT model can perform both deep intra-span and deep inter-span interactions, and thus generate multi-grained representations fully contextualized with other spans.Moreover, the CIO layers can be jointly pre-trained with Transformers, making ReCAT enjoy scaling ability, strong performance, and interpretability at the same time. We conduct experiments on various sentence-level and span-level tasks. Evaluation results indicate that ReCAT can significantly outperform vanilla Transformer models on all span-level tasks and recursive models on natural language inference tasks. More interestingly, the hierarchical structures induced by ReCAT exhibit strong consistency with human-annotated syntactic trees, indicating good interpretability brought by the CIO layers.

Deep Learning · Robustness

Ziqiang Li, Hong Sun, Pengfei Xia, Heng Li, Beihao Xia, Yi Wu, Bin Li

Recent deep neural networks (DNNs) have came to rely on vast amounts of training data, providing an opportunity for malicious attackers to exploit and contaminate the data to carry out backdoor attacks. However, existing backdoor attack methods make unrealistic assumptions, assuming that all training data comes from a single source and that attackers have full access to the training data. In this paper, we introduce a more realistic attack scenario where victims collect data from multiple sources, and attackers cannot access the complete training data. We refer to this scenario as $\textbf{data-constrained backdoor attacks}$. In such cases, previous attack methods suffer from severe efficiency degradation due to the $\textbf{entanglement}$ between benign and poisoning features during the backdoor injection process. To tackle this problem, we introduce three CLIP-based technologies from two distinct streams: $\textit{Clean Feature Suppression}$ and $\textit{Poisoning Feature Augmentation}$. The results demonstrate remarkable improvements, with some settings achieving over $\textbf{100}$% improvement compared to existing attacks in data-constrained scenarios.

Reinforcement Learning · Deep RL

Guozheng Ma, Lu Li, Sen Zhang, Zixuan Liu, Zhen Wang, Yixin Chen, Li Shen, Xueqian Wang, Dacheng Tao

Plasticity, the ability of a neural network to evolve with new data, is crucial for high-performance and sample-efficient visual reinforcement learning (VRL). Although methods like resetting and regularization can potentially mitigate plasticity loss, the influences of various components within the VRL framework on the agent's plasticity are still poorly understood. In this work, we conduct a systematic empirical exploration focusing on three primary underexplored facets and derive the following insightful conclusions: (1) data augmentation is essential in maintaining plasticity; (2) the critic's plasticity loss serves as the principal bottleneck impeding efficient training; and (3) without timely intervention to recover critic's plasticity in the early stages, its loss becomes catastrophic. These insights suggest a novel strategy to address the high replay ratio (RR) dilemma, where exacerbated plasticity loss hinders the potential improvements of sample efficiency brought by increased reuse frequency. Rather than setting a static RR for the entire training process, we propose Adaptive RR, which dynamically adjusts the RR based on the critic’s plasticity level. Extensive evaluations indicate that Adaptive RR not only avoids catastrophic plasticity loss in the early stages but also benefits from more frequent reuse in later phases, resulting in superior sample efficiency.

Applications · Computer Vision

Kim-Celine Kahl, Carsten Lüth, Maximilian Zenk, Klaus Maier-Hein, Paul F. Jaeger

Uncertainty estimation is an essential and heavily-studied component for the reliable application of semantic segmentation methods. While various studies exist claiming methodological advances on the one hand, and successful application on the other hand, the field is currently hampered by a gap between theory and practice leaving fundamental questions unanswered: Can data-related and model-related uncertainty really be separated in practice? Which components of an uncertainty method are essential for real-world performance? Which uncertainty method works well for which application? In this work, we link this research gap to a lack of systematic and comprehensive evaluation of uncertainty methods. Specifically, we identify three key pitfalls in current literature and present an evaluation framework that bridges the research gap by providing 1) a controlled environment for studying data ambiguities as well as distribution shifts, 2) systematic ablations of relevant method components, and 3) test-beds for the five predominant uncertainty applications: OoD-detection, active learning, failure detection, calibration, and ambiguity modeling. Empirical results on simulated as well as real-world data demonstrate how the proposed framework is able to answer the predominant questions in the field revealing for instance that 1) separation of uncertainty types works on simulated data but does not necessarily translate to real-world data, 2) aggregation of scores is a crucial but currently neglected component of uncertainty methods, 3) While ensembles are performing most robustly across the different downstream tasks and settings, test-time augmentation often constitutes a light-weight alternative. Code is at: https://github.com/IML-DKFZ/values

Applications · Health

xinlu zhang, Shiyang Li, Xianjun Yang, Chenxin Tian, Yao Qin, Linda Petzold

Large language models (LLMs) demonstrate remarkable medical expertise, but data privacy concerns impede their direct use in healthcare environments. Although offering improved data privacy protection, domain-specific small language models (SLMs) often underperform LLMs, emphasizing the need for methods that reduce this performance gap while alleviating privacy concerns. In this paper, we present a simple yet effective method that harnesses LLMs' medical proficiency to boost SLM performance in medical tasks under $privacy-restricted$ scenarios. Specifically, we mitigate patient privacy issues by extracting keywords from medical data and prompting the LLM to generate a medical knowledge-intensive context by simulating clinicians' thought processes. This context serves as additional input for SLMs, augmenting their decision-making capabilities. Our method significantly enhances performance in both few-shot and full training settings across three medical knowledge-intensive tasks, achieving up to a 22.57% increase in absolute accuracy compared to SLM fine-tuning without context, and sets new state-of-the-art results in two medical tasks within privacy-restricted scenarios. Further out-of-domain testing and experiments in two general domain datasets showcase its generalizability and broad applicability.

Alexander Shypula, Aman Madaan, Yimeng Zeng, Uri Alon, Jacob Gardner, Yiming Yang, Milad Hashemi, Graham Neubig, Parthasarathy Ranganathan, Osbert Bastani 等

With the decline of Moore's law, optimizing program performance has become a major focus of software research. However, high-level optimizations such as API and algorithm changes remain elusive due to the difficulty of understanding the semantics of code. Simultaneously, pretrained large language models (LLMs) have demonstrated strong capabilities at solving a wide range of programming tasks. To that end, we introduce a framework for adapting LLMs to high-level program optimization. First, we curate a dataset of performance-improving edits made by human programmers of over 77,000 competitive C++ programming submission pairs, accompanied by extensive unit tests. A major challenge is the significant variability of measuring performance on commodity hardware, which can lead to spurious "improvements." To isolate and reliably evaluate the impact of program optimizations, we design an environment based on the gem5 full system simulator, the de facto simulator used in academia and industry. Next, we propose a broad range of adaptation strategies for code optimization; for prompting, these include retrieval-based few-shot prompting and chain-of-thought, and for finetuning, these include performance-conditioned generation and synthetic data augmentation based on self-play. A combination of these techniques achieves a mean speedup of 6.86$\times$ with eight generations, higher than average optimizations from individual programmers (3.66$\times$). Using our model's fastest generations, we set a new upper limit on the fastest speedup possible for our dataset at 9.64$\times$ compared to using the fastest human submissions available (9.56$\times$).

Applications · Time Series

Xu Zheng, Tianchun Wang, Wei Cheng, Aitian Ma, Haifeng Chen, Mo Sha, Dongsheng Luo

Modern techniques like contrastive learning have been effectively used in many areas, including computer vision, natural language processing, and graph-structured data. Creating positive examples that assist the model in learning robust and discriminative representations is a crucial stage in contrastive learning approaches. Usually, preset human intuition directs the selection of relevant data augmentations. Due to patterns that are easily recognized by humans, this rule of thumb works well in the vision and language domains. However, it is impractical to visually inspect the temporal structures in time series. The diversity of time series augmentations at both the dataset and instance levels makes it difficult to choose meaningful augmentations on the fly. Thus, although prevalent, contrastive learning with data augmentation has been less studied in the time series domain. In this study, we address this gap by analyzing time series data augmentation using information theory and summarizing the most commonly adopted augmentations in a unified format. We then propose a parametric augmentation method, AutoTCL, which can be adaptively employed to support time series representation learning. The proposed approach is encoder-agnostic, allowing it to be seamlessly integrated with different backbone encoders. Experiments on univariate forecasting tasks demonstrate the highly competitive results of our method, with an average 6.5\% reduction in MSE and 4.7\% in MAE over the leading baselines. In classification tasks, AutoTCL achieves a $1.2\%$ increase in average accuracy.

Jiyang Zheng, Yu Yao, Bo Han, Dadong Wang, Tongliang Liu

Contrastive learning, while highly effective for a lot of tasks, shows limited improvement in ordinal regression. We find that the limitation comes from the predefined strong data augmentations employed in contrastive learning. Intuitively, for ordinal regression datasets, the discriminative information (ordinal content information) contained in instances is subtle. The strong augmentations can easily overshadow or diminish this ordinal content information. As a result, when contrastive learning is used to extract common features between weakly and strongly augmented images, the derived features often lack this essential ordinal content, rendering them less useful in training models for ordinal regression. To improve contrastive learning's utility for ordinal regression, we propose a novel augmentation method to replace the predefined strong argumentation based on the principle of minimal change. Our method is designed in a generative manner that can effectively generate images with different styles but contains desired ordinal content information. Extensive experiments validate the effectiveness of our proposed method, which serves as a plug-and-play solution and consistently improves the performance of existing state-of-the-art methods in ordinal regression tasks.

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Mucong Ding, Bang An, Yuancheng Xu, Anirudh Satheesh, Furong Huang

Data augmentation, a cornerstone technique in deep learning, is crucial in enhancing model performance, especially with scarce labeled data. While traditional techniques are effective, their reliance on hand-crafted methods limits their applicability across diverse data types and tasks. Although modern learnable augmentation methods offer increased adaptability, they are computationally expensive and challenging to incorporate within prevalent augmentation workflows. In this work, we present a novel, efficient method for data augmentation, effectively bridging the gap between existing augmentation strategies and emerging datasets and learning tasks. We introduce SAFLEX (Self-Adaptive Augmentation via Feature Label EXtrapolation), which learns the sample weights and soft labels of augmented samples provided by any given upstream augmentation pipeline, using a specifically designed efficient bilevel optimization algorithm. Remarkably, SAFLEX effectively reduces the noise and label errors of the upstream augmentation pipeline with a marginal computational cost. As a versatile module, SAFLEX excels across diverse datasets, including natural and medical images and tabular data, showcasing its prowess in few-shot learning and out-of-distribution generalization. SAFLEX seamlessly integrates with common augmentation strategies like RandAug, CutMix, and those from large pre-trained generative models like stable diffusion and is also compatible with frameworks such as CLIP's fine-tuning. Our findings highlight the potential to adapt existing augmentation pipelines for new data types and tasks, signaling a move towards more adaptable and resilient training frameworks.

Deep Learning · Other Representation Learning

Jianhao Yuan, Jie Zhang, Shuyang Sun, Philip Torr, Bo ZHAO

Synthetic training data has gained prominence in numerous learning tasks and scenarios, offering advantages such as dataset augmentation, generalization evaluation, and privacy preservation. Despite these benefits, the efficiency of synthetic data generated bycurrent methodologies remains inferior when training advanced deep models exclusively, limiting its practical utility. To address this challenge, we analyze the principles underlying training data synthesis for supervised learning and elucidate a principled theoretical framework from the distribution-matching perspective that explicates the mechanisms governing synthesis efficacy. Through extensive experiments, we demonstrate the effectiveness of our synthetic data across diverse image classification tasks, both as a replacement for and augmentation to real datasets, while also benefits such as out-of-distribution generalization, privacy preservation, and scalability. Specifically, we achieve 70.9% top1 classification accuracy on ImageNet1K when training solely with synthetic data equivalentto 1 × the original real data size, which increases to 76.0% when scaling up to 10 × synthetic data.

Applications · Language, Speech and Dialog

Wenting Zhao, Xiang Ren, Jack Hessel, Claire Cardie, Yejin Choi, Yuntian Deng

Chatbots such as GPT-4 and ChatGPT are now serving millions of users. Despite their widespread use, there remains a lack of public datasets showcasing how these tools are used by a population of users in practice. To bridge this gap, we offered free access to ChatGPT for online users in exchange for their affirmative, consensual opt-in to anonymously collect their chat transcripts and request headers. From this, we compiled WildChat, a corpus of 1 million user-ChatGPT conversations, which consists of over 2.5 million interaction turns. We compare WildChat with other popular user-chatbot interaction datasets, and find that our dataset offers the most diverse user prompts, contains the largest number of languages, and presents the richest variety of potentially toxic use-cases for researchers to study. In addition to timestamped chat transcripts, we enrich the dataset with demographic data, including state, country, and hashed IP addresses, alongside request headers. This augmentation allows for more detailed analysis of user behaviors across different geographical regions and temporal dimensions. Finally, because it captures a broad range of use cases, we demonstrate the dataset’s potential utility in fine-tuning instruction-following models. WildChat is released at https://wildchat.allen.ai under AI2 ImpACT Licenses.

Deep Learning · Large Language Models

Xian Li, Ping Yu, Chunting Zhou, Timo Schick, Omer Levy, Luke Zettlemoyer, Jason E Weston, Mike Lewis

We present a scalable method to build a high quality instruction following language model by automatically labelling human-written text with corresponding instructions. Our approach, named instruction backtranslation, starts with a language model finetuned on a small amount of seed data, and a given web corpus. The seed model is used to construct training examples by generating instruction prompts for web documents (self-augmentation), and then selecting high quality examples from among these candidates (self-curation). This data is then used to finetune a stronger model. Finetuning LLaMa on two iterations of our approach yields a model that outperforms all other LLaMa-based models on the Alpaca leaderboard not relying on distillation data, demonstrating highly effective self-alignment.