Daily Papers

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex functions, different works have established the optimal O(log(1/delta)log T/T) or O(log(1/delta)/T) high-probability convergence rates for the final iterate, where T is the time horizon and delta is the failure probability. However, to prove these bounds, all the existing works are either limited to compact domains or require almost surely bounded noises. It is natural to ask whether the last iterate of SGD can still guarantee the optimal convergence rate but without these two restrictive assumptions. Besides this important question, there are still lots of theoretical problems lacking an answer. For example, compared with the last-iterate convergence of SGD for non-smooth problems, only few results for smooth optimization have yet been developed. Additionally, the existing results are all limited to a non-composite objective and the standard Euclidean norm. It still remains unclear whether the last-iterate convergence can be provably extended to wider composite optimization and non-Euclidean norms. In this work, to address the issues mentioned above, we revisit the last-iterate convergence of stochastic gradient methods and provide the first unified way to prove the convergence rates both in expectation and in high probability to accommodate general domains, composite objectives, non-Euclidean norms, Lipschitz conditions, smoothness, and (strong) convexity simultaneously. Additionally, we extend our analysis to obtain the last-iterate convergence under heavy-tailed noises.

In the domain of Large Language Model (LLM), LLMs demonstrate significant capabilities in natural language understanding and generation. With the growing needs of applying LLMs on various domains, it is a research question that how to efficiently train and build a model that has expertise in different domains but with a low training cost. We propose CCoE architecture, a framework of easily coupling multiple strong domain experts together to fuse into a big LLM, provides a collective way of utilizing the different domain expert LLMs. Besides, training a large collaborative of multiple expert LLMs requires a high requirements on training sources. CCoE bypasses this problem through isolating other experts and train each expert separately. The design of CCoE assembles multiple expert LLMs through the CoE (Collaboration of Experts) layer. Each CoE layer could have one or more expert LLMs. Expert LLMs have different number of layers and have been well-trained for different domain tasks. Each expert is fine-tuned to be able to achieve the comparable results with SOTA domain LLMs. We start from 5 experts in the domain of Code, Math, Law, text-to-SQL and Medical. The results indicate that our CCoE framework can easily and efficiently boost nearly 10%-20% performance on original base model in different domains but using less resources on training, as well as inference.

There is a growing interest in designing models that can deal with images from different visual domains. If there exists a universal structure in different visual domains that can be captured via a common parameterization, then we can use a single model for all domains rather than one model per domain. A model aware of the relationships between different domains can also be trained to work on new domains with less resources. However, to identify the reusable structure in a model is not easy. In this paper, we propose a multi-domain learning architecture based on depthwise separable convolution. The proposed approach is based on the assumption that images from different domains share cross-channel correlations but have domain-specific spatial correlations. The proposed model is compact and has minimal overhead when being applied to new domains. Additionally, we introduce a gating mechanism to promote soft sharing between different domains. We evaluate our approach on Visual Decathlon Challenge, a benchmark for testing the ability of multi-domain models. The experiments show that our approach can achieve the highest score while only requiring 50% of the parameters compared with the state-of-the-art approaches.

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable mathcal O(1) compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation.

With the rise of Transformers as the standard for language processing, and their advancements in computer vision, there has been a corresponding growth in parameter size and amounts of training data. Many have come to believe that because of this, transformers are not suitable for small sets of data. This trend leads to concerns such as: limited availability of data in certain scientific domains and the exclusion of those with limited resource from research in the field. In this paper, we aim to present an approach for small-scale learning by introducing Compact Transformers. We show for the first time that with the right size, convolutional tokenization, transformers can avoid overfitting and outperform state-of-the-art CNNs on small datasets. Our models are flexible in terms of model size, and can have as little as 0.28M parameters while achieving competitive results. Our best model can reach 98% accuracy when training from scratch on CIFAR-10 with only 3.7M parameters, which is a significant improvement in data-efficiency over previous Transformer based models being over 10x smaller than other transformers and is 15% the size of ResNet50 while achieving similar performance. CCT also outperforms many modern CNN based approaches, and even some recent NAS-based approaches. Additionally, we obtain a new SOTA result on Flowers-102 with 99.76% top-1 accuracy, and improve upon the existing baseline on ImageNet (82.71% accuracy with 29% as many parameters as ViT), as well as NLP tasks. Our simple and compact design for transformers makes them more feasible to study for those with limited computing resources and/or dealing with small datasets, while extending existing research efforts in data efficient transformers. Our code and pre-trained models are publicly available at https://github.com/SHI-Labs/Compact-Transformers.

The remarkable predictive performance of deep neural networks (DNNs) has led to their adoption in service domains of unprecedented scale and scope. However, the widespread adoption and growing commercialization of DNNs have underscored the importance of intellectual property (IP) protection. Devising techniques to ensure IP protection has become necessary due to the increasing trend of outsourcing the DNN computations on the untrusted accelerators in cloud-based services. The design methodologies and hyper-parameters of DNNs are crucial information, and leaking them may cause massive economic loss to the organization. Furthermore, the knowledge of DNN's architecture can increase the success probability of an adversarial attack where an adversary perturbs the inputs and alter the prediction. In this work, we devise a two-stage attack methodology "DeepPeep" which exploits the distinctive characteristics of design methodologies to reverse-engineer the architecture of building blocks in compact DNNs. We show the efficacy of "DeepPeep" on P100 and P4000 GPUs. Additionally, we propose intelligent design maneuvering strategies for thwarting IP theft through the DeepPeep attack and proposed "Secure MobileNet-V1". Interestingly, compared to vanilla MobileNet-V1, secure MobileNet-V1 provides a significant reduction in inference latency (approx60%) and improvement in predictive performance (approx2%) with very-low memory and computation overheads.

As an efficient alternative to conventional full finetuning, parameter-efficient finetuning (PEFT) is becoming the prevailing method to adapt pretrained language models. In PEFT, a lightweight module is learned on each dataset while the underlying pretrained language model remains unchanged, resulting in multiple compact modules representing diverse skills when applied to various domains and tasks. In this paper, we propose to compose these parameter-efficient modules through linear arithmetic operations in the weight space, thereby integrating different module capabilities. Specifically, we first define addition and negation operators for the module, and then further compose these two basic operators to perform flexible arithmetic. Our approach requires no additional training and enables highly flexible module composition. We apply different arithmetic operations to compose the parameter-efficient modules for (1) distribution generalization, (2) multi-tasking, (3) unlearning, and (4) domain transfer. Additionally, we extend our approach to detoxify Alpaca-LoRA, the latest instruction-tuned large language model based on LLaMA. Empirical results demonstrate that our approach produces new and effective parameter-efficient modules that significantly outperform existing ones across all settings.

It has been shown that deep neural networks of a large enough width are universal approximators but they are not if the width is too small. There were several attempts to characterize the minimum width w_{min} enabling the universal approximation property; however, only a few of them found the exact values. In this work, we show that the minimum width for L^p approximation of L^p functions from [0,1]^{d_x} to mathbb R^{d_y} is exactly max{d_x,d_y,2} if an activation function is ReLU-Like (e.g., ReLU, GELU, Softplus). Compared to the known result for ReLU networks, w_{min}=max{d_x+1,d_y} when the domain is mathbb R^{d_x}, our result first shows that approximation on a compact domain requires smaller width than on mathbb R^{d_x}. We next prove a lower bound on w_{min} for uniform approximation using general activation functions including ReLU: w_{min}ge d_y+1 if d_x<d_yle2d_x. Together with our first result, this shows a dichotomy between L^p and uniform approximations for general activation functions and input/output dimensions.

Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains. However, we argue that the domain variantions also contain useful information, ie, classification-aware information, for downstream tasks, which has been largely ignored. Different from learning domain invariant features from source domains, we decouple the input images into Domain Expert Features and noise. The proposed domain expert features lie in a learned latent space where the images in each domain can be classified independently, enabling the implicit use of classification-aware domain variations. Based on the analysis, we proposed a novel paradigm called Domain Disentanglement Network (DDN) to disentangle the domain expert features from the source domain images and aggregate the source domain expert features for representing the target test domain. We also propound a new contrastive learning method to guide the domain expert features to form a more balanced and separable feature space. Experiments on the widely-used benchmarks of PACS, VLCS, OfficeHome, DomainNet, and TerraIncognita demonstrate the competitive performance of our method compared to the recently proposed alternatives.

The objective of domain generalization (DG) is to enhance the transferability of the model learned from a source domain to unobserved domains. To prevent overfitting to a specific domain, Sharpness-Aware Minimization (SAM) reduces source domain's loss sharpness. Although SAM variants have delivered significant improvements in DG, we highlight that there's still potential for improvement in generalizing to unknown domains through the exploration on data space. This paper introduces an objective rooted in both parameter and data perturbed regions for domain generalization, coined Unknown Domain Inconsistency Minimization (UDIM). UDIM reduces the loss landscape inconsistency between source domain and unknown domains. As unknown domains are inaccessible, these domains are empirically crafted by perturbing instances from the source domain dataset. In particular, by aligning the loss landscape acquired in the source domain to the loss landscape of perturbed domains, we expect to achieve generalization grounded on these flat minima for the unknown domains. Theoretically, we validate that merging SAM optimization with the UDIM objective establishes an upper bound for the true objective of the DG task. In an empirical aspect, UDIM consistently outperforms SAM variants across multiple DG benchmark datasets. Notably, UDIM shows statistically significant improvements in scenarios with more restrictive domain information, underscoring UDIM's generalization capability in unseen domains. Our code is available at https://github.com/SJShin-AI/UDIM.

We introduce Domain-specific Masks for Generalization, a model for improving both in-domain and out-of-domain generalization performance. For domain generalization, the goal is to learn from a set of source domains to produce a single model that will best generalize to an unseen target domain. As such, many prior approaches focus on learning representations which persist across all source domains with the assumption that these domain agnostic representations will generalize well. However, often individual domains contain characteristics which are unique and when leveraged can significantly aid in-domain recognition performance. To produce a model which best generalizes to both seen and unseen domains, we propose learning domain specific masks. The masks are encouraged to learn a balance of domain-invariant and domain-specific features, thus enabling a model which can benefit from the predictive power of specialized features while retaining the universal applicability of domain-invariant features. We demonstrate competitive performance compared to naive baselines and state-of-the-art methods on both PACS and DomainNet.

Domain generalization (DG) aims to tackle the distribution shift between training domains and unknown target domains. Generating new domains is one of the most effective approaches, yet its performance gain depends on the distribution discrepancy between the generated and target domains. Distributionally robust optimization is promising to tackle distribution discrepancy by exploring domains in an uncertainty set. However, the uncertainty set may be overwhelmingly large, leading to low-confidence prediction in DG. It is because a large uncertainty set could introduce domains containing semantically different factors from training domains. To address this issue, we propose to perform a moderately distributional exploration (MODE) for domain generalization. Specifically, MODE performs distribution exploration in an uncertainty subset that shares the same semantic factors with the training domains. We show that MODE can endow models with provable generalization performance on unknown target domains. The experimental results show that MODE achieves competitive performance compared to state-of-the-art baselines.

We introduce CompAct, a technique that reduces peak memory utilization on GPU by 25-30% for pretraining and 50% for fine-tuning of LLMs. Peak device memory is a major limiting factor in training LLMs, with various recent works aiming to reduce model memory. However most works don't target the largest component of allocated memory during training: the model's compute graph, which is stored for the backward pass. By storing low-rank, compressed activations to be used in the backward pass we greatly reduce the required memory, unlike previous methods which only reduce optimizer overheads or the number of trained parameters. Our compression uses random projection matrices, thus avoiding additional memory overheads. Comparisons with previous techniques for either pretraining or fine-tuning show that CompAct substantially improves existing compute-performance tradeoffs. We expect CompAct's savings to scale even higher for larger models.

Compact neural networks are specially designed for applications on edge devices with faster inference speed yet modest performance. However, training strategies of compact models are borrowed from that of conventional models at present, which ignores their difference in model capacity and thus may impede the performance of compact models. In this paper, by systematically investigating the impact of different training ingredients, we introduce a strong training strategy for compact models. We find that the appropriate designs of re-parameterization and knowledge distillation are crucial for training high-performance compact models, while some commonly used data augmentations for training conventional models, such as Mixup and CutMix, lead to worse performance. Our experiments on ImageNet-1K dataset demonstrate that our specialized training strategy for compact models is applicable to various architectures, including GhostNetV2, MobileNetV2 and ShuffleNetV2. Specifically, equipped with our strategy, GhostNetV3 1.3times achieves a top-1 accuracy of 79.1% with only 269M FLOPs and a latency of 14.46ms on mobile devices, surpassing its ordinarily trained counterpart by a large margin. Moreover, our observation can also be extended to object detection scenarios. PyTorch code and checkpoints can be found at https://github.com/huawei-noah/Efficient-AI-Backbones/tree/master/ghostnetv3_pytorch.

Domain adaptation framework of GANs has achieved great progress in recent years as a main successful approach of training contemporary GANs in the case of very limited training data. In this work, we significantly improve this framework by proposing an extremely compact parameter space for fine-tuning the generator. We introduce a novel domain-modulation technique that allows to optimize only 6 thousand-dimensional vector instead of 30 million weights of StyleGAN2 to adapt to a target domain. We apply this parameterization to the state-of-art domain adaptation methods and show that it has almost the same expressiveness as the full parameter space. Additionally, we propose a new regularization loss that considerably enhances the diversity of the fine-tuned generator. Inspired by the reduction in the size of the optimizing parameter space we consider the problem of multi-domain adaptation of GANs, i.e. setting when the same model can adapt to several domains depending on the input query. We propose the HyperDomainNet that is a hypernetwork that predicts our parameterization given the target domain. We empirically confirm that it can successfully learn a number of domains at once and may even generalize to unseen domains. Source code can be found at https://github.com/MACderRu/HyperDomainNet

Domain Generalization (DG) is a challenging task in machine learning that requires a coherent ability to comprehend shifts across various domains through extraction of domain-invariant features. DG performance is typically evaluated by performing image classification in domains of various image styles. However, current methodology lacks quantitative understanding about shifts in stylistic domain, and relies on a vast amount of pre-training data, such as ImageNet1K, which are predominantly in photo-realistic style with weakly supervised class labels. Such a data-driven practice could potentially result in spurious correlation and inflated performance on DG benchmarks. In this paper, we introduce a new DG paradigm to address these risks. We first introduce two new quantitative measures ICV and IDD to describe domain shifts in terms of consistency of classes within one domain and similarity between two stylistic domains. We then present SuperMarioDomains (SMD), a novel synthetic multi-domain dataset sampled from video game scenes with more consistent classes and sufficient dissimilarity compared to ImageNet1K. We demonstrate our DG method SMOS. SMOS first uses SMD to train a precursor model, which is then used to ground the training on a DG benchmark. We observe that SMOS contributes to state-of-the-art performance across five DG benchmarks, gaining large improvements to performances on abstract domains along with on-par or slight improvements to those on photo-realistic domains. Our qualitative analysis suggests that these improvements can be attributed to reduced distributional divergence between originally distant domains. Our data are available at https://github.com/fpsluozi/SMD-SMOS .

Catastrophic forgetting remains a major challenge when adapting large language models (LLMs) to new tasks or domains. Conventional fine-tuning often overwrites existing knowledge, causing performance degradation on original tasks. We introduce Superposition in Transformers, a novel architecture that leverages autoencoders to superimpose the hidden representations of a base model and a fine-tuned model within a shared parameter space. By using B-spline-based blending coefficients and autoencoders that adaptively reconstruct hidden states based on the input data distribution, our method effectively mitigates catastrophic forgetting and enables a new paradigm of "in-model" superposition. This approach preserves original model capabilities while allowing compact domain-specific expertise to be added, and it supports dynamic switching between model states during inference.

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep networks with bounded widths are more effective than wide networks in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show that a deep RNN with ReLU activation can approximate any continuous function or L^p function with the widths d_x+d_y+2 and max{d_x+1,d_y}, respectively, where the target function maps a finite sequence of vectors in R^{d_x} to a finite sequence of vectors in R^{d_y}. We also compute the additional width required if the activation function is tanh or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and proof technique can be an initial step toward further research on deep RNNs.

Can one inject new concepts into an already trained generative model, while respecting its existing structure and knowledge? We propose a new task - domain expansion - to address this. Given a pretrained generator and novel (but related) domains, we expand the generator to jointly model all domains, old and new, harmoniously. First, we note the generator contains a meaningful, pretrained latent space. Is it possible to minimally perturb this hard-earned representation, while maximally representing the new domains? Interestingly, we find that the latent space offers unused, "dormant" directions, which do not affect the output. This provides an opportunity: By "repurposing" these directions, we can represent new domains without perturbing the original representation. In fact, we find that pretrained generators have the capacity to add several - even hundreds - of new domains! Using our expansion method, one "expanded" model can supersede numerous domain-specific models, without expanding the model size. Additionally, a single expanded generator natively supports smooth transitions between domains, as well as composition of domains. Code and project page available at https://yotamnitzan.github.io/domain-expansion/.

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width w^*_{min}=max(d_x,d_y), where d_x and d_y are the dimensions of the input and output, respectively. Recently, cai2022achieve shows that a leaky-ReLU NN with this critical width can achieve UAP for L^p functions on a compact domain K, i.e., the UAP for L^p(K,R^{d_y}). This paper examines a uniform UAP for the function class C(K,R^{d_y}) and gives the exact minimum width of the leaky-ReLU NN as w_{min}=max(d_x+1,d_y)+1_{d_y=d_x+1}, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

Distribution shift presents a significant challenge in machine learning, where models often underperform during the test stage when faced with a different distribution than the one they were trained on. This paper focuses on domain shifts, which occur when the model is applied to new domains that are different from the ones it was trained on, and propose a new approach called D^3G. Unlike previous methods that aim to learn a single model that is domain invariant, D^3G leverages domain similarities based on domain metadata to learn domain-specific models. Concretely, D^3G learns a set of training-domain-specific functions during the training stage and reweights them based on domain relations during the test stage. These domain relations can be directly obtained and learned from domain metadata. Under mild assumptions, we theoretically prove that using domain relations to reweight training-domain-specific functions achieves stronger out-of-domain generalization compared to the conventional averaging approach. Empirically, we evaluate the effectiveness of D^3G using real-world datasets for tasks such as temperature regression, land use classification, and molecule-protein binding affinity prediction. Our results show that D^3G consistently outperforms state-of-the-art methods.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Dense retrieval approaches can overcome the lexical gap and lead to significantly improved search results. However, they require large amounts of training data which is not available for most domains. As shown in previous work (Thakur et al., 2021b), the performance of dense retrievers severely degrades under a domain shift. This limits the usage of dense retrieval approaches to only a few domains with large training datasets. In this paper, we propose the novel unsupervised domain adaptation method Generative Pseudo Labeling (GPL), which combines a query generator with pseudo labeling from a cross-encoder. On six representative domain-specialized datasets, we find the proposed GPL can outperform an out-of-the-box state-of-the-art dense retrieval approach by up to 9.3 points nDCG@10. GPL requires less (unlabeled) data from the target domain and is more robust in its training than previous methods. We further investigate the role of six recent pre-training methods in the scenario of domain adaptation for retrieval tasks, where only three could yield improved results. The best approach, TSDAE (Wang et al., 2021) can be combined with GPL, yielding another average improvement of 1.4 points nDCG@10 across the six tasks. The code and the models are available at https://github.com/UKPLab/gpl.

Both real and fake news in various domains, such as politics, health, and entertainment are spread via online social media every day, necessitating fake news detection for multiple domains. Among them, fake news in specific domains like politics and health has more serious potential negative impacts on the real world (e.g., the infodemic led by COVID-19 misinformation). Previous studies focus on multi-domain fake news detection, by equally mining and modeling the correlation between domains. However, these multi-domain methods suffer from a seesaw problem: the performance of some domains is often improved at the cost of hurting the performance of other domains, which could lead to an unsatisfying performance in specific domains. To address this issue, we propose a Domain- and Instance-level Transfer Framework for Fake News Detection (DITFEND), which could improve the performance of specific target domains. To transfer coarse-grained domain-level knowledge, we train a general model with data of all domains from the meta-learning perspective. To transfer fine-grained instance-level knowledge and adapt the general model to a target domain, we train a language model on the target domain to evaluate the transferability of each data instance in source domains and re-weigh each instance's contribution. Offline experiments on two datasets demonstrate the effectiveness of DITFEND. Online experiments show that DITFEND brings additional improvements over the base models in a real-world scenario.

Can a pre-trained generator be adapted to the hybrid of multiple target domains and generate images with integrated attributes of them? In this work, we introduce a new task -- Few-shot Hybrid Domain Adaptation (HDA). Given a source generator and several target domains, HDA aims to acquire an adapted generator that preserves the integrated attributes of all target domains, without overriding the source domain's characteristics. Compared with Domain Adaptation (DA), HDA offers greater flexibility and versatility to adapt generators to more composite and expansive domains. Simultaneously, HDA also presents more challenges than DA as we have access only to images from individual target domains and lack authentic images from the hybrid domain. To address this issue, we introduce a discriminator-free framework that directly encodes different domains' images into well-separable subspaces. To achieve HDA, we propose a novel directional subspace loss comprised of a distance loss and a direction loss. Concretely, the distance loss blends the attributes of all target domains by reducing the distances from generated images to all target subspaces. The direction loss preserves the characteristics from the source domain by guiding the adaptation along the perpendicular to subspaces. Experiments show that our method can obtain numerous domain-specific attributes in a single adapted generator, which surpasses the baseline methods in semantic similarity, image fidelity, and cross-domain consistency.