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We propose expanding the shared Transformer module to produce and initialize Transformers of varying depths, enabling adaptation to diverse resource constraints. Drawing an analogy to genetic expansibility, we term such module as learngene. To identify the expansion mechanism, we delve into the relationship between the layer's position and its corresponding weight value, and find that linear function appropriately approximates this relationship. Building on this insight, we present Transformer as Linear Expansion of learnGene (TLEG), a novel approach for flexibly producing and initializing Transformers of diverse depths. Specifically, to learn learngene, we firstly construct an auxiliary Transformer linearly expanded from learngene, after which we train it through employing soft distillation. Subsequently, we can produce and initialize Transformers of varying depths via linearly expanding the well-trained learngene, thereby supporting diverse downstream scenarios. Extensive experiments on ImageNet-1K demonstrate that TLEG achieves comparable or better performance in contrast to many individual models trained from scratch, while reducing around 2x training cost. When transferring to several downstream classification datasets, TLEG surpasses existing initialization methods by a large margin (e.g., +6.87% on iNat 2019 and +7.66% on CIFAR-100). Under the situation where we need to produce models of varying depths adapting for different resource constraints, TLEG achieves comparable results while reducing around 19x parameters stored to initialize these models and around 5x pre-training costs, in contrast to the pre-training and fine-tuning approach. When transferring a fixed set of parameters to initialize different models, TLEG presents better flexibility and competitive performance while reducing around 2.9x parameters stored to initialize, compared to the pre-training approach.

The problem of fairly allocating a set of indivisible items is a well-known challenge in the field of (computational) social choice. In this scenario, there is a fundamental incompatibility between notions of fairness (such as envy-freeness and proportionality) and economic efficiency (such as Pareto-optimality). However, in the real world, items are not always allocated once and for all, but often repeatedly. For example, the items may be recurring chores to distribute in a household. Motivated by this, we initiate the study of the repeated fair division of indivisible goods and chores, and propose a formal model for this scenario. In this paper, we show that, if the number of repetitions is a multiple of the number of agents, there always exists a sequence of allocations that is proportional and Pareto-optimal. On the other hand, irrespective of the number of repetitions, an envy-free and Pareto-optimal sequence of allocations may not exist. For the case of two agents, we show that if the number of repetitions is even, it is always possible to find a sequence of allocations that is overall envy-free and Pareto-optimal. We then prove even stronger fairness guarantees, showing that every allocation in such a sequence satisfies some relaxation of envy-freeness. Finally, in case that the number of repetitions can be chosen freely, we show that envy-free and Pareto-optimal allocations are achievable for any number of agents.

Identifying root causes of anomalies in causal processes is vital across disciplines. Once identified, one can isolate the root causes and implement necessary measures to restore the normal operation. Causal processes are often modelled as graphs with entities being nodes and their paths/interconnections as edge. Existing work only consider the contribution of nodes in the generative process, thus can not attribute the outlier score to the edges of the mechanism if the anomaly occurs in the connections. In this paper, we consider both individual edge and node of each mechanism when identifying the root causes. We introduce a noisy functional causal model to account for this purpose. Then, we employ Bayesian learning and inference methods to infer the noises of the nodes and edges. We then represent the functional form of a target outlier leaf as a function of the node and edge noises. Finally, we propose an efficient gradient-based attribution method to compute the anomaly attribution scores which scales linearly with the number of nodes and edges. Experiments on simulated datasets and two real-world scenario datasets show better anomaly attribution performance of the proposed method compared to the baselines. Our method scales to larger graphs with more nodes and edges.

We propose automatic optimisation methods considering the geometry of matrix manifold for the normalised parameters of neural networks. Layerwise weight normalisation with respect to Frobenius norm is utilised to bound the Lipschitz constant and to enhance gradient reliability so that the trained networks are suitable for control applications. Our approach first initialises the network and normalises the data with respect to the $\ell^{2}$-$\ell^{2}$ gain of the initialised network. Then, the proposed algorithms take the update structure based on the exponential map on high-dimensional spheres. Given an update direction such as that of the negative Riemannian gradient, we propose two different ways to determine the stepsize for descent. The first algorithm utilises automatic differentiation of the objective function along the update curve defined on the combined manifold of spheres. The directional second-order derivative information can be utilised without requiring explicit construction of the Hessian. The second algorithm utilises the majorisation-minimisation framework via architecture-aware majorisation for neural networks. With these new developments, the proposed methods avoid manual tuning and scheduling of the learning rate, thus providing an automated pipeline for optimizing normalised neural networks.

For machine learning models to be reliable and trustworthy, their decisions must be interpretable. As these models find increasing use in safety-critical applications, it is important that not just the model predictions but also their explanations (as feature attributions) be robust to small human-imperceptible input perturbations. Recent works have shown that many attribution methods are fragile and have proposed improvements in either these methods or the model training. We observe two main causes for fragile attributions: first, the existing metrics of robustness (e.g., top-k intersection) over-penalize even reasonable local shifts in attribution, thereby making random perturbations to appear as a strong attack, and second, the attribution can be concentrated in a small region even when there are multiple important parts in an image. To rectify this, we propose simple ways to strengthen existing metrics and attribution methods that incorporate locality of pixels in robustness metrics and diversity of pixel locations in attributions. Towards the role of model training in attributional robustness, we empirically observe that adversarially trained models have more robust attributions on smaller datasets, however, this advantage disappears in larger datasets. Code is available at //github.com/ksandeshk/LENS.

In the global context, while mixed reality has been an emerging concept for years, recent technological and scientific advancements have now made it poised to revolutionize industries and daily life by offering enhanced functionalities and improved services. Besides reviewing the highly cited papers in the last 20 years among over a thousand research papers on mixed reality, this systematic review provides the state-of-the-art applications and utilities of the mixed reality by primarily scrutinizing the associated papers in 2022 and 2023. Focusing on the potentials that this technology have in providing digitally supported simulations and other utilities in the era of large language models, highlighting the potential and limitations of the innovative solutions and also bringing focus to emerging research directions, such as telemedicine, remote control and optimization of direct volume rendering. The paper's associated repository is publicly accessible at //aizierjiang.github.io/mr.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

Transformer, an attention-based encoder-decoder architecture, has revolutionized the field of natural language processing. Inspired by this significant achievement, some pioneering works have recently been done on adapting Transformerliked architectures to Computer Vision (CV) fields, which have demonstrated their effectiveness on various CV tasks. Relying on competitive modeling capability, visual Transformers have achieved impressive performance on multiple benchmarks such as ImageNet, COCO, and ADE20k as compared with modern Convolution Neural Networks (CNN). In this paper, we have provided a comprehensive review of over one hundred different visual Transformers for three fundamental CV tasks (classification, detection, and segmentation), where a taxonomy is proposed to organize these methods according to their motivations, structures, and usage scenarios. Because of the differences in training settings and oriented tasks, we have also evaluated these methods on different configurations for easy and intuitive comparison instead of only various benchmarks. Furthermore, we have revealed a series of essential but unexploited aspects that may empower Transformer to stand out from numerous architectures, e.g., slack high-level semantic embeddings to bridge the gap between visual and sequential Transformers. Finally, three promising future research directions are suggested for further investment.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.