Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local linear maps may vary along a curve, and the resulting tensor is expressed as a limit along this curve. In this work we introduce and study partial degeneration, a special version of degeneration where one of the local linear maps is constant whereas the others vary along a curve. Motivated by algebraic complexity, quantum entanglement and tensor networks, we present constructions based on matrix multiplication tensors and find examples by making a connection to the theory of prehomogeneous tensor spaces. We highlight the subtleties of this new notion by showing obstruction and classification results for the unit tensor. To this end, we study the notion of aided rank, a natural generalization of tensor rank. The existence of partial degenerations gives strong upper bounds on the aided rank of a tensor, which allows one to turn degenerations into restrictions. In particular, we present several examples, based on the W-tensor and the Coppersmith-Winograd tensors, where lower bounds on aided rank provide obstructions to the existence of certain partial degenerations.
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Learning dynamics, which describes how the learning of specific training examples influences the model's prediction of other examples, give us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during finetuning, by analyzing the step-wise decomposition and accumulated influence among different responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. The analysis not only explains where the benefits of these methods come from but also inspires a simple, effective method to further improve the alignment performance. Code for experiments is available at //github.com/Joshua-Ren/Learning_dynamics_LLM.
To assess the quality of a probabilistic prediction for stochastic dynamical systems (SDSs), scoring rules assign a numerical score based on the predictive distribution and the measured state. In this paper, we propose an $\epsilon$-logarithm score that generalizes the celebrated logarithm score by considering a neighborhood with radius $\epsilon$. We characterize the probabilistic predictability of an SDS by optimizing the expected score over the space of probability measures. We show how the probabilistic predictability is quantitatively determined by the neighborhood radius, the differential entropies of process noises, and the system dimension. Given any predictor, we provide approximations for the expected score with an error of scale $\mathcal{O}(\epsilon)$. In addition to the expected score, we also analyze the asymptotic behaviors of the score on individual trajectories. Specifically, we prove that the score on a trajectory can converge to the expected score when the process noises are independent and identically distributed. Moreover, the convergence speed against the trajectory length $T$ is of scale $\mathcal{O}(T^{-\frac{1}{2}})$ in the sense of probability. Finally, numerical examples are given to elaborate the results.
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by directly inverting the dynamics using regularized linear regression, is based on new design and analysis ideas for differentiation filtering and regularized least squares. Combined in series, they yield a novel finite-sample bound on mean absolute error of estimation.
Recent advancements in Large Language Models (LLMs) have significantly extended their capabilities, evolving from basic text generation to complex, human-like interactions. In light of the possibilities that LLMs could assume significant workplace responsibilities, it becomes imminently necessary to explore LLMs' capacities as professional assistants. This study focuses on the aspect of career interests by applying the Occupation Network's Interest Profiler short form to LLMs as if they were human participants and investigates their hypothetical career interests and competence, examining how these vary with language changes and model advancements. We analyzed the answers using a general linear mixed model approach and found distinct career interest inclinations among LLMs, particularly towards the social and artistic domains. Interestingly, these preferences did not align with the occupations where LLMs exhibited higher competence. This novel approach of using psychometric instruments and sophisticated statistical tools on LLMs unveils fresh perspectives on their integration into professional environments, highlighting human-like tendencies and promoting a reevaluation of LLMs' self-perception and competency alignment in the workforce.
This work uniquely identifies and characterizes four prevalent multimodal model architectural patterns in the contemporary multimodal landscape. Systematically categorizing models by architecture type facilitates monitoring of developments in the multimodal domain. Distinct from recent survey papers that present general information on multimodal architectures, this research conducts a comprehensive exploration of architectural details and identifies four specific architectural types. The types are distinguished by their respective methodologies for integrating multimodal inputs into the deep neural network model. The first two types (Type A and B) deeply fuses multimodal inputs within the internal layers of the model, whereas the following two types (Type C and D) facilitate early fusion at the input stage. Type-A employs standard cross-attention, whereas Type-B utilizes custom-designed layers for modality fusion within the internal layers. On the other hand, Type-C utilizes modality-specific encoders, while Type-D leverages tokenizers to process the modalities at the model's input stage. The identified architecture types aid the monitoring of any-to-any multimodal model development. Notably, Type-C and Type-D are currently favored in the construction of any-to-any multimodal models. Type-C, distinguished by its non-tokenizing multimodal model architecture, is emerging as a viable alternative to Type-D, which utilizes input-tokenizing techniques. To assist in model selection, this work highlights the advantages and disadvantages of each architecture type based on data and compute requirements, architecture complexity, scalability, simplification of adding modalities, training objectives, and any-to-any multimodal generation capability.
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.
As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.
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.
Transformers have achieved great success in many artificial intelligence fields, such as natural language processing, computer vision, and audio processing. Therefore, it is natural to attract lots of interest from academic and industry researchers. Up to the present, a great variety of Transformer variants (a.k.a. X-formers) have been proposed, however, a systematic and comprehensive literature review on these Transformer variants is still missing. In this survey, we provide a comprehensive review of various X-formers. We first briefly introduce the vanilla Transformer and then propose a new taxonomy of X-formers. Next, we introduce the various X-formers from three perspectives: architectural modification, pre-training, and applications. Finally, we outline some potential directions for future research.
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.
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