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Recent work has shown that Transformers trained from scratch can successfully solve various arithmetic and algorithmic tasks, such as adding numbers and computing parity. While these Transformers generalize well on unseen inputs of the same length, they struggle with length generalization, i.e., handling inputs of unseen lengths. In this work, we demonstrate that looped Transformers with an adaptive number of steps significantly improve length generalization. We focus on tasks with a known iterative solution, involving multiple iterations of a RASP-L operation—a length-generalizable operation that can be expressed by a finite-sized Transformer. We train looped Transformers using our proposed learning algorithm and observe that they learn highly length-generalizable solutions for various tasks. 

We focus on addressing the object counting limitations of vision-language models, with a particular emphasis on Contrastive Language-Image Pre-training (CLIP) models. Centered on our hypothesis that counting knowledge can be abstracted into linear vectors within the text embedding space, we develop a parameter-efficient fine-tuning method and several zero-shot methods to improve CLIP's counting accuracy. Through comprehensive experiments, we demonstrate that our learning-based method not only outperforms full-model fine-tuning in counting accuracy but also retains the broad capabilities of pre-trained CLIP models. Our zero-shot text embedding editing techniques are also effective in situations where training data is scarce, and can be extended to improve Stable Diffusion's ability to generate images with precise object counts. We also contribute two specialized datasets to train and evaluate CLIP’s counting capabilities. Our code is available at https://github.com/UW-Madison-Lee-Lab/CLIP_Counting. 

In-context learning (ICL) exhibits dual operating modes: task learning, i.e., acquiring a new skill from in-context samples, and task retrieval, i.e., locating and activating a relevant pretrained skill. Recent theoretical work proposes various mathematical models to analyze ICL, but they cannot fully explain the duality. In this work, we analyze a generalized probabilistic model for pretraining data, obtaining a quantitative understanding of the two operating modes of ICL. Leveraging our analysis, we provide the first explanation of an unexplained phenomenon observed with real-world large language models (LLMs). Under some settings, the ICL risk initially increases and then decreases with more in-context examples. Our analysis offers a plausible explanation for this "early ascent" phenomenon: a limited number of in-context samples may lead to the retrieval of an incorrect skill, thereby increasing the risk, which will eventually diminish as task learning takes effect with more in-context samples. We also analyze ICL with biased labels, e.g., zero-shot ICL, where in-context examples are assigned random labels, and predict the bounded efficacy of such approaches. We corroborate our analysis and predictions with extensive experiments with Transformers and LLMs. 

The evolution from Large Language Models (LLMs) to Multimodal Large Language Models (MLLMs) has spurred research into extending In-Context Learning (ICL) to its multimodal counterpart. Existing such studies have primarily concentrated on image-to-text ICL. However, the Text-to-Image ICL (T2I-ICL), with its unique characteristics and potential applications, remains underexplored. To address this gap, we formally define the task of T2I-ICL and present CoBSAT, the first T2I-ICL benchmark dataset, encompassing ten tasks. Utilizing our dataset to benchmark six state-of-the-art MLLMs, we uncover considerable difficulties MLLMs encounter in solving T2I-ICL. We identify the primary challenges as the inherent complexity of multimodality and image generation, and show that strategies such as fine-tuning and Chain-of-Thought prompting help to mitigate these difficulties, leading to notable improvements in performance. Our code and dataset are available at https://github.com/UW-Madison-Lee-Lab/CoBSAT. 

This paper introduces a novel theoretical framework for the analysis of vector-valued neu- ral networks through the development of vector-valued variation spaces, a new class of reproducing kernel Banach spaces. These spaces emerge from studying the regularization e↵ect of weight decay in training networks with activation functions like the rectified linear unit (ReLU). This framework o↵ers a deeper understanding of multi-output networks and their function-space characteristics. A key contribution of this work is the development of a representer theorem for the vector-valued variation spaces. This representer theorem estab- lishes that shallow vector-valued neural networks are the solutions to data-fitting problems over these infinite-dimensional spaces, where the network widths are bounded by the square of the number of training data. This observation reveals that the norm associated with these vector-valued variation spaces encourages the learning of features that are useful for multiple tasks, shedding new light on multi-task learning with neural networks. Finally, this paper develops a connection between weight-decay regularization and the multi-task lasso problem. This connection leads to novel bounds for layer widths in deep networks that depend on the intrinsic dimensions of the training data representations. This insight not only deepens the understanding of the deep network architectural requirements, but also yields a simple convex optimization method for deep neural network compression. The performance of this compression procedure is evaluated on various architectures. 

State-space models (SSMs), such as Mamba (Gu & Dao, 2023), have been proposed as alternatives to Transformer networks in language modeling, incorporating gating, convolutions, and input-dependent token selection to mitigate the quadratic cost of multi-head attention. Although SSMs exhibit competitive performance, their in-context learning (ICL) capabilities, a remarkable emergent property of modern language models that enables task execution without parameter optimization, remain less explored compared to Transformers. In this study, we evaluate the ICL performance of SSMs, focusing on Mamba, against Transformer models across various tasks. Our results show that SSMs perform comparably to Transformers in standard regression ICL tasks, while outperforming them in tasks like sparse parity learning. However, SSMs fall short in tasks involving non-standard retrieval functionality. To address these limitations, we introduce a hybrid model, MambaFormer, that combines Mamba with attention blocks, surpassing individual models in tasks where they struggle independently. Our findings suggest that hybrid architectures offer promising avenues for enhancing ICL in language models. 

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction objective. This study investigates how even small transformers, trained from random initialization, can efficiently learn arithmetic operations such as addition, multiplication, and elementary functions like square root, using the next-token prediction objective. We first demonstrate that conventional training data is not the most effective for arithmetic learning, and simple formatting changes can significantly improve accuracy. This leads to sharp phase transitions as a function of training data scale, which, in some cases, can be explained through connections to low-rank matrix completion. Building on prior work, we then train on chain-of-thought style data that includes intermediate step results. Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed. We also study the interplay between arithmetic and text data during training and examine the effects of few-shot prompting, pretraining, and parameter scaling. Additionally, we discuss the challenges associated with length generalization. Our work highlights the importance of high-quality, instructive data that considers the particular characteristics of the next-word prediction loss for rapidly eliciting arithmetic capabilities. 

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. (2022). However, the absence of an inherent iterative structure in the transformer architecture presents a challenge in emulating the iterative algorithms, which are commonly employed in traditional machine learning methods. To address this, we propose the utilization of looped transformer architecture and its associated training methodology, with the aim of incorporating iterative characteristics into the transformer architectures. Experimental results suggest that the looped transformer achieves performance comparable to the standard transformer in solving various data-fitting problems, while utilizing less than 10% of the parameter count.