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Large language models based on the Transformer architecture have demonstrated impressive capabilities to learn in context. However, existing theoretical studies on how this phenomenon arises are limited to the dynamics of a single layer of attention trained on linear regression tasks. In this paper, we study the optimization of a Transformer consisting of a fully connected layer followed by a linear attention layer. The MLP acts as a common nonlinear representation or feature map, greatly enhancing the power of in-context learning. We prove in the mean-field and two-timescale limit that the infinite-dimensional loss landscape for the distribution of parameters, while highly nonconvex, becomes quite benign. We also analyze the second-order stability of mean-field dynamics and show that Wasserstein gradient flow almost always avoids saddle points. Furthermore, we establish novel methods for obtaining concrete improvement rates both away from and near critical points. This represents the first saddle point analysis of mean-field dynamics in general and the techniques are of independent interest.

Modern computer vision pipelines handle large images in one of two sub-optimal ways: down-sampling or cropping. These two methods incur significant losses in the amount of information and context present in an image. There are many downstream applications in which global context matters as much as high frequency details, such as in real-world satellite imagery; in such cases researchers have to make the uncomfortable choice of which information to discard. We introduce *xT*, a simple framework for vision transformers which effectively aggregates global context with local details and can model large images end-to-end on contemporary GPUs. We select a set of benchmark datasets across classic vision tasks which accurately reflect a vision model's ability to understand truly large images and incorporate fine details over large scales and assess our method's improvement on them. *xT* is a streaming, two-stage architecture that adapts existing vision backbones and long sequence language models to effectively model large images without quadratic memory growth. We are able to increase accuracy by up to 8.6% on challenging classification tasks and F1 score by 11.6 on context-dependent segmentation on images as large as 29,000 x 29,000 pixels.

Large Language Models (LLMs) are trained on massive text corpora, which are encoded with diverse personality traits. This triggers an interesting goal of eliciting a desired personality trait from the LLM, and probing its behavioral preferences. Accordingly, we formalize the persona elicitation task, aiming to customize LLM behaviors to align with a target persona. We present Persona In-Context Learning (PICLe), a novel persona elicitation framework grounded in Bayesian inference. At the core, PICLe introduces a new ICL example selection criterion based on likelihood ratio, which is designed to optimally guide the model in eliciting a specific target persona. We demonstrate the effectiveness of PICLe through extensive comparisons against baseline methods across three contemporary LLMs. Code is available at https://github.com/deeplearning-wisc/picle.

Many computational factors limit broader deployment of large language models. In this paper, we focus on a memory bottleneck imposed by the key-value (KV) cache, a computational shortcut that requires storing previous KV pairs during decoding. While existing KV cache methods approach this problem by pruning or evicting large swaths of relatively less important KV pairs to dramatically reduce the memory footprint of the cache, they can have limited success in tasks that require recollecting a majority of previous tokens. To alleviate this issue, we propose LESS, a simple integration of a (nearly free) constant sized cache with eviction-based cache methods, such that all tokens can be queried at later decoding steps. Its ability to retain information throughout time shows merit on a variety of tasks where we demonstrate LESS can help reduce the performance gap from caching everything, sometimes even matching it, all while being efficient. Relevant code can be found at https://github.com/hdong920/LESS.

The past few years have seen an intense research interest in the practical needs of the "right to be forgotten", which has motivated researchers to develop machine unlearning methods to unlearn a fraction of training data and its lineage. While existing machine unlearning methods prioritize the protection of individuals' private data, they overlook investigating the unlearned models' susceptibility to adversarial attacks and security breaches. In this work, we uncover a novel security vulnerability of machine unlearning based on the insight that adversarial vulnerabilities can be bolstered, especially for adversarially robust models. To exploit this observed vulnerability, we propose a novel attack called Adversarial Unlearning Attack (AdvUA), which aims to generate a small fraction of malicious unlearning requests during the unlearning process. AdvUA causes a significant reduction of adversarial robustness in the unlearned model compared to the original model, providing an entirely new capability for adversaries that is infeasible in conventional machine learning pipelines. Notably, we also show that AdvUA can effectively enhance model stealing attacks by extracting additional decision boundary information, further emphasizing the breadth and significance of our research. We also conduct both theoretical analysis and computational complexity of AdvUA. Extensive numerical studies are performed to demonstrate the effectiveness and efficiency of the proposed attack.

Transformer-based neural sequence models exhibit a remarkable ability to perform in-context learning. Given some training examples, a pre-trained model can make accurate predictions on an unseen input. This paper studies why transformers can learn different types of function classes in-context. We first show by construction that there exists a family of transformers (with different activation functions) that implement approximate gradient descent on the parameters of neural networks, and we provide an upper bound for the number of heads, hidden dimensions, and layers of the transformer. We also show that a transformer can learn linear functions, the indicator function of a unit ball, and smooth functions in-context by learning neural networks that approximate them. The above instances mainly focus on a transformer pre-trained on single tasks. We also prove that when pre-trained on two tasks: linear regression and classification, a transformer can make accurate predictions on both tasks simultaneously. Our results move beyond linearity in terms of in-context learning instances and provide a comprehensive understanding of why transformers can learn many types of function classes through the bridge of neural networks.

It is well known that LLMs cannot generalize well to long contexts whose lengths are larger than the training sequence length. This poses challenges when employing LLMs for processing long input sequences during inference. In this work, we argue that LLMs themselves have inherent capabilities to handles s long contexts without fine-tuning. To achieve this goal, we propose SelfExtend to extend the context window of LLMs by constructing bi-level attention information: the grouped attention and the neighbor attention. The grouped attention captures the dependencies among tokens that are far apart, while neighbor attention captures dependencies among adjacent tokens within a specified range. The two-level attentions are computed based on the original model's self-attention mechanism during inference. With minor code modification, our SelfExtend can effortlessly extend existing LLMs' context window without any fine-tuning. We conduct comprehensive experiments on multiple benchmarks and the results show that our SelfExtend can effectively extend existing LLMs' context window length.

Large language models (LLMs) show excellent performance in difficult tasks, but they often require massive memories and computational resources. How to reduce the parameter scale of LLMs has become research hotspots. In this study, we get an important observation that the multi-head self-attention (MHA) sub-layer of Transformer exhibits noticeable low-rank structure, while the feed-forward network (FFN) sub-layer does not. With this regard, we design a novel structured compression method LoRAP, which organically combines **Lo**w-**R**ank matrix approximation **A**nd structured **P**runing. For the MHA sub-layer, we proposal an input activation weighted singular value decomposition method and allocate different parameter amounts for each weight matrix based on the differences in low-rank properties of matrices.For the FFN sub-layer, we propose a gradient-free structured channel pruning method and save the least important 1% of parameters which actually play a vital role in model performance. Extensive evaluations on zero-shot perplexity and zero-shot task classification indicate that our proposal is superior to previous structured compression rivals under multiple compression ratios. Our code will be released soon.

Transformers have achieved state-of-the-art performance in language modeling tasks. However, the reasons behind their tremendous success are still unclear. In this paper, towards a better understanding, we train a Transformer model on a simple next token prediction task, where sequences are generated as a first-order autoregressive process $s_{t+1} = W s_t$. We show how a trained Transformer predicts the next token by first learning $W$ in-context, then applying a prediction mapping. We call the resulting procedure *in-context autoregressive learning*. More precisely, focusing on commuting orthogonal matrices $W$, we first show that a trained one-layer linear Transformer implements one step of gradient descent for the minimization of an inner objective function, when considering augmented tokens. When the tokens are not augmented, we characterize the global minima of a one-layer diagonal linear multi-head Transformer. Importantly, we exhibit orthogonality between heads and show that positional encoding captures trigonometric relations in the data. On the experimental side, we consider the general case of non-commuting orthogonal matrices and generalize our theoretical findings.

Language models can learn sophisticated language understanding skills from fitting raw text. They also unselectively learn useless corpus statistics and biases, especially during finetuning on domain-specific corpora. In this paper, we propose a simple modification to causal language modeling called conditional finetuning, which performs language modeling conditioned on a context. We show that a context can "explain away" certain corpus statistics and make the model avoid learning them. In this fashion, conditional finetuning achieves selective learning from a corpus, learning knowledge useful for downstream tasks while avoiding learning useless corpus statistics like topic biases. This selective learning effect leads to less forgetting and better stability-plasticity tradeoff in domain finetuning, potentially benefitting lifelong learning with language models.

Large language models (LLM) have recently attracted significant attention in the field of artificial intelligence. However, the training process of these models poses significant challenges in terms of computational and storage capacities, thus compressing checkpoints has become an urgent problem. In this paper, we propose a novel Extreme Checkpoint Compression (ExCP) framework, which significantly reduces the required storage of training checkpoints while achieving nearly lossless performance. We first calculate the residuals of adjacent checkpoints to obtain the essential but sparse information for higher compression ratio. To further excavate the redundancy parameters in checkpoints, we then propose a weight-momentum joint shrinking method to utilize another important information during the model optimization, i.e., momentum. In particular, we exploit the information of both model and optimizer to discard as many parameters as possible while preserving critical information to ensure optimal performance. Furthermore, we utilize non-uniform quantization to further compress the storage of checkpoints. We extensively evaluate our proposed ExCP framework on several models ranging from 410M to 7B parameters and demonstrate significant storage reduction while maintaining strong performance. For instance, we achieve approximately $70\times$ compression for the Pythia-410M model, with the final performance being as accurate as the original model on various downstream tasks. Codes will be available at https://github.com/Gaffey/ExCP.

In-context learning (ICL) has emerged as a particularly remarkable characteristic of Large Language Models (LLM): given a pretrained LLM and an observed dataset, LLMs can make predictions for new data points from the same distribution without fine-tuning. Numerous works have postulated ICL as approximately Bayesian inference, rendering this a natural hypothesis. In this work, we analyse this hypothesis from a new angle through the *martingale property*, a fundamental requirement of a Bayesian learning system for exchangeable data. We show that the martingale property is a necessary condition for unambiguous predictions in such scenarios, and enables a principled, decomposed notion of uncertainty vital in trustworthy, safety-critical systems. We derive actionable checks with corresponding theory and test statistics which must hold if the martingale property is satisfied. We also examine if uncertainty in LLMs decreases as expected in Bayesian learning when more data is observed. In three experiments, we provide evidence for violations of the martingale property, and deviations from a Bayesian scaling behaviour of uncertainty, falsifying the hypothesis that ICL is Bayesian.

Many neural network architectures are known to be Turing Complete, and can thus, in principle implement arbitrary algorithms. However, Transformers are unique in that they can implement gradient-based learning algorithms *under simple parameter configurations*. This paper provides theoretical and empirical evidence that (non-linear) Transformers naturally learn to implement gradient descent *in function space*, which in turn enable them to learn non-linear functions in context. Our results apply to a broad class of combinations of non-linear architectures and non-linear in-context learning tasks. Additionally, we show that the optimal choice of non-linear activation depends in a natural way on the class of functions that need to be learned.

The emergence of In-Context Learning (ICL) in LLMs remains a remarkable phenomenon that is partially understood. To explain ICL, recent studies have created theoretical connections to Gradient Descent (GD). We ask, do such connections hold up in actual pre-trained language models? We highlight the limiting assumptions in prior works that make their setup considerably different from the practical setup in which language models are trained. For example, their experimental verification uses *ICL objective* (training models explicitly for ICL), which differs from the emergent ICL in the wild. Furthermore, the theoretical hand-constructed weights used in these studies have properties that don't match those of real LLMs. We also look for evidence in real models. We observe that ICL and GD have different sensitivity to the order in which they observe demonstrations. Finally, we probe and compare the ICL vs. GD hypothesis in a natural setting. We conduct comprehensive empirical analyses on language models pre-trained on natural data (LLaMa-7B). Our comparisons of three performance metrics highlight the inconsistent behavior of ICL and GD as a function of various factors such as datasets, models, and the number of demonstrations. We observe that ICL and GD modify the output distribution of language models differently. These results indicate that *the equivalence between ICL and GD remains an open hypothesis* and calls for further studies.

Large language models (LLM) have emerged as a powerful tool for AI, with the key ability of in-context learning (ICL), where they can perform well on unseen tasks based on a brief series of task examples without necessitating any adjustments to the model parameters. One recent interesting mysterious observation is that models of different scales may have different ICL behaviors: larger models tend to be more sensitive to noise in the test context. This work studies this observation theoretically aiming to improve the understanding of LLM and ICL. We analyze two stylized settings: (1) linear regression with one-layer single-head linear transformers and (2) parity classification with two-layer multiple attention heads transformers (non-linear data and non-linear model). In both settings, we give closed-form optimal solutions and find that smaller models emphasize important hidden features while larger ones cover more hidden features; thus, smaller models are more robust to noise while larger ones are more easily distracted, leading to different ICL behaviors. This sheds light on where transformers pay attention to and how that affects ICL. Preliminary experimental results on large base and chat models provide positive support for our analysis.

In-context learning (ICL, also known as few-shot prompting) has been the standard method of adapting LLMs to downstream tasks, by learning from a few input-output examples. Nonetheless, all ICL-based approaches only learn from correct input-output pairs. In this paper, we revisit this paradigm, by learning more from the few given input-output examples. We introduce Learning Principles (LEAP): First, we intentionally induce the model to make mistakes on these few examples; then we reflect on these mistakes, and learn explicit task-specific “principles” from them, which help solve similar problems and avoid common mistakes; finally, we prompt the model to answer unseen test questions using the original few-shot examples and these learned general principles. We evaluate LEAP on a wide range of benchmarks, including multi-hop question answering (Hotpot QA), textual QA (DROP), Big-Bench Hard reasoning, and math problems (GSM8K and MATH); in all these benchmarks, LEAP improves the strongest available LLMs such as GPT-3.5-turbo, GPT-4, GPT-4-turbo and Claude-2.1. For example, LEAP improves over the standard few-shot prompting using GPT-4 by 7.5% in DROP, and by 3.3% in HotpotQA. Importantly, LEAP does not require any more input or examples than the standard few-shot prompting settings.

Large context window is a desirable feature in large language models (LLMs). However, due to high fine-tuning costs, scarcity of long texts, and catastrophic values introduced by new token positions, current extended context windows are limited to around 128k tokens. This paper introduces LongRoPE that, for the first time, extends the context window of pre-trained LLMs to an impressive 2048k tokens, with up to only 1k fine-tuning steps at within 256k training lengths, while maintaining performance at the original short context window. This is achieved by three key innovations: (i) we identify and exploit two forms of non-uniformities in positional interpolation through an efficient search, providing a better initialization for fine-tuning and enabling an 8x extension in non-fine-tuning scenarios; (ii) we introduce a progressive extension strategy that first fine-tunes a 256k length LLM and then conducts a second positional interpolation on the fine-tuned extended LLM to achieve a 2048k context window; (iii) we readjust LongRoPE on 8k length to recover the short context window performance. Extensive experiments on LLaMA2 and Mistral across various tasks demonstrate the effectiveness of our method. Models extended via LongRoPE retain the original architecture with minor modifications to the positional embedding, and can reuse most pre-existing optimizations. Code is available at https://github.com/microsoft/LongRoPE

This paper tackles the memory hurdle of of processing long context sequences in Large Language Models (LLMs), by presenting a novel approach, Dropping In Convolutions for **Lo**ng **Co**ntext **Co**mpression (**LoCoCo**). LoCoCo employs only a fixed-size Key-Value (KV) cache, and can enhance efficiency in both inference and fine-tuning stages. Diverging from prior methods that selectively drop KV pairs based on heuristics, LoCoCo leverages a data-driven adaptive fusion technique, blending previous KV pairs with incoming tokens to minimize the loss of contextual information and ensure accurate attention modeling. This token integration is achieved through injecting one-dimensional convolutional kernels that dynamically calculate mixing weights for each KV cache slot. Designed for broad compatibility with existing LLM frameworks, LoCoCo allows for straightforward "drop-in" integration without needing architectural modifications, while incurring minimal tuning overhead. Experiments demonstrate that LoCoCo maintains consistently outstanding performance across various context lengths and can achieve a high context compression rate during both inference and fine-tuning phases. During inference, we successfully compressed up to $3482$ tokens into a $128$-size KV cache, while retaining comparable performance to the full sequence - an accuracy improvement of up to $0.2791$ compared to baselines at the same cache size. During post-training tuning, we also effectively extended the context length from 4K to 32K using a KV cache of fixed size 512, achieving performance similar to fine-tuning with entire sequences.

Previous theoretical results pertaining to meta-learning on sequences build on contrived and convoluted mixing time assumptions. We introduce new information-theoretic tools that lead to a concise yet general decomposition of error for a Bayes optimal predictor into two components: meta-learning error and intra-task error. These tools unify analyses across many meta-learning challenges. To illustrate, we apply them to establish new results about in-context learning with transformers and corroborate existing results a simple linear setting. Our theoretical results characterize how error decays in both the number of training sequences and sequence lengths. Our results are very general; for example, they avoid contrived mixing time assumptions made by all prior results that establish decay of error with sequence length.

In-Context Learning (ICL) has been a powerful emergent property of large language models that has attracted increasing attention in recent years. In contrast to regular gradient-based learning, ICL is highly interpretable and does not require parameter updates. In this paper, we show that, for linearized transformer networks, ICL can be made explicit and permanent through the inclusion of bias terms. We mathematically demonstrate the equivalence between a model with ICL demonstration prompts and the same model with the additional bias terms. Our algorithm (ICLCA) allows for exact conversion in an inexpensive manner. Existing methods are not exact and require expensive parameter updates. We demonstrate the efficacy of our approach through experiments that show the exact incorporation of ICL tokens into a linear transformer. We further suggest how our method can be adapted to achieve cheap approximate conversion of ICL tokens, even in regular transformer networks that are not linearized. Our experiments on GPT-2 show that, even though the conversion is only approximate, the model still gains valuable context from the included bias terms.