Large language models (LLMs) have made fundamental contributions over the last a few years. To train an LLM, one needs to alternatingly run `forward' computations and backward computations. The forward computation can be viewed as attention function evaluation, and the backward computation can be viewed as a gradient computation. In previous work by [Alman and Song, NeurIPS 2023], it was proved that the forward step can be performed in almost-linear time in certain parameter regimes, but that there is no truly sub-quadratic time algorithm in the remaining parameter regimes unless the popular hypothesis $\mathsf{SETH}$ is false. In this work, we show nearly identical results for the harder-seeming problem of computing the gradient of loss function of one layer attention network, and thus for the entire process of LLM training. This completely characterizes the fine-grained complexity of every step of LLM training.

Although it is known that transformer language models (LMs) pass features from early layers to later layers, it is not well understood how this information is represented and routed by the model. We analyze a mechanism used in two LMs to selectively inhibit items in a context in one task, and find that it underlies a commonly used abstraction across many context-retrieval behaviors. Specifically, we find that models write into low-rank subspaces of the residual stream to represent features which are then read out by later layers, forming low-rank (Elhage et al., 2021) between layers. A particular 3D subspace in model activations in GPT-2 can be traversed to positionally index items in lists, and we show that this mechanism can explain an otherwise arbitrary-seeming sensitivity of the model to the order of items in the prompt. That is, the model has trouble copying the correct information from context when many items ``crowd this limited space. By decomposing attention heads with the Singular Value Decomposition (SVD), we find that previously described interactions between heads separated by one or more layers can be predicted via analysis of their weight matrices alone. We show that it is possible to manipulate the internal model representations as well as edit model weights based on the mechanism we discover in order to significantly improve performance on our synthetic Laundry List task, which requires recall from a list, often improving task accuracy by over 20\%. Our analysis reveals a surprisingly intricate interpretable structure learned from language model pretraining, and helps us understand why sophisticated LMs sometimes fail in simple domains, facilitating future analysis of more complex behaviors.

When prompting a language model (LM), users often expect the model to adhere to a set of behavioral principles across diverse tasks, such as producing insightful content while avoiding harmful or biased language. Instilling such principles (i.e., a constitution) into a model is resource-intensive, technically challenging, and generally requires human preference labels or examples. We introduce SAMI, an iterative algorithm that finetunes a pretrained language model (without requiring preference labels or demonstrations) to increase the conditional mutual information between constitutions and self-generated responses given queries from a dataset. On single-turn dialogue and summarization, a SAMI-trained mistral-7b outperforms the initial pretrained model, with win rates between 66% and 77%.

Estimating the homography between two images is crucial for mid-or high-level vision tasks, such as image stitching and fusion. However, using supervised learning methods is often challenging or costly due to the difficulty of collecting ground-truth data. In response, unsupervised learning approaches have emerged. Most early methods, though, assume that the given image pairs are from the same camera or have minor lighting differences. Consequently, while these methods perform effectively under such conditions, they generally fail when input image pairs come from different domains, referred to as multimodal image pairs.To address these limitations, we propose AltO, an unsupervised learning framework for estimating homography in multimodal image pairs. Our method employs a two-phase alternating optimization framework, similar to Expectation-Maximization (EM), where one phase reduces the geometry gap and the other addresses the modality gap. To handle these gaps, we use Barlow Twins loss for the modality gap and propose an extended version, Geometry Barlow Twins, for the geometry gap. As a result, we demonstrate that our method, AltO, can be trained on multimodal datasets without any ground-truth data. It not only outperforms other unsupervised methods but is also compatible with various architectures of homography estimators.The source code can be found at: https://github.com/songsang7/AltO

Real-time decision-making gets more attention in the big data era. Here, we consider the problem of sample selection in the online setting, where one encounters a possibly infinite sequence of individuals collected over time with covariate information available. The goal is to select samples of interest that are characterized by their unobserved responses until the user-specified stopping time. We derive a new decision rule that enables us to find more preferable samples that meet practical requirements by simultaneously controlling two types of general constraints: individual and interactive constraints, which include the widely utilized False Selection Rate (FSR), cost limitations, and diversity of selected samples. The key elements of our approach involve quantifying the uncertainty of response predictions via predictive inference and addressing individual and interactive constraints in a sequential manner. Theoretical and numerical results demonstrate the effectiveness of the proposed method in controlling both individual and interactive constraints.

However, the optimization of tasks performance often comes at the cost of generalizability in fine-tuned models. To address this issue, we theoretically connect smaller weight gradient norms during training and larger datasets to the improvements in model generalization. Motivated by this connection, we propose reducing gradient norms for enhanced generalization and aligning fine-tuned model with the pre-trained counterpart to retain knowledge from large-scale pre-training data. Yet, naive alignment does not guarantee gradient reduction and can potentially cause gradient explosion, complicating efforts to manage gradients. To address such an issue, we propose PACE, marrying generalization of PArameter-efficient fine-tuning with Consistency rEgularization. We perturb features learned from the adapter with the multiplicative noise and ensure the fine-tuned model remains consistent for same sample under different perturbations. Theoretical analysis shows that PACE not only implicitly regularizes gradients for enhanced generalization, but also implicitly aligns the fine-tuned and pre-trained models to retain knowledge. Experimental evidence supports our theories.

Low-rank adapters (LoRA) and their variants are popular parameter-efficient fine-tuning (PEFT) techniques that closely match full model fine-tune performance while requiring only a small number of additional parameters. These additional LoRA parameters are specific to the base model being adapted. When the base model needs to be deprecated and replaced with a new one, all the associated LoRA modules need to be re-trained. Such re-training requires access to the data used to train the LoRA for the original base model. This is especially problematic for commercial cloud applications where the LoRA modules and the base models are hosted by service providers who may not be allowed to host proprietary client task data. To address this challenge, we propose $\textit{Trans-LoRA}$ --- a novel method for lossless, nearly data-free transfer of LoRAs across base models. Our approach relies on synthetic data to transfer LoRA modules. Using large language models, we design a synthetic data generator to approximate the data-generating process of the $\textit{observed}$ task data subset.

The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its exceptional rendering quality and performance on standard datasets, 3D-GS frequently encounters difficulties in accurately modeling specular and anisotropic components. This issue stems from the limited ability of spherical harmonics (SH) to represent high-frequency information. To overcome this challenge, we introduce Spec-Gaussian, an approach that utilizes an anisotropic spherical Gaussian (ASG) appearance field instead of SH for modeling the view-dependent appearance of each 3D Gaussian. Additionally, we have developed a coarse-to-fine training strategy to improve learning efficiency and eliminate floaters caused by overfitting in real-world scenes. Our experimental results demonstrate that our method surpasses existing approaches in terms of rendering quality. Thanks to ASG, we have significantly improved the ability of 3D-GS to model scenes with specular and anisotropic components without increasing the number of 3D Gaussians. This improvement extends the applicability of 3D GS to handle intricate scenarios with specular and anisotropic surfaces.

Exploring unknown environments efficiently is a fundamental challenge in unsupervised goal-conditioned reinforcement learning. While selecting exploratory goals at the frontier of previously explored states is an effective strategy, the policy during training may still have limited capability of reaching rare goals on the frontier, resulting in reduced exploratory behavior. We propose Cluster Edge Exploration (CE$^2$), a new goal-directed exploration algorithm that when choosing goals in sparsely explored areas of the state space gives priority to goal states that remain accessible to the agent. The key idea is clustering to group states that are easily reachable from one another by the current policy under training in a latent space, and traversing to states holding significant exploration potential on the boundary of these clusters before doing exploratory behavior. In challenging robotics environments including navigating a maze with a multi-legged ant robot, manipulating objects with a robot arm on a cluttered tabletop, and rotating objects in the palm of an anthropomorphic robotic hand, CE$^2$ demonstrates superior efficiency in exploration compared to baseline methods and ablations.

Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However, existing diffusion priors-based methods either consider simple noise types or rely on approximate posterior estimation, limiting their effectiveness in addressing structured and signal-dependent noise commonly found in real-world images. In this paper, we build upon diffusion priors and propose adaptive likelihood estimation and MAP inference during the reverse diffusion process to tackle real-world noise. We introduce an independent, non-identically distributed likelihood combined with the noise precision (inverse variance) prior and dynamically infer the precision posterior using variational Bayes during the generation process. Meanwhile, we rectify the estimated noise variance through local Gaussian convolution. The final denoised image is obtained by propagating intermediate MAP solutions that balance the updated likelihood and diffusion prior. Additionally, we explore the local diffusion prior inherent in low-resolution diffusion models, enabling direct handling of high-resolution noisy images. Extensive experiments and analyses on diverse real-world datasets demonstrate the effectiveness of our method.