Circuit Complexity Bounds for RoPE-based Transformer Architecture

Characterizing the express power of the Transformer architecture is critical to understanding its capacity limits and scaling law. Recent works provide the circuit complexity bounds to Transformer-like architecture. On the other hand, Rotary Position Embedding ($\mathsf{RoPE}$) has emerged as a crucial technique in modern large language models, offering superior performance in capturing positional information compared to traditional position embeddings, which shows great potential in application prospects, particularly for the long context scenario. Empirical evidence also suggests that $\mathsf{RoPE}$-based Transformer architectures demonstrate greater generalization capabilities compared to conventional Transformer models. In this work, we establish a tighter circuit complexity bound for Transformers with $\mathsf{RoPE}$ attention. Our key contribution is that we show that unless $\mathsf{TC}^0 = \mathsf{NC}^1$, a $\mathsf{RoPE}$-based Transformer with $\mathrm{poly}(n)$-precision, $O(1)$ layers, hidden dimension $d \leq O(n)$ cannot solve the arithmetic problem or the Boolean formula value problem. This result significantly demonstrates the fundamental limitation of the expressivity of the $\mathsf{RoPE}$-based Transformer architecture, although it achieves giant empirical success. Our theoretical framework not only establishes tighter complexity bounds but also may instruct further work on the $\mathsf{RoPE}$-based Transformer.

Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent

In-context learning has been recognized as a key factor in the success of Large Language Models (LLMs). It refers to the model's ability to learn patterns on the fly from provided in-context examples in the prompt during inference. Previous studies have demonstrated that the Transformer architecture used in LLMs can implement a single-step gradient descent update by processing in-context examples in a single forward pass. Recent work has further shown that, during in-context learning, a looped Transformer can implement multi-step gradient descent updates in forward passes. However, their theoretical results require an exponential number of in-context examples, $n = \exp(\Omega(T))$, where $T$ is the number of loops or passes, to achieve a reasonably low error. In this paper, we study linear looped Transformers in-context learning on linear vector generation tasks. We show that linear looped Transformers can implement multi-step gradient descent efficiently for in-context learning. Our results demonstrate that as long as the input data has a constant condition number, e.g., $n = O(d)$, the linear looped Transformers can achieve a small error by multi-step gradient descent during in-context learning. Furthermore, our preliminary experiments validate our theoretical analysis. Our findings reveal that the Transformer architecture possesses a stronger in-context learning capability than previously understood, offering new insights into the mechanisms behind LLMs and potentially guiding the better design of efficient inference algorithms for LLMs.

Advancing the Understanding of Fixed Point Iterations in Deep Neural Networks: A Detailed Analytical Study

Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the development of practical methodologies, such as accelerating inference by bypassing certain layers once the hidden state stabilizes, selectively fine-tuning layers to modify the iteration process, and implementing loops of specific layers to maintain fixed point iterations. Despite these advancements, the understanding of fixed point iterations remains superficial, particularly in high-dimensional spaces, due to the inadequacy of current analytical tools. In this study, we conduct a detailed analysis of fixed point iterations in a vector-valued function modeled by neural networks. We establish a sufficient condition for the existence of multiple fixed points of looped neural networks based on varying input regions. Additionally, we expand our examination to include a robust version of fixed point iterations. To demonstrate the effectiveness and insights provided by our approach, we provide case studies that looped neural networks may exist $2^d$ number of robust fixed points under exponentiation or polynomial activation functions, where $d$ is the feature dimension. Furthermore, our preliminary empirical results support our theoretical findings. Our methodology enriches the toolkit available for analyzing fixed point iterations of deep neural networks and may enhance our comprehension of neural network mechanisms.

Fine-grained Attention I/O Complexity: Comprehensive Analysis for Backward Passes

Large Language Models (LLMs) have demonstrated remarkable capabilities in processing long-context information. However, the quadratic complexity of attention computation with respect to sequence length poses significant computational challenges, and I/O aware algorithms have been proposed. This paper presents a comprehensive analysis of the I/O complexity for attention mechanisms, focusing on backward passes by categorizing into small and large cache scenarios. Using the red-blue pebble game framework, we establish tight bounds on I/O complexity across all cache sizes. We confirm that the de facto standard I/O aware algorithm FlashAttention is optimal for both forward and backward passes for the large cache size scenario. For small cache sizes, we provide an algorithm that improves over existing methods and achieves the tight bounds. Additionally, we extend our analysis to sparse attention, a mainstream speeding-up approach, deriving fine-grained lower bounds for both forward and backward passes and both small and large caches. Our findings complete the theoretical foundation for I/O complexity in attention mechanisms, offering insights for designing efficient algorithms of LLM training and inference.

Array2BR: An End-to-End Noise-immune Binaural Audio Synthesis from Microphone-array Signals

Telepresence technology aims to provide an immersive virtual presence for remote conference applications, and it is extremely important to synthesize high-quality binaural audio signals for this aim. Because the ambient noise is often inevitable in practical application scenarios, it is highly desired that binaural audio signals without noise can be obtained from microphone-array signals directly. For this purpose, this paper proposes a new end-to-end noise-immune binaural audio synthesis framework from microphone-array signals, abbreviated as Array2BR, and experimental results show that binaural cues can be correctly mapped and noise can be well suppressed simultaneously using the proposed framework. Compared with existing methods, the proposed method achieved better performance in terms of both objective and subjective metric scores.

Efficient PAC Learning of Halfspaces with Constant Malicious Noise Rate

Understanding noise tolerance of learning algorithms under certain conditions is a central quest in learning theory. In this work, we study the problem of computationally efficient PAC learning of halfspaces in the presence of malicious noise, where an adversary can corrupt both instances and labels of training samples. The best-known noise tolerance either depends on a target error rate under distributional assumptions or on a margin parameter under large-margin conditions. In this work, we show that when both types of conditions are satisfied, it is possible to achieve {\em constant} noise tolerance by minimizing a reweighted hinge loss. Our key ingredients include: 1) an efficient algorithm that finds weights to control the gradient deterioration from corrupted samples, and 2) a new analysis on the robustness of the hinge loss equipped with such weights.

RockTrack: A 3D Robust Multi-Camera-Ken Multi-Object Tracking Framework

3D Multi-Object Tracking (MOT) obtains significant performance improvements with the rapid advancements in 3D object detection, particularly in cost-effective multi-camera setups. However, the prevalent end-to-end training approach for multi-camera trackers results in detector-specific models, limiting their versatility. Moreover, current generic trackers overlook the unique features of multi-camera detectors, i.e., the unreliability of motion observations and the feasibility of visual information. To address these challenges, we propose RockTrack, a 3D MOT method for multi-camera detectors. Following the Tracking-By-Detection framework, RockTrack is compatible with various off-the-shelf detectors. RockTrack incorporates a confidence-guided preprocessing module to extract reliable motion and image observations from distinct representation spaces from a single detector. These observations are then fused in an association module that leverages geometric and appearance cues to minimize mismatches. The resulting matches are propagated through a staged estimation process, forming the basis for heuristic noise modeling. Additionally, we introduce a novel appearance similarity metric for explicitly characterizing object affinities in multi-camera settings. RockTrack achieves state-of-the-art performance on the nuScenes vision-only tracking leaderboard with 59.1% AMOTA while demonstrating impressive computational efficiency.

StereoCrafter: Diffusion-based Generation of Long and High-fidelity Stereoscopic 3D from Monocular Videos

This paper presents a novel framework for converting 2D videos to immersive stereoscopic 3D, addressing the growing demand for 3D content in immersive experience. Leveraging foundation models as priors, our approach overcomes the limitations of traditional methods and boosts the performance to ensure the high-fidelity generation required by the display devices. The proposed system consists of two main steps: depth-based video splatting for warping and extracting occlusion mask, and stereo video inpainting. We utilize pre-trained stable video diffusion as the backbone and introduce a fine-tuning protocol for the stereo video inpainting task. To handle input video with varying lengths and resolutions, we explore auto-regressive strategies and tiled processing. Finally, a sophisticated data processing pipeline has been developed to reconstruct a large-scale and high-quality dataset to support our training. Our framework demonstrates significant improvements in 2D-to-3D video conversion, offering a practical solution for creating immersive content for 3D devices like Apple Vision Pro and 3D displays. In summary, this work contributes to the field by presenting an effective method for generating high-quality stereoscopic videos from monocular input, potentially transforming how we experience digital media.

DepthCrafter: Generating Consistent Long Depth Sequences for Open-world Videos

Despite significant advancements in monocular depth estimation for static images, estimating video depth in the open world remains challenging, since open-world videos are extremely diverse in content, motion, camera movement, and length. We present DepthCrafter, an innovative method for generating temporally consistent long depth sequences with intricate details for open-world videos, without requiring any supplementary information such as camera poses or optical flow. DepthCrafter achieves generalization ability to open-world videos by training a video-to-depth model from a pre-trained image-to-video diffusion model, through our meticulously designed three-stage training strategy with the compiled paired video-depth datasets. Our training approach enables the model to generate depth sequences with variable lengths at one time, up to 110 frames, and harvest both precise depth details and rich content diversity from realistic and synthetic datasets. We also propose an inference strategy that processes extremely long videos through segment-wise estimation and seamless stitching. Comprehensive evaluations on multiple datasets reveal that DepthCrafter achieves state-of-the-art performance in open-world video depth estimation under zero-shot settings. Furthermore, DepthCrafter facilitates various downstream applications, including depth-based visual effects and conditional video generation.

ViewCrafter: Taming Video Diffusion Models for High-fidelity Novel View Synthesis

Despite recent advancements in neural 3D reconstruction, the dependence on dense multi-view captures restricts their broader applicability. In this work, we propose \textbf{ViewCrafter}, a novel method for synthesizing high-fidelity novel views of generic scenes from single or sparse images with the prior of video diffusion model. Our method takes advantage of the powerful generation capabilities of video diffusion model and the coarse 3D clues offered by point-based representation to generate high-quality video frames with precise camera pose control. To further enlarge the generation range of novel views, we tailored an iterative view synthesis strategy together with a camera trajectory planning algorithm to progressively extend the 3D clues and the areas covered by the novel views. With ViewCrafter, we can facilitate various applications, such as immersive experiences with real-time rendering by efficiently optimizing a 3D-GS representation using the reconstructed 3D points and the generated novel views, and scene-level text-to-3D generation for more imaginative content creation. Extensive experiments on diverse datasets demonstrate the strong generalization capability and superior performance of our method in synthesizing high-fidelity and consistent novel views.