PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models

As the parameters of LLMs expand, the computational cost of fine-tuning the entire model becomes prohibitive. To address this challenge, we introduce a PEFT method, Principal Singular values and Singular vectors Adaptation (PiSSA), which optimizes a significantly reduced parameter space while achieving or surpassing the performance of full-parameter fine-tuning. PiSSA is inspired by Intrinsic SAID, which suggests that pre-trained, over-parametrized models inhabit a space of low intrinsic dimension. Consequently, PiSSA represents a matrix W within the model by the product of two trainable matrices A and B, plus a residual matrix $W^{res}$ for error correction. SVD is employed to factorize W, and the principal singular values and vectors of W are utilized to initialize A and B. The residual singular values and vectors initialize the residual matrix $W^{res}$, which keeps frozen during fine-tuning. Notably, PiSSA shares the same architecture with LoRA. However, LoRA approximates Delta W through the product of two matrices, A, initialized with Gaussian noise, and B, initialized with zeros, while PiSSA initializes A and B with principal singular values and vectors of the original matrix W. PiSSA can better approximate the outcomes of full-parameter fine-tuning at the beginning by changing the essential parts while freezing the "noisy" parts. In comparison, LoRA freezes the original matrix and updates the "noise". This distinction enables PiSSA to convergence much faster than LoRA and also achieve better performance in the end. Due to the same architecture, PiSSA inherits many of LoRA's advantages, such as parameter efficiency and compatibility with quantization. Leveraging a fast SVD method, the initialization of PiSSA takes only a few seconds, inducing negligible cost of switching LoRA to PiSSA.

Chain of Images for Intuitively Reasoning

The human brain is naturally equipped to comprehend and interpret visual information rapidly. When confronted with complex problems or concepts, we use flowcharts, sketches, and diagrams to aid our thought process. Leveraging this inherent ability can significantly enhance logical reasoning. However, current Large Language Models (LLMs) do not utilize such visual intuition to help their thinking. Even the most advanced version language models (e.g., GPT-4V and LLaVA) merely align images into textual space, which means their reasoning processes remain purely verbal. To mitigate such limitations, we present a Chain of Images (CoI) approach, which can convert complex language reasoning problems to simple pattern recognition by generating a series of images as intermediate representations. Furthermore, we have developed a CoI evaluation dataset encompassing 15 distinct domains where images can intuitively aid problem-solving. Based on this dataset, we aim to construct a benchmark to assess the capability of future multimodal large-scale models to leverage images for reasoning. In supporting our CoI reasoning, we introduce a symbolic multimodal large language model (SyMLLM) that generates images strictly based on language instructions and accepts both text and image as input. Experiments on Geometry, Chess and Common Sense tasks sourced from the CoI evaluation dataset show that CoI improves performance significantly over the pure-language Chain of Thoughts (CoT) baselines. The code is available at https://github.com/GraphPKU/CoI.

Explaining the Complex Task Reasoning of Large Language Models with Template-Content Structure

The continuous evolution of pre-trained large language models with ever-growing parameters and corpus sizes has augmented their capacity to solve complex tasks. This ability, which obviates the necessity for task-specific training or fine-tuning, relies on providing the model with a language description or some task exemplars -- referred to the prompt -- that guide the desired autoregressive generation. Despite the remarkable success, the underlying mechanisms that facilitate such exceptional generalization abilities remain an open question. In this paper, we present a novel framework that formally conceptualizes answer generation for complex natural language tasks as a hierarchical ``template-content'' structure. According to our modeling, there exist pre-trained models that can automatically decompose tasks into constituent steps during autoregressive generation, through language modeling on a sufficiently large corpus, thereby solving them. Our framework offers an explanatory tool for the complex reasoning abilities of large language models from the perspective of modeling autoregressive generation tasks. Our experiments show that practical models exhibit different behaviors for ``template'' and ``content'' providing support for our modeling.

Large Language Models are In-Context Semantic Reasoners rather than Symbolic Reasoners

The emergent few-shot reasoning capabilities of Large Language Models (LLMs) have excited the natural language and machine learning community over recent years. Despite of numerous successful applications, the underlying mechanism of such in-context capabilities still remains unclear. In this work, we hypothesize that the learned \textit{semantics} of language tokens do the most heavy lifting during the reasoning process. Different from human's symbolic reasoning process, the semantic representations of LLMs could create strong connections among tokens, thus composing a superficial logical chain. To test our hypothesis, we decouple semantics from the language reasoning process and evaluate three kinds of reasoning abilities, i.e., deduction, induction and abduction. Our findings reveal that semantics play a vital role in LLMs' in-context reasoning -- LLMs perform significantly better when semantics are consistent with commonsense but struggle to solve symbolic or counter-commonsense reasoning tasks by leveraging in-context new knowledge. The surprising observations question whether modern LLMs have mastered the inductive, deductive and abductive reasoning abilities as in human intelligence, and motivate research on unveiling the magic existing within the black-box LLMs. On the whole, our analysis provides a novel perspective on the role of semantics in developing and evaluating language models' reasoning abilities. Code is available at {\url{https://github.com/XiaojuanTang/ICSR}}.

RMNet: Equivalently Removing Residual Connection from Networks

Although residual connection enables training very deep neural networks, it is not friendly for online inference due to its multi-branch topology. This encourages many researchers to work on designing DNNs without residual connections at inference. For example, RepVGG re-parameterizes multi-branch topology to a VGG-like (single-branch) model when deploying, showing great performance when the network is relatively shallow. However, RepVGG can not transform ResNet to VGG equivalently because re-parameterizing methods can only be applied to linear blocks and the non-linear layers (ReLU) have to be put outside of the residual connection which results in limited representation ability, especially for deeper networks. In this paper, we aim to remedy this problem and propose to remove the residual connection in a vanilla ResNet equivalently by a reserving and merging (RM) operation on ResBlock. Specifically, the RM operation allows input feature maps to pass through the block while reserving their information and merges all the information at the end of each block, which can remove residual connections without changing the original output. As a plug-in method, RM Operation basically has three advantages: 1) its implementation makes it naturally friendly for high ratio network pruning. 2) it helps break the depth limitation of RepVGG. 3) it leads to better accuracy-speed trade-off network (RMNet) compared to ResNet and RepVGG. We believe the ideology of RM Operation can inspire many insights on model design for the community in the future. Code is available at: https://github.com/fxmeng/RMNet.

On The Consistency Training for Open-Set Semi-Supervised Learning

Conventional semi-supervised learning (SSL) methods, e.g., MixMatch, achieve great performance when both labeled and unlabeled dataset are drawn from the same distribution. However, these methods often suffer severe performance degradation in a more realistic setting, where unlabeled dataset contains out-of-distribution (OOD) samples. Recent approaches mitigate the negative influence of OOD samples by filtering them out from the unlabeled data. Our studies show that it is not necessary to get rid of OOD samples during training. On the contrary, the network can benefit from them if OOD samples are properly utilized. We thoroughly study how OOD samples affect DNN training in both low- and high-dimensional spaces, where two fundamental SSL methods are considered: Pseudo Labeling (PL) and Data Augmentation based Consistency Training (DACT). Conclusion is twofold: (1) unlike PL that suffers performance degradation, DACT brings improvement to model performance; (2) the improvement is closely related to class-wise distribution gap between the labeled and the unlabeled dataset. Motivated by this observation, we further improve the model performance by bridging the gap between the labeled and the unlabeled datasets (containing OOD samples). Compared to previous algorithms paying much attention to distinguishing between ID and OOD samples, our method makes better use of OOD samples and achieves state-of-the-art results.

Pruning Filter in Filter

Pruning has become a very powerful and effective technique to compress and accelerate modern neural networks. Existing pruning methods can be grouped into two categories: filter pruning (FP) and weight pruning (WP). FP wins at hardware compatibility but loses at the compression ratio compared with WP. To converge the strength of both methods, we propose to prune the filter in the filter. Specifically, we treat a filter $F \in \mathbb{R}^{C\times K\times K}$ as $K \times K$ stripes, \emph{i.e.}, $1\times 1$ filters $\in \mathbb{R}^{C}$, then by pruning the stripes instead of the whole filter, we can achieve finer granularity than traditional FP while being hardware friendly. We term our method as SWP (\emph{Stripe-Wise Pruning}). SWP is implemented by introducing a novel learnable matrix called Filter Skeleton, whose values reflect the shape of each filter. As some recent work has shown that the pruned architecture is more crucial than the inherited important weights, we argue that the architecture of a single filter, \emph{i.e.}, the shape, also matters. Through extensive experiments, we demonstrate that SWP is more effective compared to the previous FP-based methods and achieves the state-of-art pruning ratio on CIFAR-10 and ImageNet datasets without obvious accuracy drop. Code is available at https://github.com/fxmeng/Pruning-Filter-in-Filter

DGD: Densifying the Knowledge of Neural Networks with Filter Grafting and Knowledge Distillation

With a fixed model structure, knowledge distillation and filter grafting are two effective ways to boost single model accuracy. However, the working mechanism and the differences between distillation and grafting have not been fully unveiled. In this paper, we evaluate the effect of distillation and grafting in the filter level, and find that the impacts of the two techniques are surprisingly complementary: distillation mostly enhances the knowledge of valid filters while grafting mostly reactivates invalid filters. This observation guides us to design a unified training framework called DGD, where distillation and grafting are naturally combined to increase the knowledge density inside the filters given a fixed model structure. Through extensive experiments, we show that the knowledge densified network in DGD shares both advantages of distillation and grafting, lifting the model accuracy to a higher level.