Baichuan-Omni-1.5 Technical Report

We introduce Baichuan-Omni-1.5, an omni-modal model that not only has omni-modal understanding capabilities but also provides end-to-end audio generation capabilities. To achieve fluent and high-quality interaction across modalities without compromising the capabilities of any modality, we prioritized optimizing three key aspects. First, we establish a comprehensive data cleaning and synthesis pipeline for multimodal data, obtaining about 500B high-quality data (text, audio, and vision). Second, an audio-tokenizer (Baichuan-Audio-Tokenizer) has been designed to capture both semantic and acoustic information from audio, enabling seamless integration and enhanced compatibility with MLLM. Lastly, we designed a multi-stage training strategy that progressively integrates multimodal alignment and multitask fine-tuning, ensuring effective synergy across all modalities. Baichuan-Omni-1.5 leads contemporary models (including GPT4o-mini and MiniCPM-o 2.6) in terms of comprehensive omni-modal capabilities. Notably, it achieves results comparable to leading models such as Qwen2-VL-72B across various multimodal medical benchmarks.

In-Context Learning Distillation for Efficient Few-Shot Fine-Tuning

We applied few-shot in-context learning on the OPT-1.3B model for the natural language inference task and employed knowledge distillation to internalize the context information, reducing model parameter from 1.3B to 125M and achieving a size reduction from 2.5GB to 0.25GB. Compared to using in-context learning alone on similarly sized models, this context distillation approach achieved a nearly 50% improvement in out-of-domain accuracy, demonstrating superior knowledge transfer capabilities over prompt-based methods. Furthermore, this approach reduced memory consumption by up to 60% while delivering a 20% improvement in out-of-domain accuracy compared to conventional pattern-based fine-tuning.

A Minimal Control Family of Dynamical Syetem for Universal Approximation

The universal approximation property (UAP) of neural networks is a fundamental characteristic of deep learning. It is widely recognized that a composition of linear functions and non-linear functions, such as the rectified linear unit (ReLU) activation function, can approximate continuous functions on compact domains. In this paper, we extend this efficacy to the scenario of dynamical systems with controls. We prove that the control family $\mathcal{F}_1 = \mathcal{F}_0 \cup \{ \text{ReLU}(\cdot)\} $ is enough to generate flow maps that can uniformly approximate diffeomorphisms of $\mathbb{R}^d$ on any compact domain, where $\mathcal{F}_0 = \{x \mapsto Ax+b: A\in \mathbb{R}^{d\times d}, b \in \mathbb{R}^d\}$ is the set of linear maps and the dimension $d\ge2$. Since $\mathcal{F}_1$ contains only one nonlinear function and $\mathcal{F}_0$ does not hold the UAP, we call $\mathcal{F}_1$ a minimal control family for UAP. Based on this, some sufficient conditions, such as the affine invariance, on the control family are established and discussed. Our result reveals an underlying connection between the approximation power of neural networks and control systems.

Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximation

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width $w^*_{\min}=\max(d_x,d_y)$, where $d_x$ and $d_y$ are the dimensions of the input and output, respectively. Recently, \cite{cai2022achieve} shows that a leaky-ReLU NN with this critical width can achieve UAP for $L^p$ functions on a compact domain $K$, \emph{i.e.,} the UAP for $L^p(K,\mathbb{R}^{d_y})$. This paper examines a uniform UAP for the function class $C(K,\mathbb{R}^{d_y})$ and gives the exact minimum width of the leaky-ReLU NN as $w_{\min}=\max(d_x+1,d_y)+1_{d_y=d_x+1}$, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

Vanilla feedforward neural networks as a discretization of dynamic systems

Deep learning has made significant applications in the field of data science and natural science. Some studies have linked deep neural networks to dynamic systems, but the network structure is restricted to the residual network. It is known that residual networks can be regarded as a numerical discretization of dynamic systems. In this paper, we back to the classical network structure and prove that the vanilla feedforward networks could also be a numerical discretization of dynamic systems, where the width of the network is equal to the dimension of the input and output. Our proof is based on the properties of the leaky-ReLU function and the numerical technique of splitting method to solve differential equations. Our results could provide a new perspective for understanding the approximation properties of feedforward neural networks.