Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabularies

Research on scaling large language models (LLMs) has primarily focused on model parameters and training data size, overlooking the role of vocabulary size. % Intuitively, larger vocabularies enable more efficient tokenization by representing sentences with fewer tokens, but they also increase the risk of under-fitting representations for rare tokens. We investigate how vocabulary size impacts LLM scaling laws by training models ranging from 33M to 3B parameters on up to 500B characters with various vocabulary configurations. We propose three complementary approaches for predicting the compute-optimal vocabulary size: IsoFLOPs analysis, derivative estimation, and parametric fit of the loss function. Our approaches converge on the same result that the optimal vocabulary size depends on the available compute budget and that larger models deserve larger vocabularies. However, most LLMs use too small vocabulary sizes. For example, we predict that the optimal vocabulary size of Llama2-70B should have been at least 216K, 7 times larger than its vocabulary of 32K. We validate our predictions empirically by training models with 3B parameters across different FLOPs budgets. Adopting our predicted optimal vocabulary size consistently improves downstream performance over commonly used vocabulary sizes. By increasing the vocabulary size from the conventional 32K to 43K, we improve performance on ARC-Challenge from 29.1 to 32.0 with the same 2.3e21 FLOPs. Our work emphasizes the necessity of jointly considering model parameters and vocabulary size for efficient scaling.

Mixture-of-Subspaces in Low-Rank Adaptation

In this paper, we introduce a subspace-inspired Low-Rank Adaptation (LoRA) method, which is computationally efficient, easy to implement, and readily applicable to large language, multimodal, and diffusion models. Initially, we equivalently decompose the weights of LoRA into two subspaces, and find that simply mixing them can enhance performance. To study such a phenomenon, we revisit it through a fine-grained subspace lens, showing that such modification is equivalent to employing a fixed mixer to fuse the subspaces. To be more flexible, we jointly learn the mixer with the original LoRA weights, and term the method Mixture-of-Subspaces LoRA (MoSLoRA). MoSLoRA consistently outperforms LoRA on tasks in different modalities, including commonsense reasoning, visual instruction tuning, and subject-driven text-to-image generation, demonstrating its effectiveness and robustness. Codes are available at \href{https://github.com/wutaiqiang/MoSLoRA}{github}.

ASMR: Activation-sharing Multi-resolution Coordinate Networks For Efficient Inference

Coordinate network or implicit neural representation (INR) is a fast-emerging method for encoding natural signals (such as images and videos) with the benefits of a compact neural representation. While numerous methods have been proposed to increase the encoding capabilities of an INR, an often overlooked aspect is the inference efficiency, usually measured in multiply-accumulate (MAC) count. This is particularly critical in use cases where inference throughput is greatly limited by hardware constraints. To this end, we propose the Activation-Sharing Multi-Resolution (ASMR) coordinate network that combines multi-resolution coordinate decomposition with hierarchical modulations. Specifically, an ASMR model enables the sharing of activations across grids of the data. This largely decouples its inference cost from its depth which is directly correlated to its reconstruction capability, and renders a near O(1) inference complexity irrespective of the number of layers. Experiments show that ASMR can reduce the MAC of a vanilla SIREN model by up to 500x while achieving an even higher reconstruction quality than its SIREN baseline.

Nonparametric Teaching of Implicit Neural Representations

We investigate the learning of implicit neural representation (INR) using an overparameterized multilayer perceptron (MLP) via a novel nonparametric teaching perspective. The latter offers an efficient example selection framework for teaching nonparametrically defined (viz. non-closed-form) target functions, such as image functions defined by 2D grids of pixels. To address the costly training of INRs, we propose a paradigm called Implicit Neural Teaching (INT) that treats INR learning as a nonparametric teaching problem, where the given signal being fitted serves as the target function. The teacher then selects signal fragments for iterative training of the MLP to achieve fast convergence. By establishing a connection between MLP evolution through parameter-based gradient descent and that of function evolution through functional gradient descent in nonparametric teaching, we show for the first time that teaching an overparameterized MLP is consistent with teaching a nonparametric learner. This new discovery readily permits a convenient drop-in of nonparametric teaching algorithms to broadly enhance INR training efficiency, demonstrating 30%+ training time savings across various input modalities.

Poisoning-based Backdoor Attacks for Arbitrary Target Label with Positive Triggers

Poisoning-based backdoor attacks expose vulnerabilities in the data preparation stage of deep neural network (DNN) training. The DNNs trained on the poisoned dataset will be embedded with a backdoor, making them behave well on clean data while outputting malicious predictions whenever a trigger is applied. To exploit the abundant information contained in the input data to output label mapping, our scheme utilizes the network trained from the clean dataset as a trigger generator to produce poisons that significantly raise the success rate of backdoor attacks versus conventional approaches. Specifically, we provide a new categorization of triggers inspired by the adversarial technique and develop a multi-label and multi-payload Poisoning-based backdoor attack with Positive Triggers (PPT), which effectively moves the input closer to the target label on benign classifiers. After the classifier is trained on the poisoned dataset, we can generate an input-label-aware trigger to make the infected classifier predict any given input to any target label with a high possibility. Under both dirty- and clean-label settings, we show empirically that the proposed attack achieves a high attack success rate without sacrificing accuracy across various datasets, including SVHN, CIFAR10, GTSRB, and Tiny ImageNet. Furthermore, the PPT attack can elude a variety of classical backdoor defenses, proving its effectiveness.

Stochastic Multivariate Universal-Radix Finite-State Machine: a Theoretically and Practically Elegant Nonlinear Function Approximator

Nonlinearities are crucial for capturing complex input-output relationships especially in deep neural networks. However, nonlinear functions often incur various hardware and compute overheads. Meanwhile, stochastic computing (SC) has emerged as a promising approach to tackle this challenge by trading output precision for hardware simplicity. To this end, this paper proposes a first-of-its-kind stochastic multivariate universal-radix finite-state machine (SMURF) that harnesses SC for hardware-simplistic multivariate nonlinear function generation at high accuracy. We present the finite-state machine (FSM) architecture for SMURF, as well as analytical derivations of sampling gate coefficients for accurately approximating generic nonlinear functions. Experiments demonstrate the superiority of SMURF, requiring only 16.07% area and 14.45% power consumption of Taylor-series approximation, and merely 2.22% area of look-up table (LUT) schemes.

Rethinking Kullback-Leibler Divergence in Knowledge Distillation for Large Language Models

Kullback-Leiber divergence has been widely used in Knowledge Distillation (KD) to compress Large Language Models (LLMs). Contrary to prior assertions that reverse Kullback-Leibler (RKL) divergence is mode-seeking and thus preferable over the mean-seeking forward Kullback-Leibler (FKL) divergence, this study empirically and theoretically demonstrates that neither mode-seeking nor mean-seeking properties manifest in KD for LLMs. Instead, RKL and FKL are found to share the same optimization objective and both converge after a sufficient number of epochs. However, due to practical constraints, LLMs are seldom trained for such an extensive number of epochs. Meanwhile, we further find that RKL focuses on the tail part of the distributions, while FKL focuses on the head part at the beginning epochs. Consequently, we propose a simple yet effective Adaptive Kullback-Leiber (AKL) divergence method, which adaptively allocates weights to combine FKL and RKL. Metric-based and GPT-4-based evaluations demonstrate that the proposed AKL outperforms the baselines across various tasks and improves the diversity and quality of generated responses.

Taming Lookup Tables for Efficient Image Retouching

The widespread use of high-definition screens in edge devices, such as end-user cameras, smartphones, and televisions, is spurring a significant demand for image enhancement. Existing enhancement models often optimize for high performance while falling short of reducing hardware inference time and power consumption, especially on edge devices with constrained computing and storage resources. To this end, we propose Image Color Enhancement Lookup Table (ICELUT) that adopts LUTs for extremely efficient edge inference, without any convolutional neural network (CNN). During training, we leverage pointwise (1x1) convolution to extract color information, alongside a split fully connected layer to incorporate global information. Both components are then seamlessly converted into LUTs for hardware-agnostic deployment. ICELUT achieves near-state-of-the-art performance and remarkably low power consumption. We observe that the pointwise network structure exhibits robust scalability, upkeeping the performance even with a heavily downsampled 32x32 input image. These enable ICELUT, the first-ever purely LUT-based image enhancer, to reach an unprecedented speed of 0.4ms on GPU and 7ms on CPU, at least one order faster than any CNN solution. Codes are available at https://github.com/Stephen0808/ICELUT.

APTQ: Attention-aware Post-Training Mixed-Precision Quantization for Large Language Models

Large Language Models (LLMs) have greatly advanced the natural language processing paradigm. However, the high computational load and huge model sizes pose a grand challenge for deployment on edge devices. To this end, we propose APTQ (Attention-aware Post-Training Mixed-Precision Quantization) for LLMs, which considers not only the second-order information of each layer's weights, but also, for the first time, the nonlinear effect of attention outputs on the entire model. We leverage the Hessian trace as a sensitivity metric for mixed-precision quantization, ensuring an informed precision reduction that retains model performance. Experiments show APTQ surpasses previous quantization methods, achieving an average of 4 bit width a 5.22 perplexity nearly equivalent to full precision in the C4 dataset. In addition, APTQ attains state-of-the-art zero-shot accuracy of 68.24\% and 70.48\% at an average bitwidth of 3.8 in LLaMa-7B and LLaMa-13B, respectively, demonstrating its effectiveness to produce high-quality quantized LLMs.

LoRETTA: Low-Rank Economic Tensor-Train Adaptation for Ultra-Low-Parameter Fine-Tuning of Large Language Models

Various parameter-efficient fine-tuning (PEFT) techniques have been proposed to enable computationally efficient fine-tuning while maintaining model performance. However, existing PEFT methods are still limited by the growing number of trainable parameters with the rapid deployment of Large Language Models (LLMs). To address this challenge, we present LoRETTA, an ultra-parameter-efficient framework that significantly reduces trainable parameters through tensor-train decomposition. Specifically, we propose two methods, named {LoRETTA}$_{adp}$ and {LoRETTA}$_{rep}$. The former employs tensorized adapters, offering a high-performance yet lightweight approach for the fine-tuning of LLMs. The latter emphasizes fine-tuning via weight parameterization with a set of small tensor factors. LoRETTA achieves comparable or better performance than most widely used PEFT methods with up to $100\times$ fewer parameters on the LLaMA-2-7B models. Furthermore, empirical results demonstrate that the proposed method effectively improves training efficiency, enjoys better multi-task learning performance, and enhances the anti-overfitting capability. Plug-and-play codes built upon the Huggingface framework and PEFT library will be released.