TinyLlama: An Open-Source Small Language Model

We present TinyLlama, a compact 1.1B language model pretrained on around 1 trillion tokens for approximately 3 epochs. Building on the architecture and tokenizer of Llama 2, TinyLlama leverages various advances contributed by the open-source community (e.g., FlashAttention), achieving better computational efficiency. Despite its relatively small size, TinyLlama demonstrates remarkable performance in a series of downstream tasks. It significantly outperforms existing open-source language models with comparable sizes. Our model checkpoints and code are publicly available on GitHub at https://github.com/jzhang38/TinyLlama.

OtterHD: A High-Resolution Multi-modality Model

In this paper, we present OtterHD-8B, an innovative multimodal model evolved from Fuyu-8B, specifically engineered to interpret high-resolution visual inputs with granular precision. Unlike conventional models that are constrained by fixed-size vision encoders, OtterHD-8B boasts the ability to handle flexible input dimensions, ensuring its versatility across various inference requirements. Alongside this model, we introduce MagnifierBench, an evaluation framework designed to scrutinize models' ability to discern minute details and spatial relationships of small objects. Our comparative analysis reveals that while current leading models falter on this benchmark, OtterHD-8B, particularly when directly processing high-resolution inputs, outperforms its counterparts by a substantial margin. The findings illuminate the structural variances in visual information processing among different models and the influence that the vision encoders' pre-training resolution disparities have on model effectiveness within such benchmarks. Our study highlights the critical role of flexibility and high-resolution input capabilities in large multimodal models and also exemplifies the potential inherent in the Fuyu architecture's simplicity for handling complex visual data.

One Network, Many Masks: Towards More Parameter-Efficient Transfer Learning

Fine-tuning pre-trained language models for multiple tasks tends to be expensive in terms of storage. To mitigate this, parameter-efficient transfer learning (PETL) methods have been proposed to address this issue, but they still require a significant number of parameters and storage when being applied to broader ranges of tasks. To achieve even greater storage reduction, we propose PROPETL, a novel method that enables efficient sharing of a single PETL module which we call prototype network (e.g., adapter, LoRA, and prefix-tuning) across layers and tasks. We then learn binary masks to select different sub-networks from the shared prototype network and apply them as PETL modules into different layers. We find that the binary masks can determine crucial information from the network, which is often ignored in previous studies. Our work can also be seen as a type of pruning method, where we find that overparameterization also exists in the seemingly small PETL modules. We evaluate PROPETL on various downstream tasks and show that it can outperform other PETL methods with approximately 10% of the parameter storage required by the latter.

Lower Generalization Bounds for GD and SGD in Smooth Stochastic Convex Optimization

Recent progress was made in characterizing the generalization error of gradient methods for general convex loss by the learning theory community. In this work, we focus on how training longer might affect generalization in smooth stochastic convex optimization (SCO) problems. We first provide tight lower bounds for general non-realizable SCO problems. Furthermore, existing upper bound results suggest that sample complexity can be improved by assuming the loss is realizable, i.e. an optimal solution simultaneously minimizes all the data points. However, this improvement is compromised when training time is long and lower bounds are lacking. Our paper examines this observation by providing excess risk lower bounds for gradient descent (GD) and stochastic gradient descent (SGD) in two realizable settings: 1) realizable with $T = O(n)$, and (2) realizable with $T = \Omega(n)$, where $T$ denotes the number of training iterations and $n$ is the size of the training dataset. These bounds are novel and informative in characterizing the relationship between $T$ and $n$. In the first small training horizon case, our lower bounds almost tightly match and provide the first optimal certificates for the corresponding upper bounds. However, for the realizable case with $T = \Omega(n)$, a gap exists between the lower and upper bounds. We provide a conjecture to address this problem, that the gap can be closed by improving upper bounds, which is supported by our analyses in one-dimensional and linear regression scenarios.

Better Few-Shot Relation Extraction with Label Prompt Dropout

Few-shot relation extraction aims to learn to identify the relation between two entities based on very limited training examples. Recent efforts found that textual labels (i.e., relation names and relation descriptions) could be extremely useful for learning class representations, which will benefit the few-shot learning task. However, what is the best way to leverage such label information in the learning process is an important research question. Existing works largely assume such textual labels are always present during both learning and prediction. In this work, we argue that such approaches may not always lead to optimal results. Instead, we present a novel approach called label prompt dropout, which randomly removes label descriptions in the learning process. Our experiments show that our approach is able to lead to improved class representations, yielding significantly better results on the few-shot relation extraction task.

Minimax in Geodesic Metric Spaces: Sion's Theorem and Algorithms

Determining whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. We take a step towards understanding certain nonconvex-nonconcave minimax problems that do remain tractable. Specifically, we study minimax problems cast in geodesic metric spaces, which provide a vast generalization of the usual convex-concave saddle point problems. The first main result of the paper is a geodesic metric space version of Sion's minimax theorem; we believe our proof is novel and transparent, as it relies on Helly's theorem only. In our second main result, we specialize to geodesically complete Riemannian manifolds: we devise and analyze the complexity of first-order methods for smooth minimax problems.

Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization

Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often supposed to be linked to the quality of the integrator (accuracy, energy preservation, symplecticity). In this work, we propose a novel ordinary differential equation that questions this connection: both the explicit and the semi-implicit (a.k.a symplectic) Euler discretizations on this ODE lead to an accelerated algorithm for convex programming. Although semi-implicit methods are well-known in numerical analysis to enjoy many desirable features for the integration of physical systems, our findings show that these properties do not necessarily relate to acceleration.

Mixing of Stochastic Accelerated Gradient Descent

We study the mixing properties for stochastic accelerated gradient descent (SAGD) on least-squares regression. First, we show that stochastic gradient descent (SGD) and SAGD are simulating the same invariant distribution. Motivated by this, we then establish mixing rate for SAGD-iterates and compare it with those of SGD-iterates. Theoretically, we prove that the chain of SAGD iterates is geometrically ergodic --using a proper choice of parameters and under regularity assumptions on the input distribution. More specifically, we derive an explicit mixing rate depending on the first 4 moments of the data distribution. By means of illustrative examples, we prove that SAGD-iterate chain mixes faster than the chain of iterates obtained by SGD. Furthermore, we highlight applications of the established mixing rate in the convergence analysis of SAGD on realizable objectives. The proposed analysis is based on a novel non-asymptotic analysis of products of random matrices. This theoretical result is substantiated and validated by experiments.