Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant learning rate to produce a main branch of iterates that can in principle continue indefinitely without a pre-specified compute budget. Then, given any compute budget, one can branch out from the main branch at a proper time with a rapidly decaying learning rate to produce a strong model. Empirically, WSD generates a non-traditional loss curve: the loss remains elevated during the stable phase but sharply declines during the decay phase. Towards explaining this phenomenon, we conjecture that pretraining loss exhibits a river valley landscape, which resembles a deep valley with a river at its bottom. Under this assumption, we show that during the stable phase, the iterate undergoes large oscillations due to the high learning rate, yet it progresses swiftly along the river. During the decay phase, the rapidly dropping learning rate minimizes the iterate's oscillations, moving it closer to the river and revealing true optimization progress. Therefore, the sustained high learning rate phase and fast decaying phase are responsible for progress in the river and the mountain directions respectively, and are both critical. Our analysis predicts phenomenons consistent with empirical observations and shows that this landscape can emerge from pretraining on a simple bi-gram dataset. Inspired by the theory, we introduce WSD-S, a variant of WSD that reuses previous checkpoints' decay phases and keeps only one main branch, where we resume from a decayed checkpoint. WSD-S empirically outperforms WSD and Cyclic-Cosine in obtaining multiple language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

The remarkable generalization ability of neural networks is usually attributed to the implicit bias of SGD, which often yields models with lower complexity using simpler (e.g. linear) and low-rank features. Recent works have provided empirical and theoretical evidence for the bias of particular variants of SGD (such as label noise SGD) toward flatter regions of the loss landscape. Despite the folklore intuition that flat solutions are 'simple', the connection with the simplicity of the final trained model (e.g. low-rank) is not well understood. In this work, we take a step toward bridging this gap by studying the simplicity structure that arises from minimizers of the sharpness for a class of two-layer neural networks. We show that, for any high dimensional training data and certain activations, with small enough step size, label noise SGD always converges to a network that replicates a single linear feature across all neurons; thereby, implying a simple rank one feature matrix. To obtain this result, our main technical contribution is to show that label noise SGD always minimizes the sharpness on the manifold of models with zero loss for two-layer networks. Along the way, we discover a novel property -- a local geodesic convexity -- of the trace of Hessian of the loss at approximate stationary points on the manifold of zero loss, which links sharpness to the geometry of the manifold. This tool may be of independent interest.

Adam outperforms SGD when training language models. Yet this advantage is not well-understood theoretically -- previous convergence analysis for Adam and SGD mainly focuses on the number of steps $T$ and is already minimax-optimal in non-convex cases, which are both $\widetilde{O}(T^{-1/4})$. In this work, we argue that the exploitation of nice $\ell_\infty$-geometry is the key advantage of Adam over SGD. More specifically, we give a new convergence analysis for Adam under novel assumptions that loss is smooth under $\ell_\infty$-geometry rather than the more common $\ell_2$-geometry, which yields a much better empirical smoothness constant for GPT-2 and ResNet models. Our experiments confirm that Adam performs much worse when the favorable $\ell_\infty$-geometry is changed while SGD provably remains unaffected. We also extend the convergence analysis to blockwise Adam under novel blockwise smoothness assumptions.

An incomplete field-of-view (FOV) in diffusion magnetic resonance imaging (dMRI) can severely hinder the volumetric and bundle analyses of whole-brain white matter connectivity. Although existing works have investigated imputing the missing regions using deep generative models, it remains unclear how to specifically utilize additional information from paired multi-modality data and whether this can enhance the imputation quality and be useful for downstream tractography. To fill this gap, we propose a novel framework for imputing dMRI scans in the incomplete part of the FOV by integrating the learned diffusion features in the acquired part of the FOV to the complete brain anatomical structure. We hypothesize that by this design the proposed framework can enhance the imputation performance of the dMRI scans and therefore be useful for repairing whole-brain tractography in corrupted dMRI scans with incomplete FOV. We tested our framework on two cohorts from different sites with a total of 96 subjects and compared it with a baseline imputation method that treats the information from T1w and dMRI scans equally. The proposed framework achieved significant improvements in imputation performance, as demonstrated by angular correlation coefficient (p < 1E-5), and in downstream tractography accuracy, as demonstrated by Dice score (p < 0.01). Results suggest that the proposed framework improved imputation performance in dMRI scans by specifically utilizing additional information from paired multi-modality data, compared with the baseline method. The imputation achieved by the proposed framework enhances whole brain tractography, and therefore reduces the uncertainty when analyzing bundles associated with neurodegenerative.

Recent advancements in Vision-Language (VL) research have sparked new benchmarks for complex visual reasoning, challenging models' advanced reasoning ability. Traditional Vision-Language Models (VLMs) perform well in visual perception tasks while struggling with complex reasoning scenarios. Conversely, Large Language Models (LLMs) demonstrate robust text reasoning capabilities; however, they lack visual acuity. To bridge this gap, we propose Complex Visual Reasoning Large Language Models (CVR-LLM), capitalizing on VLMs' visual perception proficiency and LLMs' extensive reasoning capability. Unlike recent multimodal large language models (MLLMs) that require a projection layer, our approach transforms images into detailed, context-aware descriptions using an iterative self-refinement loop and leverages LLMs' text knowledge for accurate predictions without extra training. We also introduce a novel multi-modal in-context learning (ICL) methodology to enhance LLMs' contextual understanding and reasoning. Additionally, we introduce Chain-of-Comparison (CoC), a step-by-step comparison technique enabling contrasting various aspects of predictions. Our CVR-LLM presents the first comprehensive study across a wide array of complex visual reasoning tasks and achieves SOTA performance among all.

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel regime'' approximately holds, no permutation-equivariant model can achieve small population error on modular addition unless it sees at least a constant fraction of all possible data points. Eventually, however, models escape the kernel regime. We show that two-layer quadratic networks that achieve zero training loss with bounded $\ell_{\infty}$ norm generalize well with substantially fewer training points, and further show such networks exist and can be found by gradient descent with small $\ell_{\infty}$ regularization. We further provide empirical evidence that these networks as well as simple Transformers, leave the kernel regime only after initially overfitting. Taken together, our results strongly support the case for grokking as a consequence of the transition from kernel-like behavior to limiting behavior of gradient descent on deep networks.

AI agents have become increasingly significant in various domains, enabling autonomous decision-making and problem-solving. To function effectively, these agents require a planning process that determines the best course of action and then executes the planned actions. In this paper, we present an efficient on-device Planner-Action framework that separates planning and action execution into two distinct components: a planner agent based on Phi-3 Mini, a 3.8 billion parameter LLM optimized for edge devices, and an action agent using the Octopus model for function execution. The planner agent first responds to user queries by decomposing tasks into a sequence of sub-steps, which are then executed by the action agent. To optimize performance on resource-constrained devices, we employ model fine-tuning instead of in-context learning, reducing computational costs and energy consumption while improving response times. Our approach involves using GPT-4 to generate diverse planning queries and responses based on available functions, with subsequent validations to ensure data quality. We fine-tune the Phi-3 Mini model on this curated dataset, achieving a 97\% success rate in our in-domain test environment. To address multi-domain planning challenges, we developed a multi-LoRA training method that merges weights from LoRAs trained on distinct function subsets. This approach enables flexible handling of complex, multi-domain queries while maintaining computational efficiency on resource-constrained devices. To support further research, we have open-sourced our model weights at \url{https://huggingface.co/NexaAIDev/octopus-planning}. For the demo, please refer to \url{https://www.nexa4ai.com/octo-planner}.

The increase in academic dishonesty cases among college students has raised concern, particularly due to the shift towards online learning caused by the pandemic. We aim to develop and implement a method capable of generating tailored questions for each student. The use of Automatic Question Generation (AQG) is a possible solution. Previous studies have investigated AQG frameworks in education, which include validity, user-defined difficulty, and personalized problem generation. Our new AQG approach produces logical equivalence problems for Discrete Mathematics, which is a core course for year-one computer science students. This approach utilizes a syntactic grammar and a semantic attribute system through top-down parsing and syntax tree transformations. Our experiments show that the difficulty level of questions generated by our AQG approach is similar to the questions presented to students in the textbook [1]. These results confirm the practicality of our AQG approach for automated question generation in education, with the potential to significantly enhance learning experiences.

Language models have been effective in a wide range of applications, yet the most sophisticated models are often proprietary. For example, GPT-4 by OpenAI and various models by Anthropic are expensive and consume substantial energy. In contrast, the open-source community has produced competitive models, like Llama3. Furthermore, niche-specific smaller language models, such as those tailored for legal, medical or financial tasks, have outperformed their proprietary counterparts. This paper introduces a novel approach that employs \textit{functional tokens} to integrate \textbf{multiple open-source models}, each optimized for particular tasks. Our newly developed Octopus v4 model leverages \textit{functional tokens} to intelligently direct user queries to the most appropriate vertical model and reformat the query to achieve the best performance. Octopus v4, an evolution of the Octopus v1, v2, and v3 models, excels in selection and parameter understanding and reformatting. Additionally, we explore the use of graph as a versatile data structure that effectively coordinates multiple open-source models by harnessing the capabilities of the Octopus model and \textit{functional tokens}. Use our open-sourced GitHub (\url{https://www.nexa4ai.com/}) to try Octopus v4 models (\url{https://huggingface.co/NexaAIDev/Octopus-v4}), and contrite to a larger graph of language models. By activating models less than 10B parameters, we achieved SOTA MMLU score of 74.8 among the same level models.

Language models have shown effectiveness in a variety of software applications, particularly in tasks related to automatic workflow. These models possess the crucial ability to call functions, which is essential in creating AI agents. Despite the high performance of large-scale language models in cloud environments, they are often associated with concerns over privacy and cost. Current on-device models for function calling face issues with latency and accuracy. Our research presents a new method that empowers an on-device model with 2 billion parameters to surpass the performance of GPT-4 in both accuracy and latency, and decrease the context length by 95\%. When compared to Llama-7B with a RAG-based function calling mechanism, our method enhances latency by 35-fold. This method reduces the latency to levels deemed suitable for deployment across a variety of edge devices in production environments, aligning with the performance requisites for real-world applications.