Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering mechanism remains unclear. This paper proves that this phenomenon is a result of floating-point arithmetic precision limits. As training enters a high-confidence stage, the difference between the correct-class logit and the other logits may exceed the absorption-error threshold. Then during backpropagation, the gradient of the correct class is rounded exactly to zero, while the gradients of the incorrect classes remain nonzero. This breaks the zero-sum constraint of gradients across classes and introduces a systematic drift in the parameter update of the classifier layer. We prove that this drift forms a positive feedback loop with the feature, causing the global classifier mean and the global feature mean to grow exponentially. We call this mechanism Numerical Feature Inflation (NFI). This mechanism explains the rapid norm growth before a Slingshot spike, the subsequent reappearance of gradients, and the resulting loss spike. We further show that NFI is not equivalent to an observed loss spike: in more practical tasks, partial absorption may not produce visible spikes, but it can still break the zero-sum constraint and drive rapid growth of parameter norms. Our results reinterpret Slingshot as a numerical dynamic of finite-precision training, and provide a testable explanation for abnormal parameter growth and logit divergence in late-stage training.

We introduce new methods for 1) accelerating and 2) stabilizing training for large language-vision models.

Our main focus is int8 as GPU support for float8 is rare, though we also analyze float8 training through simulation.

We introduce new methods for 1) accelerating and 2) stabilizing training for large language-vision models.

Adam has proven remarkable successful in training deep neural networks, but the mechanisms underlying its empirical successes and limitations remain underexplored. In this study, we demonstrate that the effectiveness of Adam stems largely from its similarity to SignSGD in robustly handling large gradient fluctuations, yet it is also vulnerable to destabilizing loss spikes due to its uncontrolled update scaling. To enhance the advantage of Adam and mitigate its limitation, we propose SignSoftSGD (S3), a novel optimizer with three key innovations. \emph{First}, S3 generalizes the sign-like update by employing a flexible $p$-th order momentum ($p \geq 1$) in the denominator, departing from the conventional second-order momentum (variance) preconditioning. This design enables enhanced performance while achieving stable training even with aggressive learning rates. \emph{Second}, S3 minimizes the occurrences of loss spikes through unified exponential moving average coefficients for numerator and denominator momenta, which inherently bound updates to $[-1, 1]$ and simplify hyperparameter tuning. \emph{Third}, S3 incorporates an equivalent Nesterov's accelerated gradient(NAG) module, accelerating convergence without memory overhead. Theoretically, we prove that S3 achieves the optimal convergence rate of $O\left(\frac{1}{T^{\sfrac{1}{4}}}\right)$ for general nonconvex stochastic optimization under weak assumptions. Extensive experiments across a range of vision and language tasks show that \textsf{\small S3} not only converges more rapidly and improves performance but also rarely experiences loss spikes, even with a \textbf{$\bm{10 \times}$} larger learning rate. In fact, S3 delivers performance comparable to or better than AdamW with \textbf{$2 \times$} the training steps, establishing its efficacy in both efficiency and final task performance.

Loss spikes emerge commonly during training across neural networks of varying architectures and scales when using the Adam optimizer. In this work, we investigate the underlying mechanism responsible for Adam spikes. While previous explanations attribute these phenomena to the lower-loss-as-sharper characteristics of the loss landscape, our analysis reveals that Adam's adaptive preconditioners themselves can trigger spikes. Specifically, we identify a critical regime where squared gradients become substantially smaller than the second-order moment estimates, causing the latter to undergo a $β_2$-exponential decay and to respond sluggishly to current gradient information. This mechanism can push the maximum eigenvalue of the preconditioned Hessian beyond the classical stability threshold $2/η$ for a sustained period, inducing instability. This instability further leads to an alignment between the gradient and the maximum eigendirection, and a loss spike occurs precisely when the gradient-directional curvature exceeds $2/η$. We verify this mechanism through extensive experiments on fully connected networks, convolutional networks, and Transformer architectures.

In this technical report, we tackle the challenges of training large-scale Mixture of Experts (MoE) models, focusing on overcoming cost inefficiency and resource limitations prevalent in such systems. To address these issues, we present two differently sized MoE large language models (LLMs), namely Ling-Lite and Ling-Plus (referred to as "Bailing" in Chinese, spelled B\v{a}il\'ing in Pinyin). Ling-Lite contains 16.8 billion parameters with 2.75 billion activated parameters, while Ling-Plus boasts 290 billion parameters with 28.8 billion activated parameters. Both models exhibit comparable performance to leading industry benchmarks. This report offers actionable insights to improve the efficiency and accessibility of AI development in resource-constrained settings, promoting more scalable and sustainable technologies. Specifically, to reduce training costs for large-scale MoE models, we propose innovative methods for (1) optimization of model architecture and training processes, (2) refinement of training anomaly handling, and (3) enhancement of model evaluation efficiency. Additionally, leveraging high-quality data generated from knowledge graphs, our models demonstrate superior capabilities in tool use compared to other models. Ultimately, our experimental findings demonstrate that a 300B MoE LLM can be effectively trained on lower-performance devices while achieving comparable performance to models of a similar scale, including dense and MoE models. Compared to high-performance devices, utilizing a lower-specification hardware system during the pre-training phase demonstrates significant cost savings, reducing computing costs by approximately 20%. The models can be accessed at https://huggingface.co/inclusionAI.

To adapt to real-world data streams, continual learning (CL) systems must rapidly learn new concepts while preserving and utilizing prior knowledge. When it comes to adding new information to continually-trained deep neural networks (DNNs), classifier weights for newly encountered categories are typically initialized randomly, leading to high initial training loss (spikes) and instability. Consequently, achieving optimal convergence and accuracy requires prolonged training, increasing computational costs. Inspired by Neural Collapse (NC), we propose a weight initialization strategy to improve learning efficiency in CL. In DNNs trained with mean-squared-error, NC gives rise to a Least-Square (LS) classifier in the last layer, whose weights can be analytically derived from learned features. Our method mitigates initial loss spikes and accelerates adaptation to new tasks. We evaluate our approach in large-scale CL settings, demonstrating faster adaptation and improved CL performance. Deep learning models excel in static environments where the data follows an independent and identically distributed (IID) assumption. However, in real-world scenarios, data distributions shift over time (non-IID), and new data arrives sequentially. Conventional deep neural networks (DNNs) struggle under such conditions, often requiring periodic re-training from scratch, which is not only computationally expensive but also contributes significantly to the carbon footprint of AI (Schwartz et al., 2020). Despite frequent retraining from scratch, real-world models still suffer up to 40% accuracy drops (Mallick et al., 2022). Continual learning (CL) aims to address this inefficiency by enabling models to learn from evolving data streams while preserving previously acquired knowledge (Parisi et al., 2019). CL is a promising solution to model decay, where predictive performance deteriorates over time due to concept drift--a shift in the meaning or distribution of target variables (Tsymbal, 2004; Gama et al., 2014; Lu et al., 2018).