Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer architectures using highly flexible non-autonomous neural ordinary differential equations (ODEs). Our proposed model parameterizes all weights of attention and feed-forward blocks through neural networks, expressing these weights as functions of a continuous layer index. Through spectral analysis of the model's dynamics, we uncover an increase in eigenvalue magnitude that challenges the weight-sharing assumption prevalent in existing theoretical studies. We also leverage the Lyapunov exponent to examine token-level sensitivity, enhancing model interpretability. Our neural ODE transformer demonstrates performance comparable to or better than vanilla transformers across various configurations and datasets, while offering flexible fine-tuning capabilities that can adapt to different architectural constraints.

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 an intriguing, 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 naturally 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 pretrained language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

Given the massive cost of language model pre-training, a non-trivial improvement of the optimization algorithm would lead to a material reduction on the time and cost of training. Adam and its variants have been state-of-the-art for years, and more sophisticated second-order (Hessian-based) optimizers often incur too much per-step overhead. In this paper, we propose Sophia, a simple scalable second-order optimizer that uses a light-weight estimate of the diagonal Hessian as the pre-conditioner. The update is the moving average of the gradients divided by the moving average of the estimated Hessian, followed by element-wise clipping. The clipping controls the worst-case update size and tames the negative impact of non-convexity and rapid change of Hessian along the trajectory. Sophia only estimates the diagonal Hessian every handful of iterations, which has negligible average per-step time and memory overhead. On language modeling with GPT models of sizes ranging from 125M to 1.5B, Sophia achieves a 2x speed-up compared to Adam in the number of steps, total compute, and wall-clock time, achieving the same perplexity with 50\% fewer steps, less total compute, and reduced wall-clock time.

We describe an approach to task-oriented dialogue in which dialogue state is represented as a dataflow graph. A dialogue agent maps each user utterance to a program that extends this graph. Programs include metacomputation operators for reference and revision that reuse dataflow fragments from previous turns. Our graph-based state enables the expression and manipulation of complex user intents, and explicit metacomputation makes these intents easier for learned models to predict. We introduce a new dataset, SMCalFlow, featuring complex dialogues about events, weather, places, and people. Experiments show that dataflow graphs and metacomputation substantially improve representability and predictability in these natural dialogues. Additional experiments on the MultiWOZ dataset show that our dataflow representation enables an otherwise off-the-shelf sequence-to-sequence model to match the best existing task-specific state tracking model. The SMCalFlow dataset, code for replicating experiments, and a public leaderboard are available at https://www.microsoft.com/en-us/research/project/dataflow-based-dialogue-semantic-machines .

Due to their origin in computer graphics, graphics processing units (GPUs) are highly optimized for dense problems, where the exact same operation is applied repeatedly to all data points.Natural language processing algorithms, on the other hand, are traditionally constructed in ways that exploit structural sparsity.Recently, Canny et al. (2013) presented an approach to GPU parsing that sacrifices traditional sparsity in exchange for raw computational power, obtaining a system that can compute Viterbi parses for a high-quality grammar at about 164 sentences per second on a mid-range GPU.In this work, we reintroduce sparsity to GPU parsing by adapting a coarse-to-fine pruning approach to the constraints of a GPU.The resulting system is capable of computing over 404 Viterbi parses per second-more than a 2x speedup-on the same hardware.Moreover, our approach allows us to efficiently implement less GPU-friendly minimum Bayes risk inference, improving throughput for this more accurate algorithm from only 32 sentences per second unpruned to over 190 sentences per second using pruning-nearly a 6x speedup.

We present a parser that relies primar-ily on extracting information directly from surface spans rather than on propagat-ing information through enriched gram-mar structure. For example, instead of cre-ating separate grammar symbols to mark the definiteness of an NP, our parser might instead capture the same information from the first word of the NP. Moving context out of the grammar and onto surface fea-tures can greatly simplify the structural component of the parser: because so many deep syntactic cues have surface reflexes, our system can still parse accurately with context-free backbones as minimal as X-bar grammars. Keeping the structural backbone simple and moving features to the surface also allows easy adaptation to new languages and even to new tasks. On the SPMRL 2013 multilingual con-stituency parsing shared task (Seddah et al., 2013), our system outperforms the top single parser system of Björkelund et al. (2013) on a range of languages. In addi-tion, despite being designed for syntactic analysis, our system also achieves state-of-the-art numbers on the structural senti-ment task of Socher et al. (2013). Finally, we show that, in both syntactic parsing and sentiment analysis, many broad linguistic trends can be captured via surface features. 1

Constituency parsing with rich grammars remains a computational challenge.Graphics Processing Units (GPUs) have previously been used to accelerate CKY chart evaluation, but gains over CPU parsers were modest.In this paper, we describe a collection of new techniques that enable chart evaluation at close to the GPU's practical maximum speed (a Teraflop), or around a half-trillion rule evaluations per second.Net parser performance on a 4-GPU system is over 1 thousand length-30 sentences/second (1 trillion rules/sec), and 400 general sentences/second for the Berkeley Parser Grammar.The techniques we introduce include grammar compilation, recursive symbol blocking, and cache-sharing.

Informed search algorithms such as A* use heuristics to focus exploration on states with low total path cost. To the extent that heuristics underestimate forward costs, a wider cost radius of suboptimal states will be explored. For many weighted graphs, however, a small distance in terms of cost may encompass a large fraction of the unweighted graph. We present a new informed search algorithm, Iterative Monotonically Bounded A* (IMBA*), which first proves that no optimal paths exist in a bounded cut of the graph before considering larger cuts. We prove that IMBA* has the same optimality and completeness guarantees as A* and, in a non-uniform pathfinding application, we empirically demonstrate substantial speed improvements over classic A*.