A Solvable Model of Adaptive Learning Rate Rescaling: Acceleration, Stability & Scaling
1mes
- Publicado
- Recolectado
A recurring design principle in modern optimizers is to decouple update magnitude from the raw gradient norm, yet its consequences for learning-curve and resource scaling remain unclear. We isolate this mechanism by studying normalized SGD in a random-feature model with power-law teacher and data covariance. Fixed-norm updates induce an effective learning rate that grows as gradients shrink. We derive a dynamical mean-field theory (DMFT) describing the joint dependence of the loss on training time, model width and batch size. Normalization initially accelerates SGD, mapping the power-law exponent r_{SGD}<1 to 2r_{SGD}/(1-r_{SGD}), with exponential convergence at r_{SGD}=1 and formal finite-time convergence for r_{SGD}>1. At finite step size, however, the same feedback ultimately breaks the acceleration and leads to marginal stability. The late-time theory yields width-limited, edge-of-stochastic-stability (EoSS), and deterministic edge-of-stability (EoS) regimes. These phases determine when larger batches or wider models reduce serial training time at comparable compute. We quantify in which of these phases increased batch size or width can compensate the excess compute use per step by fewer optimization steps to target loss. Linearized ResNet experiments on CIFAR-5M support the predicted acceleration, breakdown, and resource-scaling trends. Together, these results connect normalization-induced acceleration, EoS effects, and width--batch allocation within a solvable theory.
Autores
Itay Lavie, Clarissa Lauditi, Cengiz Pehlevan
Categorías
overfeed.news indexa y enlaza. Publicamos un extracto breve; el artículo completo sigue en arXiv AI Papers.
Más de arXiv AI Papers
Inicia sesión para seguir esta fuente
Unbundling Multimodal Vision Encoding
How multimodal language models should encode visual input remains up for debate. Most models use a pretrained vision encoder, while some recent recipes train the encoder from scratch with the language model or remove it entirely. Vision encoders bundle together three design choices: a visual prior from upstream pretraining, dedicated vision capacity, and pre-fusion placement of that capacity (i.e., before the multimodal backbone). Because published models also differ in data, architecture, and compute, comparing them cannot isolate the effect of each choice. We disentangle these choices via a controlled framework where we pretrain all models from scratch on common data and compare them on visual question answering and language benchmarks at matched lifetime compute. We find that the visual prior is not necessary; an encoder trained jointly from scratch is on par with a pretrained one, without a separate training stage. What matters instead is dedicated vision capacity: an encoder-free model trails on visual understanding even when its backbone is enlarged by the encoder's parameter count. Yet that capacity need not precede multimodal fusion, as vision-only modules added in-fusion to early backbone layers perform comparably to a pre-fusion encoder and can lower time to first token. These results also hold across backbone sizes, when encoder pretraining is treated as free, and when starting from a pretrained language model. Overall, our findings favor dedicated vision capacity trained jointly with the backbone and placed early within it.
ArchSpace: Recording, Reviewing, and Referencing LLM Architecture Research
Model architecture shapes the scaling behavior, training efficiency, and inference cost of LLMs, making it a central focus of both industry and academia. In industry, teams such as those behind DeepSeek, Qwen, and Kimi routinely introduce architectural innovations, yet public reports rarely document which ideas succeeded, which were abandoned, and why. In academia, limited compute and inconsistent baselines often restrict evaluations to small-scale, single-point comparisons, making it difficult to establish whether improvements hold at larger scales or translate into broader impact. ArchSpace addresses both gaps as a public platform for Recording, Reviewing, and Referencing Architecture Researc}: each proposal is recorded with its experiments and reasoning, reviewed by the community, and referenced by later work. To evaluate ideas before costly large-scale training, ArchSpace leverages scaling laws to predict model loss at larger scales from smaller experiments, a practice widely adopted in industry. We provide initial references that make the platform usable: Qwen3.5 and OLMo3 baselines, fitted scaling laws, and a reusable training recipe. Ideas validated through this review can in turn become new baselines, and ArchSpace thereby aims to broaden the range of ideas that shape the next generation of models.
Internalizing Investment Mandates: A Neurosymbolic RL Approach to Portfolio Allocation
Institutional portfolios operate under investment policy statements that specify asset allocation constraints, often conditioned on market regime information. Deep reinforcement learning has been shown to optimize financial performance but typically does not enforce rule compliance, making it unsuitable for real-world deployment. Existing neurosymbolic methods such as Probabilistic Logic Policy Gradient (PLPG) offer constraint-satisfying reinforcement learning (RL) via differentiable symbolic supervision but assume a finite, discrete action space. We present a PLPG-inspired continuous allocation method that estimates the probability that the policy's own executed action satisfies the investment mandate, using reparameterized Monte Carlo sampling, and adds it to the training objective. No post-hoc enforcement mechanism intercepts actions at inference time and compliance is learned by the agent. Audited directly on deterministic mean actions with no correction, the policy reduces violations of a six-rule regime-conditional mandate from 96-98% for unconstrained RL and 33.4% for a reward-penalty baseline to 4.8%, showing that a continuous-action neurosymbolic policy can substantially internalize a symbolic mandate.
AgentSSL: Can MLE Agents Leverage Unlabeled Data?
Applying machine learning systems to new domains introduces bottlenecks in both labeled data acquisition and manual pipeline engineering. While recent MLE agents show promise in automating pipeline design, they have been studied almost exclusively in fully supervised settings, leaving them untested in realistic regimes where labeled data is scarce but unlabeled data is abundant. In this work, we introduce Agentic Semi-Supervised Learning (AgentSSL), framing SSL as a program search problem and studying how agents navigate this space under limited supervision. We find that even under weak feedback and matched compute, agents can synthesize code that combines and adapts established SSL techniques, exceeding the strongest human-engineered baselines in 8 of 12 settings by up to +21.8%. However, our results identify program selection as a critical bottleneck in AgentSSL, where performance drops by as much as 47% when selecting based on the agent's feedback metric. To systematically study this bottleneck, we introduce ProgramSelectBench, a large-scale benchmark with a combined total of 16,977 agent-generated and human-engineered SSL programs, and evaluate both unsupervised and active program selection methods. We further evaluate AgentSSL on real-world ecology detection tasks, highlighting the opportunities and challenges of transferring agent-discovered strategies beyond controlled benchmarks.