Optimizer state is the largest single line item in the memory budget of mixture-of-experts (MoE) training: on a 6.78B-parameter MoE language model, AdamW keeps 50.6 GB of first and second moments to update 12.6 GB of bfloat16 weights. We study SkewAdam, an optimizer built on the observation that the three parameter populations of an MoE - the dense backbone, the experts, and the router - differ enough in size and gradient statistics that they should not receive the same state. SkewAdam keeps float32 momentum plus a factored second moment for the backbone (5% of parameters), a factored second moment alone for the experts (95%), and an exact second moment for the router (<0.01%). The resulting state occupies 1.29 GB, 2.6% of AdamW's, and peak training memory falls from 81.4 GB to 31.3 GB, within the budget of a 40 GB accelerator. In a controlled comparison from identical initializations over 82M tokens, SkewAdam reaches validation perplexity 108.4, ahead of AdamW (126.8), Muon (120.2), and Lion (393.7), and settles router load balance to within 1% of its uniform floor. The allocation is not what earns that perplexity: a tier ablation matches it with twenty times the state, and Adafactor, which shares the factored estimator but drops momentum, plateaus 40 points behind. The tiers buy memory at no cost to accuracy; the accuracy comes from keeping momentum, which a uniform optimizer shares too. Sweeping the baselines' learning rates narrows but does not close the gap: the best tuned AdamW reaches 118.5, tuned Adafactor 139.7. Where optimizer state lives, these results suggest, matters at least as much as how much of it there is.
ANEForge is a Python package that programs the Apple Neural Engine (ANE), the fixed-function neural accelerator on every recent Apple device, directly and without CoreML. In production the engine is reachable only through CoreML, which treats it as a scheduling option: no configuration requires the ANE, and a model can silently run on the CPU or GPU instead. ANEForge compiles a lazy tensor graph, built from 58 fused operators and 19 native bridge operators, into a single ANE program. The program is dispatched through the same ANE daemon and kernel-driver stack as Apple's internal framework. Beyond inference, the package reaches the engine's native fused attention, streams int8, int4, and sparse weights, keeps decoder and optimizer state resident across steps, and runs the forward pass, backward pass, and optimizer update of training on the engine. A small fused program completes a call in about 90us, near the engine's 70us per-program dispatch floor, and a pretrained ResNet-18 forward runs end-to-end in 0.33ms. ResNet-18, a sentence encoder, and a Vision Transformer run end-to-end against framework references, and a Stable Diffusion U-Net validates its forward pass. ANEForge targets Apple Silicon under macOS 14 and later. Each release is verified against a recorded macOS and ANE-compiler version.