Physics-Informed Neural Networks (PINNs) frequently fail on stiff or advection-dominated PDEs, and two recent accounts offer competing remedies: switching from FP32 to FP64 to repair an L-BFGS stopping artifact, or replacing the MLP with a state-space-model (SSM) backbone plus sub-sequence alignment to counter architectural simplicity bias. We test both under matched, seed-paired controls in a pre-registered 144-run study spanning convection, reaction, and wave, plus an independent 85-run convection/wave study; success is relative $\ell_2$ error below $0.05$. The two remedies act on disjoint regime-and-seed slices: neither substitutes for the other. On hard convection ($β{=}50$), alignment recovers 2/5 seeds in FP32 and 3/5 in FP64, where the unaligned SSM succeeds on 0/5 seeds at either precision and the vanilla MLP moves only from 0/5 to 1/5 across the precision switch---the recoveries trace to the alignment objective, not the backbone. On reaction the backbone alone already succeeds on 3/5--4/5 seeds, so each remedy covers a regime the other does not. Responses are also seed-specific: the same precision switch flips individual seeds in opposite directions and, on wave, lowers median error with no statistically significant success gain. Tightening the inner L-BFGS tolerance in an independent repeated-step runner likewise lowers median error at a large runtime cost, with success counts unchanged. Precision, stopping, backbone, and alignment must therefore be evaluated jointly and reported per seed.
Christopher Schröder, Lukas Gienapp, Ferdinand Schlatt +2cs.CL
We identify a previously overlooked failure mode of ALiBi positional encoding: its linear bias scaling underflows floating-point precision, which zeroes out a large fraction of attention weights and renders the affected attention heads partially blind. We analyze this failure mode, characterize its impact, and examine four mitigation strategies. We further demonstrate its occurrence in state-of-the-art pretrained models based on ALiBi. Comprehensive pretraining experiments with 148M-parameter decoder models help us to disentangle its effects from out-of-context degradation. We find that ALiBi's failure mode can substantially impair token retrieval while having only a minor effect on standard decoder benchmarks. We propose four training-time mitigation strategies and evaluate them individually and in combinations, finding that log-scaled distances yield the most consistent improvements in passkey retrieval. Despite this problem, default ALiBi slopes remain a surprisingly strong baseline, particularly for needle-in-a-haystack retrieval. Based on these findings we provide concrete recommendations on how to train models with ALiBi.
Mathematically equivalent expert-reduction orders can produce observably different sparse-MoE executions. We isolate this effect in native DeepSeek-V4-Flash by freezing local MoE state and varying only aggregation semantics. Four schemes separate operand representation from accumulator precision. At one layer-5 fork, 720 A-mode orders yield 10 continuation basins; 720 B-mode orders form 360 exact structural classes and 11 basins. Under one Chinese prompt, the B classes split into 202 layoffs, 113 hiring, and 45 other continuations. Maximum-L-infinity B-branch selection separates 12, 24, and 36 of 50 prompts by 8, 16, and 32 tokens. Across 192 persistent trajectories per scheme, P32, A, and B change every native-reference route trajectory, while C preserves routes, token sequences, and texts. A separate 192-trajectory C check matches native MoE, post-mHC, next-router, and LM states bitwise. For one controlled B branch, exact post-mHC endpoint reconstruction reproduces the measured downstream trajectory. At the next decode boundary, exact FP64 reconstruction of the branch's full persistent state yields agreement for 301 downstream post-mHC states, 301 persistent-state checkpoints, 301 routes, predictions, and text over seven steps, given the same naturally generated next input. These controls identify post-mHC as an intra-token boundary and full persistent state as a cross-token continuation boundary. Identical tokens need not imply identical autoregressive state: divergence can survive a token boundary and become visible later. These results make expert operand conversion, accumulator precision, and reduction order part of a numerical compatibility contract for sparse-MoE runtimes and hardware backends. They establish controlled causal possibility, not deployment incidence; C's order invariance is limited to evaluated six-term states and schedules.
Direct low-precision write-back can erase nonzero optimizer proposals. We ask what a high-precision reference trace establishes before a low-precision run. The exact target-code event is auditable coordinatewise on a realized target trajectory; pre-run aggregate projection also assumes the reference remains a useful counterfactual. In a controlled two-layer grid, 55/72 cells have measured and predicted post-initialization crossings: times span $384\times$, 52/55 are within 15\%, and 4/72 differ in category. Matched decoder experiments show stochastic rather than nearest write-back recovers most of the loss gap. A prospective analytic-grid E4M3 audit reuses one fp32 trace across three unseen NeoX-style seeds. It passes absolute-accuracy and skill gates (macro RMSE 0.00858) but fails directional specificity. In a target-outcome-blind comparison, a historical template has lower descriptive RMSE (0.00360) than the predeclared source predictor (0.00438); a post-outcome decomposition assigns 99.65\% of variation to common time, while a privileged matched-reference correction reaches 0.00283. Persistent-native Study~1 pairs three seeds across two schedules. Five cells are canonical; a manual sixth lacks canonical process identity, so the registered result remains inconclusive. A retrospective protocol-deviation analysis is negative because the complete constant-mid cohort is disjoint from the recovered cosine-restart cell. Study~2 reports mean full-SR/dead-zone-SR recoveries of 0.9766/0.9777 and a ratio of 1.0012, a policy contrast rather than causal mediation. Simulated-INT3 Study~3 replays six checkpoints and observes a 7.3071-nat (69.71\%) validation-loss reduction in one fixed seed. Exact events and write-back effects are auditable, but aggregate forecasts can reflect shared time rather than source-specific transfer.