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Fault-tolerant foundation models

Trevor McCourt, Ila R. Fiete, Isaac L. Chuang

arXiv:2610.10311v1cs.LGcs.AIcs.AR

TL;DR

Whether fault-hardened models retain useful capacity at arbitrary scale on realistic faulty hardware remains unresolved, despite the potential value for low-energy accelerators. The paper fits modified scaling laws for fault-hardened transformers and finds that large models perform surprisingly well relative to simple repetition-based error correction. The authors suggest this robustness may persist at larger scales, but testing that possibility would require experiments beyond current academic budgets.

  • Problem

    Whether fault-hardened models retain capacity at arbitrary scale on realistic faulty hardware remains unresolved, though this would matter for low-energy accelerators.

    Source: Towards formally fault-tolerant AI · p. 6

  • Method

    The authors identify modified scaling laws for fault-hardened transformers, including a curvature coefficient governing how their performance gap changes with model size.

    Source: The scaling behavior of fault-hardened… · p. 3

  • Results

    Fault-hardened transformers close the performance gap to fault-free counterparts as model size grows and perform surprisingly well relative to simple repetition-based error correction.

    Source: The scaling behavior of fault-hardened… · p. 3, DISCUSSION · p. 6

  • Takeaways & Limitations

    The results suggest AI trained under noisy constraints may share biological robustness, and error-detection hardware may provide a substrate for bounded-error, low-energy accelerators.

    Source: DISCUSSION · p. 6

    The authors did not test models at the roughly 10^11-weight scale needed to assess persistence there, estimating such an extension would require about 10^8 GPU-hours and be intractable within academia.

    Source: DISCUSSION · p. 6

Abstract

from arXiv · show

Emerging computer hardware often trades reliability for energy efficiency; here we show that large-language models (LLMs) can be trained to tolerate this unreliability, and that rather than degrading, their error resilience actually increases as they grow. Modified neural scaling laws inferred from 40,000 GPU-hours of training runs on simulated faulty digital hardware quantify this trend and suggest that models learn to compute within "good" error-correcting codes, whose relative overhead remains finite no matter how large the model gets. This finding leads us to conjecture that appropriately trained LLMs may be formally fault-tolerant; if true, running AI inference on low energy, faulty hardware may be a path to substantial energy savings over the status quo.

The scaling behavior of fault-hardened transformers

The experiments establish modified scaling laws for fault-hardened transformers and find that their performance gap to fault-free counterparts closes as model size grows. The fitted trends suggest capacity recovery is associated with increasing curvature, while the largest-scale asymptotic behavior remains unresolved.

The scaling behavior of fault-hardened transformers

  • The experiments simulated hardware faults by randomly zeroing blocks of four matrix elements in attention and feed-forward operations during each training or inference pass.The faults changed on every query, requiring robustness to varying failure modes rather than calibration to a fixed device.Source: The scaling behavior of fault-hardened… · p. 3
  • Fault-hardened transformers’ modified scaling law includes a curvature coefficient that lets them close the performance gap to fault-free counterparts as model size grows.The experiments trained thousands of models across model size, data size, and fault probability.Source: The scaling behavior of fault-hardened… · p. 3
  • The restoration of model capacity with size is driven by the increase of α2 with fault probability.This relation connects the fitted αk and ck coefficients.Source: The scaling behavior of fault-hardened… · p. 3
  • At small fault probabilities, decreases in α1 are mirrored by increases in α2; at large probabilities, α2 plateaus while α1 continues to shrink.The authors interpret this as correction of increasingly severe errors up to a point, followed by models being overwhelmed.Source: The scaling behavior of fault-hardened… · pp. 3–4
  • At sufficiently high inference-time fault rates, fault-blind models can lose performance as data size grows, while fault-hardened models retain almost all capacity below their training fault rate.The figure also reports rapid logit heating in fault-blind models and resistance to heating in fault-hardened models.Source: Figure 3 · p. 4
  • The experiments did not resolve the asymptotic term A, and the authors fixed E at approximately 1.5 because the tested models were too small to identify it uniquely.The choice of E had no qualitative impact on the results.Source: The scaling behavior of fault-hardened… · pp. 3–4

Fault-blind models collapse under inference-time

Inference-time faults expose a sharp contrast: fault-blind models become fragile, while models trained with matching faults preserve prediction precision until inference noise exceeds their training level.

errors

  • With peval > 0, fault-blind transformer performance can decrease with D, and at sufficiently large peval its scaling laws fail to converge.Fault-blind models have ptrain = 0, whereas fault-hardened models are trained at the fault rate they encounter during inference.Source: errors · p. 4
  • Fault-blind models’ degradation is consistent with outsized super-weights and activations acting as single points of failure.Prior observations report that super-feature counts grow with training duration.Source: errors · p. 4
  • Fault-hardened models hold effective temperature constant until peval exceeds ptrain, whereas fault-blind models heat rapidly as peval rises.The heating worsens for both model classes as D increases.Source: errors · p. 5
  • Faults do more than raise output temperature: they irreversibly scramble logits, a change that rescaling cannot undo.P* is the nearest distribution to Q that is a strict temperature shift of P.Source: errors · p. 5
  • Fault-hardened models lose almost no capacity to irreversible logit scrambling until peval exceeds ptrain, while fault-blind models deteriorate rapidly from peval = 0.The first KL-divergence term captures the gap that no temperature rescaling can close.Source: errors · p. 5

Low-energy neural network accelerators

The experiments model low-energy hardware that detects arithmetic errors during transformer matrix products and converts failed computations into dropped connections for the model to handle.

Low-energy neural network accelerators

  • Residue checks after every k = 4 fused multiply–add cells discard failed blocks of products and carry forward the previous partial sum, turning arbitrary faults into block drop-connect.Blocks fail independently with probability p.Source: Figure 4 · p. 5, Low-energy neural network accelerators · p. 6
  • Faults target attention and feed-forward matrix multiplications, which account for more than 99% of large transformers’ FLOP budget.Supporting operations are assumed to run on a separate fault-free substrate.Source: Figure 4 · p. 5, Low-energy neural network accelerators · p. 5
  • LENNAs detect errors cheaply and leave correction to the model; full hardware correction can cost more than the fused multiply–add operations themselves.In a 12-bit example with k = 4, an extra 3-bit residue adds only a few percent of overhead.Source: Low-energy neural network accelerators · p. 6

Towards formally fault-tolerant AI

The authors frame formal fault tolerance as an asymptotic question about whether fault-hardened models retain useful capacity at arbitrary scale, with possible collapse or saturation behavior.

Towards formally fault-tolerant AI

  • For realistic hardware faults, the target is to establish that fault-hardened models retain capacity at arbitrary scale.Practically, the authors say it would suffice for η/N to remain large enough at a scale such as 10^11 parameters to justify switching hardware.Source: Towards formally fault-tolerant AI · p. 6
  • If the floor-gap Δ exceeds the remaining size-loss L_N, retained capacity collapses to 0; if the gap stays small, η/N may approach 1 and capacity saturate near N.The proposed asymptotic behaviors depend on p through a smooth transition.Source: Towards formally fault-tolerant AI · p. 6
  • The fault-tolerance threshold at a given experimental scale is operationally defined as the value of p at the boundary between collapse and saturation.Source: Towards formally fault-tolerant AI · p. 6

DISCUSSION

The discussion interprets the scaling results as evidence that fault-hardened transformers may use more efficient error-correcting strategies than repetition, while emphasizing that commercial-scale persistence remains untested and expensive to establish.

DISCUSSION

  • Additional scaling-law terms let large fault-hardened transformers perform better than simple repetition-based error-correcting schemes would predict.The discussion frames this as a result that may be consistent with models learning good codes.Source: DISCUSSION · p. 6
  • Testing persistence at ∼10^11 weights is estimated to require around 10^26 FLOPs, or ∼10^8 GPU-hours, an intractable cost within academia.The estimate is compared with the total training budget of Llama-3 405B.Source: DISCUSSION · p. 6
  • Smaller natural or synthetic datasets could serve as model organisms for testing fault tolerance across dataset irreducible floors; the trained models’ weights and optimizer states are available for studying internal structure.Persistence as the irreducible floor E increases would be evidence that commercial-scale experiments are worth doing.Source: DISCUSSION · p. 6
  • The authors suggest that training under noisy constraints may yield robustness like that seen in nervous systems, and that error-detecting hardware may support bounded-error, low-energy accelerators.Source: DISCUSSION · p. 6
  • Establishing commercial viability will require substantial further investment, though future low-energy hardware could be orders of magnitude more energy efficient than current inference systems.Source: DISCUSSION · p. 6

METHODS

Models were trained on a FineWeb slice and evaluated on a held-out split from the same web crawls, with document overlap removed.

Dataset

  • Training used a 350-billion-token FineWeb slice, tokenized with an 8192-token bytepair-encoding vocabulary and packed into 1024-token sequences.The corpus was shuffled in large blocks, making contiguous slices statistically equivalent.Source: Dataset · p. 6
  • Evaluation used a held-out two-billion-token split from the same web crawls, with no shared documents between training and evaluation.Near-duplicates were removed by normalized-content hash, and the tokenizer was fit on training documents alone.Source: Dataset · p. 7

Model ladder

The study varied overall model size while holding architectural ratios fixed, injected independently sampled matrix-product faults, and trained across model sizes, token budgets, and fault rates.

Model ladder

  • Sixteen logarithmically spaced models ranged from 7.9 × 10^6 to 9.3 × 10^8 parameters, with architectural ratios held fixed as overall size varied.Models used 1024-token context, 32-dimensional attention heads, and untied embeddings.Source: Model ladder · p. 7

Fault injection

  • Faults independently zeroed contiguous blocks of four contraction-axis elements with probability p in selected transformer matrix-product operands.Faults were redrawn per sequence and forward pass and held fixed across positions; embeddings, readout, norms, rotary embeddings, nonlinearities, and residual additions remained fault-free.Source: Fault injection · p. 7

Training

  • Training covered token budgets from 7.9 × 10^7 to 3.5 × 10^10, but the size-duration grid was not fully crossed.Ten smaller architectures used 10, 20, 80, and 320 tokens per parameter; six larger ones used 20 or fewer, and each size-duration-fault-rate condition had two seeds.Source: Training · p. 7

Scaling-law fits

The authors fit scaling laws separately by fault-rate cohort and estimated uncertainty by bootstrap; they also compared fault-averaged and fault-free predictive distributions across contexts.

Scaling-law fits

  • 1500 bootstrap resamples per cohort produced conservative exponent intervals because dropping the largest models removes the only constraint on the long-N end.Each resample refit the surface; log L was fit with Huber loss from multiple starting points, and pivots N0 and D0 were fixed at 4 × 10^7.Source: Scaling-law fits · p. 7
  • The capacity relations follow by matching fault-free loss at η to faulty loss at N in the converged limit D → ∞.The asymptotic term A depends on the floor gap Δ, which was indistinguishable from zero within the experimental range.Source: Scaling-law fits · pp. 7–8

Logit-space analysis

  • For logit-space analysis, 256 held-out contexts were evaluated across 81 fault rates using distributions averaged over 1000 independent fault draws.A fitted temperature matched mean logits between the rescaled fault-free distribution and the fault-averaged distribution; the explained/residual split was exact over contexts.Source: Logit-space analysis · p. 8

DECLARATIONS

The authors report publicly available code, summary data, and access to model weights, alongside supplementary materials on scaling-law analyses.

Data and Code Availability

  • The complete codebase and figure-generating notebooks are publicly available, and summary data record trained-model performance.The summary data omit model weights; the multi-terabyte weights can be accessed through the specified AWS S3 bucket using the AWS CLI.Source: Data and Code Availability · p. 8

SUPPLEMENTARY MATERIALS

A. N-CURVATURE IN THE RAW DATA

After removing the training-data dependence, the raw data retain the model-size curvature seen in Fig. 1. The curvature term is also needed for good fits across fault levels.

A. N-CURVATURE IN THE RAW DATA

B. RESIDUALS OF THE SCALING LAW FIT

C. THE NECESSITY OF THE CURVATURE TERM

D. CORRELATIONS BETWEEN SCALING LAW PARAMETERS

The authors bootstrap experimental runs to estimate uncertainty in scaling-law parameters and examine correlations among the resulting parameter samples.

D. CORRELATIONS BETWEEN SCALING LAW PARAMETERS

  • 1,500 bootstrap datasets are formed by resampling experimental runs with replacement and refitting the scaling law.The resulting samples approximate the fit-parameter distribution; 95% confidence intervals produce Fig. 2 error bars.Source: D. CORRELATIONS BETWEEN SCALING LAW… · p. 13
  • Pairwise scatter plots show parameter correlations using a small subset of the complete bootstrap dataset to avoid overcrowding.The complete bootstrap samples are used to examine parameter relationships.Source: Figure S4 · p. 13, D. CORRELATIONS BETWEEN SCALING LAW… · p. 13
  • α2 is essentially uncorrelated with other fit parameters, while the lower-order N and D coefficients are weakly correlated.The authors attribute α2’s independence to its unique ability to produce the curvature seen in residuals.Source: D. CORRELATIONS BETWEEN SCALING LAW… · p. 13

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