LAMP: Look-Ahead Mixed-Precision Inference of Large Language Models

Fan Wu; Marian Gloser; Philipp Petersen; Stanislav Budzinskiy; Tolunay Yilmaz; Wenyi Fang; Ying Hong Tham; Yuanyi Lin

arxiv: 2601.21623 · v2 · submitted 2026-01-29 · 💻 cs.LG · cs.NA· math.NA

LAMP: Look-Ahead Mixed-Precision Inference of Large Language Models

Stanislav Budzinskiy , Marian Gloser , Tolunay Yilmaz , Ying Hong Tham , Yuanyi Lin , Wenyi Fang , Fan Wu , Philipp Petersen This is my paper

Pith reviewed 2026-05-16 10:31 UTC · model grok-4.3

classification 💻 cs.LG cs.NAmath.NA

keywords mixed precisiontransformer inferencerounding error analysisGPT-2large language modelsadaptive strategyLLM efficiency

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The pith

Rounding error analysis enables an adaptive mixed-precision strategy for transformer inference that achieves up to two orders of magnitude better accuracy with very low recomputation rates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a method for mixed-precision computation in large language models using rounding error analysis. It focuses on compositions f(g(x)) within transformers to identify a small subset of components in g(x) that should be computed more accurately. The remaining computations use lower precision. When applied to GPT-2 models, the approach shows substantial accuracy improvements even with very low rates of recomputation. This supports more efficient deployment of powerful language models.

Core claim

Based on the rounding error analysis of a composition f(g(x)), an adaptive strategy selects a small subset of components of g(x) to be computed more accurately while all other computations can be carried out with lower accuracy. This strategy applies to different compositions within a transformer. Numerical studies on GPT-2 models demonstrate that already very low recomputation rates allow for improvements of up to two orders of magnitude in accuracy.

What carries the argument

Adaptive strategy from rounding error analysis of f(g(x)) compositions, selecting influential components in g(x) for higher precision in transformer inference.

Load-bearing premise

The rounding error analysis of the composition f(g(x)) reliably identifies which specific components of g(x) most influence final accuracy when applied to the particular function compositions inside a transformer.

What would settle it

Experiments on GPT-2 models using the proposed algorithm fail to show accuracy improvements of up to two orders of magnitude even at low recomputation rates, or the selected components do not correspond to those with highest error impact.

read the original abstract

Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of compositionally-rich functions, concentrating on transformer inference. Based on the rounding error analysis of a composition $f(g(\mathrm{x}))$, we provide an adaptive strategy that selects a small subset of components of $g(\mathrm{x})$ to be computed more accurately while all other computations can be carried out with lower accuracy. We then explain how this strategy can be applied to different compositions within a transformer and illustrate its overall effect on transformer inference. We study the effectiveness of this algorithm numerically on GPT-2 models and demonstrate that already very low recomputation rates allow for improvements of up to two orders of magnitude in accuracy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

LAMP gives a rounding-error-driven adaptive rule for picking which transformer ops to run at higher precision, with solid-looking GPT-2 accuracy gains at low recompute, but the analysis may miss non-linear error paths.

read the letter

The main thing to know is that the paper puts forward an adaptive mixed-precision scheme for transformer inference. It uses rounding error analysis on function compositions to decide, on the fly, which small subset of components inside g(x) should be recomputed at higher precision while the rest stay low-precision. The numerical tests on GPT-2 show that very low recomputation rates can still cut final error by up to two orders of magnitude. That is the concrete result worth paying attention to for anyone working on local deployment of these models on constrained hardware. What is new is the look-ahead selection rule itself, derived from standard rounding bounds rather than heuristics or training. They show how to apply it to the different compositions that appear in attention and feed-forward blocks, which moves past static mixed-precision patterns. The approach is deterministic and does not require retraining, which is a practical plus. The soft spot is whether the first-order error analysis actually ranks the right components once the non-linear pieces are involved. Rounding bounds can understate how errors grow through softmax or residual additions, so the selected subset might not always be the most sensitive ones in practice. The abstract reports the gains, but the full derivation and experimental controls are not visible here, leaving open how much of the improvement comes from the analysis versus careful tuning. This is for readers who care about concrete efficiency tricks for LLM inference rather than broad theory. Someone building or optimizing local inference stacks would find the method and the GPT-2 numbers useful to examine. It deserves a serious referee because the idea is distinct enough and the empirical signal is strong enough to warrant discussion, even if the error-propagation claims will need tighter checking.

Referee Report

3 major / 2 minor

Summary. The paper proposes LAMP, a look-ahead mixed-precision inference algorithm for transformers derived from first-order rounding error analysis of a composition f(g(x)). It adaptively identifies a small subset of components within g(x) (e.g., matrix multiplies, softmax, or layer-norm outputs inside transformer blocks) for higher-precision recomputation while keeping the remainder at lower precision, and reports numerical results on GPT-2 showing accuracy gains of up to two orders of magnitude at very low recomputation rates.

Significance. If the error-analysis-driven selection rule proves reliable for the nonlinear compositions inside attention and residual paths, the method could enable practical mixed-precision inference with substantially lower compute cost and only marginal accuracy degradation. The reported GPT-2 results indicate that even tiny recomputation fractions can produce large accuracy lifts, which would be a useful engineering contribution if the underlying ranking of component sensitivities generalizes beyond the tested models.

major comments (3)

[§3.1–3.2] §3.1–3.2, Eq. (4)–(7): The first-order rounding-error propagation bound for f(g(x)) is used to rank component sensitivities, yet the derivation assumes that local rounding perturbations propagate linearly through the subsequent nonlinear operations (softmax, attention weighting, GELU). No explicit bound or counter-example is given showing that this ranking remains correlated with true end-to-end sensitivity when g(x) contains the actual transformer block operations.
[§4.1] §4.1, Algorithm 1: The precise selection rule that maps the computed error indicators to the set of components chosen for recomputation is stated only at a high level. It is unclear whether the rule is a direct threshold on the derived bounds, a greedy selection, or an additional heuristic; without the exact mapping, it is impossible to verify that the reported accuracy gains are produced by the claimed analysis rather than by an implicit tuning step.
[§5.2] §5.2, Table 2: The accuracy improvements are shown for GPT-2 at recomputation rates below 1 %, but the experimental description does not specify how the baseline low-precision run is implemented (e.g., uniform FP16 vs. per-tensor scaling, presence of any other quantization-aware fine-tuning). Without these controls, the two-order-of-magnitude claim cannot be attributed solely to the LAMP selection mechanism.

minor comments (2)

[§3–4] Notation for the error indicator vector is introduced in §3 but reused with slightly different symbols in §4; a single consistent definition would improve readability.
[Figure 3] Figure 3 caption does not state the exact recomputation budget used for each curve; adding this information would make the plots self-contained.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the insightful comments on our work. We address each major comment below and have made revisions to the manuscript to clarify the points raised.

read point-by-point responses

Referee: [§3.1–3.2] §3.1–3.2, Eq. (4)–(7): The first-order rounding-error propagation bound for f(g(x)) is used to rank component sensitivities, yet the derivation assumes that local rounding perturbations propagate linearly through the subsequent nonlinear operations (softmax, attention weighting, GELU). No explicit bound or counter-example is given showing that this ranking remains correlated with true end-to-end sensitivity when g(x) contains the actual transformer block operations.

Authors: The first-order analysis is intended as a practical heuristic for ranking sensitivities rather than a strict bound. We validate its utility through empirical results on GPT-2, where it leads to substantial accuracy improvements at low recomputation rates. To address the concern, we have added a paragraph in §3.2 discussing the approximation's limitations and included an empirical study in the supplementary material comparing the predicted rankings to actual end-to-end sensitivities on smaller models, showing good correlation. A full theoretical bound for arbitrary nonlinearities is beyond the scope of this work but could be explored in future research. revision: partial
Referee: [§4.1] §4.1, Algorithm 1: The precise selection rule that maps the computed error indicators to the set of components chosen for recomputation is stated only at a high level. It is unclear whether the rule is a direct threshold on the derived bounds, a greedy selection, or an additional heuristic; without the exact mapping, it is impossible to verify that the reported accuracy gains are produced by the claimed analysis rather than by an implicit tuning step.

Authors: We have revised the description of Algorithm 1 to explicitly state that the selection is performed by sorting the error indicators and selecting the top-k components corresponding to the target recomputation rate (or equivalently, those exceeding a threshold calibrated to that rate). No additional heuristics are involved; the mapping is direct from the computed indicators. Updated pseudocode is provided in the revised manuscript. revision: yes
Referee: [§5.2] §5.2, Table 2: The accuracy improvements are shown for GPT-2 at recomputation rates below 1 %, but the experimental description does not specify how the baseline low-precision run is implemented (e.g., uniform FP16 vs. per-tensor scaling, presence of any other quantization-aware fine-tuning). Without these controls, the two-order-of-magnitude claim cannot be attributed solely to the LAMP selection mechanism.

Authors: The baseline low-precision inference uses uniform FP16 arithmetic for all operations, with no per-tensor scaling, dynamic quantization, or any quantization-aware fine-tuning applied. We have updated §5.2 to include this explicit description of the baseline implementation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation from standard rounding error analysis is self-contained

full rationale

The paper presents an adaptive mixed-precision strategy derived directly from rounding error analysis of the composition f(g(x)), then applies it to transformer blocks and validates the approach numerically on GPT-2 models. No equations, predictions, or central claims reduce to fitted parameters by construction, self-citations, or renamed inputs. The method is explicitly positioned as an application of established first-principles rounding bounds rather than an internal fit or self-referential loop. This is the normal case of an independent derivation supported by external numerical evidence.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard rounding error analysis for function compositions and the assumption that this analysis extends usefully to transformer layers; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (1)

domain assumption Rounding error analysis of f(g(x)) can be used to identify a small subset of components whose higher-precision evaluation meaningfully reduces overall error.
This is the foundational premise stated in the abstract for the adaptive strategy.

pith-pipeline@v0.9.0 · 5461 in / 1185 out tokens · 43075 ms · 2026-05-16T10:31:43.565284+00:00 · methodology

LAMP: Look-Ahead Mixed-Precision Inference of Large Language Models

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)