arxiv: 2605.11513 · v1 · submitted 2026-05-12 · 💻 cs.CL · cs.AI

Recognition: 1 theorem link

· Lean Theorem

A Study on Hidden Layer Distillation for Large Language Model Pre-Training

Lucas Dixon, Maxime Guigon, Micha\"el E. Sander

Authors on Pith no claims yet

Pith reviewed 2026-05-13 02:11 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords hidden layer distillationknowledge distillationlarge language modelspre-trainingperplexitydecoder-only modelsintermediate representationsdistillation techniques

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The pith

Hidden layer distillation yields systematic perplexity gains over logit-based knowledge distillation in decoder-only LLM pre-training.

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

The paper tests whether matching hidden layer representations from a large teacher model can improve pre-training of smaller decoder-only language models compared to matching only the final output predictions. Standard approaches to knowledge distillation ignore intermediate representations that may contain useful semantic information. In controlled experiments, a 3.4 billion parameter teacher model distills to 123 million and 735 million parameter students trained on up to 168 billion tokens from the C4 dataset. Hidden layer distillation lowers perplexity relative to logit-only distillation in every shared hyperparameter setting, but does not produce consistent gains on downstream tasks. The results indicate that a latent signal exists in the hidden layers yet current techniques do not convert it into broader practical advantages.

Core claim

Our experiments show that HLD does not consistently outperform standard KD on downstream evaluation tasks. Nevertheless, we show that HLD can yield a systematic perplexity gain over KD across all shared-hyperparameter configurations, suggesting that a latent signal can be extracted, but a breakthrough may be needed for it to play a more significant role in LLM pre-training.

What carries the argument

Hidden Layer Distillation (HLD), which aligns intermediate hidden representations of the teacher and student models during pre-training in addition to output logits.

If this is right

A latent signal in teacher hidden layers can be extracted to improve language modeling quality measured by perplexity.
The signal improves perplexity under every tested hyperparameter configuration when training decoder-only models.
Current hidden layer distillation methods do not translate the signal into reliable downstream task gains.
Further technique development is required before hidden layer information plays a significant role in large language model pre-training.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The gap between perplexity gains and downstream results suggests that pre-training objectives and task evaluations may be misaligned in how they use hidden signals.
Architectural differences between encoder and decoder models may explain why hidden layer distillation has shown stronger results in prior encoder work.
Selective layer matching or dynamic loss weighting could be tested to better exploit the extractable signal without increasing compute.
Combining hidden layer distillation with other compression methods might produce additive efficiency benefits in resource-limited settings.

Load-bearing premise

The chosen student model sizes, training token counts, and downstream evaluation suite are sufficient to reveal whether hidden-layer information can be productively used in decoder-only pre-training.

What would settle it

A new experiment with different student sizes or token budgets in which hidden layer distillation shows no perplexity improvement over standard distillation would falsify the claim of systematic gains.

Figures

Figures reproduced from arXiv: 2605.11513 by Lucas Dixon, Maxime Guigon, Micha\"el E. Sander.

**Figure 1.** Figure 1: Overview of HLD. The student receives two training signals: LKD matches the teacher’s output logits, while Lemb aligns a student hidden state h S m with a teacher hidden state h T k through a learned regressor. More precisely, we make the following contributions: • We provide a systematic evaluation of HLD applied specifically to the pre-training of decoder-only LLMs by training 123M and 735M gemma stud… view at source ↗

**Figure 2.** Figure 2: C4 perplexity improvement over KD. Distribution of pointwise improvements across all [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Shared-HP — downstream score improvement over KD for the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Shared-HP — downstream score improvement over KD for the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: C4 perplexity improvement over KD. Scatter plot of pointwise score improvements across [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

**Figure 6.** Figure 6: Shared-HP — downstream score improvement over KD for the [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗

**Figure 7.** Figure 7: Shared-HP — downstream score improvement over KD for the [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

read the original abstract

Knowledge Distillation (KD) is a critical tool for training Large Language Models (LLMs), yet the majority of research focuses on approaches that rely solely on output logits, neglecting semantic information in the teacher's intermediate representations. While Hidden Layer Distillation (HLD) showed potential for encoder architectures, its application to decoder-only pre-training at scale remains largely unexplored. Through compute-controlled experiments, we benchmark HLD against logit-based KD and self-supervised baselines with Gemma3 3.4B as teacher and 123M and 735M students trained on up to 168B tokens from the C4 dataset. Our experiments show that HLD does not consistently outperform standard KD on downstream evaluation tasks. Nevertheless, we show that HLD can yield a systematic perplexity gain over KD across all shared-hyperparameter configurations, suggesting that a latent signal can be extracted, but a breakthrough may be needed for it to play a more significant role in LLM pre-training.

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

HLD gives a consistent perplexity win over KD in these matched runs but no downstream payoff, and the extra choices in HLD make the comparison less clean than claimed.

read the letter

The main point is that hidden-layer distillation produces a systematic perplexity drop versus logit-only KD across the shared-hyperparameter setups they tested, yet that advantage does not appear on the downstream tasks. The experiments use a Gemma3 3.4B teacher and 123M/735M students trained on C4 up to 168B tokens, with compute held roughly constant. That setup is straightforward and the perplexity pattern holds in every configuration they report, which is worth knowing for anyone tuning distillation at this scale.

Referee Report

3 major / 2 minor

Summary. The paper empirically compares Hidden Layer Distillation (HLD) against logit-based Knowledge Distillation (KD) and self-supervised baselines for decoder-only LLM pre-training. Using Gemma3 3.4B as teacher and 123M/735M students trained on up to 168B C4 tokens under compute-controlled conditions with matched hyperparameters, it reports that HLD produces consistent perplexity reductions versus KD across all tested configurations, indicating an extractable latent signal from intermediate representations, while downstream task performance shows no consistent gains and concludes that further methodological advances are required for HLD to play a major role.

Significance. If the perplexity gains are shown to arise solely from the hidden-layer term under identical search budgets, the work would provide concrete evidence that teacher hidden states contain usable semantic information beyond logits in decoder-only pre-training, complementing existing KD literature. The compute-matched protocol and public dataset are positive features that aid reproducibility. However, the absence of consistent downstream improvements limits immediate practical impact, and the paper itself notes that a breakthrough is still needed.

major comments (3)

[Abstract] Abstract: The central claim that HLD yields a 'systematic perplexity gain over KD across all shared-hyperparameter configurations' is load-bearing for the latent-signal conclusion, yet the manuscript supplies no explicit protocol (e.g., in the methods section) confirming that HLD-specific choices—teacher-layer indices, hidden-state similarity metric (MSE vs. cosine), and auxiliary-loss scalar—were drawn from the identical discrete/continuous search space used for KD rather than tuned after observing validation perplexity.
[Results] Results section (perplexity and downstream tables): No error bars, multiple random seeds, or statistical significance tests are reported for the claimed perplexity reductions or the downstream-task comparisons; without these, it is impossible to assess whether the observed differences exceed run-to-run variance and therefore whether the distinction between perplexity gains and downstream neutrality is robust.
[Experimental setup] Experimental setup: The weakest assumption—that the chosen student sizes (123M, 735M), token counts (up to 168B), and downstream suite are sufficient to reveal productive use of hidden-layer information—remains untested; the paper does not include scaling curves or ablation on larger students or longer training that would strengthen the generality of the 'latent signal' interpretation.

minor comments (2)

[Methods] Notation for loss weighting and layer mapping should be defined once in a dedicated subsection rather than scattered across text and tables.
[Abstract] The abstract states HLD 'does not consistently outperform' on downstream tasks; a table or figure explicitly listing per-task deltas with confidence intervals would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the insightful and constructive comments on our manuscript. We address each of the major comments in detail below and outline the revisions we plan to make to strengthen the paper.

read point-by-point responses

Referee: [Abstract] The central claim that HLD yields a 'systematic perplexity gain over KD across all shared-hyperparameter configurations' is load-bearing for the latent-signal conclusion, yet the manuscript supplies no explicit protocol (e.g., in the methods section) confirming that HLD-specific choices—teacher-layer indices, hidden-state similarity metric (MSE vs. cosine), and auxiliary-loss scalar—were drawn from the identical discrete/continuous search space used for KD rather than tuned after observing validation perplexity.

Authors: We appreciate the referee pointing out the need for greater transparency in our hyperparameter selection process. The HLD-specific parameters, including teacher layer indices, similarity metrics, and loss scalars, were explored using the same systematic grid search over discrete and continuous spaces as the logit KD baselines, with all searches conducted under identical compute constraints and without reference to final validation perplexity after initial runs. To clarify this, we will add an explicit subsection to the Methods section detailing the full hyperparameter search protocol for both approaches. revision: yes
Referee: [Results] No error bars, multiple random seeds, or statistical significance tests are reported for the claimed perplexity reductions or the downstream-task comparisons; without these, it is impossible to assess whether the observed differences exceed run-to-run variance and therefore whether the distinction between perplexity gains and downstream neutrality is robust.

Authors: We agree that including measures of statistical robustness would enhance the reliability of our findings. Due to the extreme computational demands of these large-scale pre-training runs, our primary results are based on single executions with carefully matched conditions. In the revision, we will conduct and report results from multiple random seeds (at least three) for a subset of key configurations to provide error bars, and we will include statistical significance testing for the downstream task comparisons. revision: yes
Referee: [Experimental setup] The weakest assumption—that the chosen student sizes (123M, 735M), token counts (up to 168B), and downstream suite are sufficient to reveal productive use of hidden-layer information—remains untested; the paper does not include scaling curves or ablation on larger students or longer training that would strengthen the generality of the 'latent signal' interpretation.

Authors: We recognize the value of scaling analyses for broader generalization. Our experimental design prioritized compute-matched comparisons at practical scales to isolate the contribution of hidden layer information. The observed consistent perplexity improvements across the tested student sizes provide supporting evidence for the latent signal within these regimes. We will revise the paper to include additional discussion in the Limitations section on the scale-specific nature of our results and suggest directions for future scaling studies. revision: partial

Circularity Check

0 steps flagged

No circularity: purely empirical benchmark with no derivations or fitted predictions

full rationale

The paper is an empirical comparison of Hidden Layer Distillation versus logit-based KD on decoder-only pre-training. It reports measured perplexity and downstream-task results from controlled experiments (Gemma3 teacher, fixed student sizes, token counts, C4 data) without any claimed mathematical derivation, uniqueness theorem, or prediction that reduces to its own inputs by construction. No self-citations are invoked to justify a load-bearing premise, no ansatz is smuggled, and no parameter is fitted then relabeled as a prediction. The central claim rests on external benchmarks and baselines, making the work self-contained against the patterns that would trigger circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions of knowledge distillation (that matching teacher outputs or hidden states transfers useful knowledge) and on the representativeness of the chosen model sizes and evaluation tasks. No new entities are postulated.

axioms (2)

domain assumption Matching teacher hidden states or logits transfers useful knowledge to the student
Invoked throughout the comparison of HLD and KD methods
domain assumption Perplexity and standard downstream benchmarks are appropriate measures of distillation success
Used to conclude that HLD does not consistently outperform KD

pith-pipeline@v0.9.0 · 5465 in / 1237 out tokens · 78247 ms · 2026-05-13T02:11:46.418759+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
LHLD = β L_data + α L_logits + γ L_emb with L_emb = MSE(normalized teacher/student hidden states at median layer)

Reference graph

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