Annotation Entropy Predicts Per-Example Learning Dynamics in LoRA Fine-Tuning

Brady Steele

cs.LGMar 12, 2026

Annotation Entropy Predicts Per-Example Learning Dynamics in LoRA Fine-Tuning

Authors: Brady Steele

Organizations: Georgia Institute of Technology

Abstract

We find that LoRA fine-tuning exhibits un-learning on contested examples: items with high annotator disagreement show increasing loss during training, a qualitatively distinct pattern largely absent under full fine-tuning and consistent across all six models tested (four encoder, two decoder-only). This discovery emerges from correlating annotation entropy, computed from ChaosNLI's 100 labels per example, with per-example area under the loss curve (AULC) on SNLI and MNLI. The correlation is positive in all 25 conditions tested (Spearman $ρ= 0.06$ - $0.43$ ), with decoder-only models showing stronger correlations than encoders at matched LoRA rank. The effect survives partial-correlation controls and replicates across seeds and datasets. A preliminary noise-injection experiment is consistent with these findings.

Figures & tables

Figure 1: Per-example loss trajectories grouped by annotation entropy (RoBERTa, LoRA $r{=}4$ , SNLI, seed 42). Clean examples show decreasing loss; contested examples exhibit increasing loss (un-learning). Lines: group means; bands: 95% CIs; dashed line: $-\!\log 0.5\approx 0.693$ .

Encoder models
Model	Method	SNLI $\rho$	MNLI $\rho$
RoBERTa	LoRA $r{=}4$	$.308{\scriptstyle\pm.016}$	$.140{\scriptstyle\pm.009}$
	LoRA $r{=}16$	$.346{\scriptstyle\pm.019}$	$.178{\scriptstyle\pm.005}$
	Full FT	$.426{\scriptstyle\pm.015}$	$.200{\scriptstyle\pm.027}$
BERT	LoRA $r{=}4$	$.160{\scriptstyle\pm.052}$	$.059{\scriptstyle\pm.015}$ c
	LoRA $r{=}16$	$.240{\scriptstyle\pm.011}$	$.064{\scriptstyle\pm.023}$ c

Table 1: Spearman

\rho

between AULC and annotation entropy (mean

\pm

std across 3 seeds unless noted). All correlations significant at

p<0.001

except those marked c (fail Bonferroni correction). d Mean of 2 converged seeds (seed 456 reached chance-level accuracy). e Mean of 2 seeds (memory crash). IA 3 row: RoBERTa on SNLI only (§ 4.3 ).

Figure 2: Per-example loss under full fine-tuning (RoBERTa, SNLI, seed 42). Unlike LoRA (Figure 1 ), all entropy categories show decreasing loss; the temporal ordering is preserved but contested examples are eventually fit. Dashed line: $-\!\log 0.5\approx 0.693$ .

		SNLI		MNLI
Model	Method	Contest.	Clean	Contest.	Clean
RoBERTa	LoRA $r{=}4$	$+.170{\scriptscriptstyle\pm.021}$	$-.586{\scriptscriptstyle\pm.032}$	$+.061{\scriptscriptstyle\pm.014}$	$-.135{\scriptscriptstyle\pm.025}$
	LoRA $r{=}16$	$+.161{\scriptscriptstyle\pm.018}$	$-.675{\scriptscriptstyle\pm.028}$	$+.086{\scriptscriptstyle\pm.011}$	$-.254{\scriptscriptstyle\pm.019}$
	Full FT	$-.751{\scriptscriptstyle\pm.035}$	$-1.054{\scriptscriptstyle\pm.019}$	$-.871{\scriptscriptstyle\pm.042}$	$-1.069{\scriptscriptstyle\pm.015}$
BERT	LoRA $r{=}4$	$+.076{\scriptscriptstyle\pm.038}$	$-.135{\scriptscriptstyle\pm.062}$	$+.039{\scriptscriptstyle\pm.018}$	$+.099{\scriptscriptstyle\pm.031}$
	LoRA $r{=}16$	$+.161{\scriptscriptstyle\pm.025}$	$-.285{\scriptscriptstyle\pm.041}$	$+.071{\scriptscriptstyle\pm.022}$	$+.118{\scriptscriptstyle\pm.028}$

Table 2: Mean loss change (

\Delta\ell

) from start to end of training for contested and clean examples (mean

\pm

std across 3 seeds unless noted). Positive

\Delta\ell

= un-learning. Under LoRA, contested examples consistently increase in loss; clean examples generally decrease, except BERT on MNLI where clean examples also show slight increases. Under full FT, all categories decrease. IA 3 shows near-zero

\Delta\ell

for contested examples, indicating no un-learning. Decoder model

\Delta\ell

values are reported in Appendix B . d Mean of 2 converged seeds.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Seed	AULC $\rho$	$p$ -value	Val Acc
LoRA $r{=}4$	42	$0.304$	$3.1{\times}10^{-27}$	$0.541$
	123	$0.327$	$1.7{\times}10^{-31}$	$0.597$
	456	$0.295$	$8.8{\times}10^{-26}$	$0.554$
LoRA $r{=}16$	42	$0.330$	$4.3{\times}10^{-32}$	$0.607$
	123	$0.366$	$1.1{\times}10^{-39}$	$0.640$
	456	$0.341$	$2.0{\times}10^{-34}$	$0.624$

Appendix

Table 3: Per-seed AULC–entropy Spearman

\rho

for RoBERTa on SNLI. All seeds yield highly significant correlations (

p<10^{-25}

). The

r{=}4<r{=}16<\text{Full FT}

ordering holds within every seed. Validation accuracy is computed on the ChaosNLI validation split (chance is 33%).

Model	Method	Seed	$\rho$	$\tau$	Val Acc
Qwen 1.5B	LoRA $r{=}4$	42	$0.354$	$0.243$	$0.700$
		123	$0.365$	$0.252$	$0.716$
		456	$0.325$	$0.220$	$0.660$
	LoRA $r{=}16$	42	$0.397$	$0.273$	$0.703$
		123	$0.409$	$0.283$	$0.729$
		456	$0.363$	$0.245$	$0.693$

Appendix

Table 4: Per-seed AULC–entropy Spearman

\rho

and Kendall

\tau

for decoder-only models on SNLI. All 11 runs yield highly significant correlations (

p<10^{-30}

). The

r{=}4<r{=}16

ordering holds within every seed for both models. Qwen2.5-3B LoRA

r{=}16

seed 456 did not complete (memory crash).

Model	Method	Contest.	Clean
Qwen	LoRA $r{=}4$	$+.085{\scriptscriptstyle\pm.019}$	$-.412{\scriptscriptstyle\pm.031}$
1.5B	LoRA $r{=}16$	$+.112{\scriptscriptstyle\pm.022}$	$-.508{\scriptscriptstyle\pm.027}$
Qwen	LoRA $r{=}4$	$+.098{\scriptscriptstyle\pm.015}$	$-.467{\scriptscriptstyle\pm.024}$
3B	LoRA $r{=}16$	$+.131{\scriptscriptstyle\pm.018}$ e	$-.553{\scriptscriptstyle\pm.021}$ e

Appendix

Table 5: Mean loss change (

\Delta\ell

) for decoder-only models on SNLI (mean

\pm

std across 3 seeds unless noted). The un-learning pattern (positive

\Delta\ell

for contested examples) is consistent with the encoder results in Table 2 . e Mean of 2 seeds (memory crash).

Figure 3: Distribution of annotation entropy across the ChaosNLI–SNLI subset ( $n{=}1{,}514$ ). Ambiguous: $0.4\leq\mathcal{H}<0.7$ ( $n{=}766$ , 50.6%); clean: $\mathcal{H}<0.4$ ( $n{=}378$ , 25.0%); contested: $\mathcal{H}\geq 0.7$ ( $n{=}370$ , 24.4%). Dashed lines mark thresholds; dotted line marks $\log 3\approx 1.099$ nats.

Model	Method	AULC $\rho$	$p$ -value	Val Acc
RoBERTa	LoRA $r{=}1$	$0.233$	$2.1{\times}10^{-16}$	$0.446$
	LoRA $r{=}2$	$0.282$	$1.4{\times}10^{-23}$	$0.518$
	LoRA $r{=}4$	$0.304$	$3.1{\times}10^{-27}$	$0.541$
	LoRA $r{=}8$	$0.325$	$2.9{\times}10^{-31}$	$0.584$
	LoRA $r{=}16$	$0.330$	$4.3{\times}10^{-32}$	$0.607$
	LoRA $r{=}32$	$0.341$	$2.6{\times}10^{-34}$	$0.601$

Appendix

Table 6: Rank sweep for RoBERTa and BERT on SNLI (seed 42). The AULC–entropy correlation increases monotonically with rank (Spearman rank–

\rho

+1.0

for both models).

Training-set composition (RoBERTa, $r{=}4$ , SNLI)
Condition	Spearman $\rho$
Original (all buckets)	$.308{\scriptstyle\pm.016}$
Low-entropy only	$.306{\scriptstyle\pm.003}$
High-entropy only	$.306{\scriptstyle\pm.002}$
Balanced	$.307{\scriptstyle\pm.001}$
Alternative rank statistic (all 54 runs)

Appendix

Table 7: Robustness checks. Top : correlation is invariant to training-set entropy composition. Bottom : Kendall

\tau

-b confirms all findings.

Figure 4: Per-example gradient norms by entropy category (RoBERTa, LoRA $r{=}4$ , SNLI, seed 42). Contested examples produce ${\sim}3.9{\times}$ larger median gradient norms than clean examples (52.67 vs. 13.68; Kruskal–Wallis $H{=}115.1$ , $p<10^{-25}$ ).

Figure 5: Mean AULC by entropy bin under three binning schemes: fixed thresholds (0.4/0.7), quartile bins, and tercile bins (RoBERTa, LoRA $r{=}4$ , SNLI, seed 42). The monotonic increase in AULC with entropy is preserved regardless of binning scheme. Error bars show $\pm$ 1 standard deviation across examples within each bin, reflecting substantial within-bin variance in individual AULC values; the monotonic increase in group means is robust across all binning schemes (Table 7 ).

Figure 6: Cross-architecture comparison of AULC–entropy Spearman $\rho$ on SNLI. Decoder-only models (Qwen2.5-1.5B, Qwen2.5-3B) show stronger and more consistent correlations than the encoder baseline (DeBERTa v3). Within each architecture family, higher LoRA rank produces stronger correlations. Error bars show $\pm$ 1 sample standard deviation across seeds.

Figure 7: Dataset Cartography map colored by annotation entropy category (pooled across all available runs). Clean examples (blue) cluster at high confidence, while contested examples (red) are spread across the confidence–variability space. The limited overlap between entropy-based and cartography-based categories reflects their different grounding: external human agreement vs. model-internal training statistics.

Figure 8: Cosine similarity between aggregated gradients of clean and contested examples over training (RoBERTa, SNLI, seed 42). Under LoRA $r{=}4$ (red), gradients remain well-aligned ( ${\sim}0.80$ ), while under full fine-tuning (blue), alignment drops to ${\sim}0.25$ by mid-training. Un-learning under LoRA occurs despite high gradient alignment, suggesting the bottleneck is subspace capacity rather than gradient direction competition.

Figure 9: Prediction entropy (left) and expected calibration error (right) by entropy category (RoBERTa, SNLI, seed 42). Full fine-tuning produces far more peaked predictions (lower entropy) than LoRA yet does not exhibit un-learning, ruling out calibration as the primary explanation. LoRA shows disproportionately high ECE on contested examples relative to clean, reflecting the rank constraint’s selective impact on high-entropy items.

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Open paper AskPDF arXiv

Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the nominal rank budget. To address this, we propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate, computed online from training-time signals and mean-normalized per module to preserve the global LR budget. AnLR-LoRA instantiates this model with two signals available during AdamW optimization, namely function-space velocity and Adam SNR, as a lightweight scheme with no extra trainable parameters. Across commonsense reasoning, natural language generation and visual instruction-tuning benchmarks, AnLR-LoRA consistently improves over LoRA while encouraging broader use of rank capacity, with gains that remain robust across a wide range of global learning rates and transfer cleanly to other LoRA variants.

Abstract

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