Supervised Fine-Tuning (SFT) of LLMs suffers from catastrophic forgetting, and prevailing mitigation strategies struggle to reconcile the plasticity-stability dilemma. To address this, we propose Entropic Control for Homeostatic Optimization (ECHO), a closed-loop control framework. By decomposing the KL divergence, we identify output entropy as a dominant observable component of KL variation. This enables us to leverage entropy as a computationally efficient online proxy to monitor forgetting risks in real-time, bypassing expensive reference-model inference. Consequently, ECHO employs an elastic controller that dynamically modulates the gradient weight of replay data via a proportional control law, using deviations from the pre-trained entropic equilibrium as an error signal. Empirical evaluations across 0.6B to 9B parameter architectures demonstrate that ECHO lies on, and in several comparisons extends, the observed plasticity-stability frontier and maintains high operational robustness against varying data mixing ratios.
Figures & tables
Figure 1: Correlation analysis: early entropy deviation vs. final performance degradation. Results demonstrate that deviation from the entropy baseline Href is strongly correlated with the loss of general capabilities.
Figure 2: Overview of the Entropic Control for Homeostatic Optimization.
Table 1: Distribution Shift Metrics. We report entropy and cross-entropy deviations during training, showing that entropy varies more than cross-entropy.
Method
Code
Math
Reasoning
General Stability
HumanEval ↑
Δ
GSM8K ↑
Δ
HellaSwag ↑
Δ
MMLU ↑
Δ
Backbone: Qwen3-0.6B
Base Model
18.90
—
10.39
—
47.35
—
49.17
—
Vanilla SFT
31.10
+12.20
55.49
+45.10
48.55
+1.20
42.91
− 6.26
Data Mixing Laws
37.80
+18.90
55.27
+44.88
50.81
+3.46
43.38
− 5.79
LoRA
23.17
+4.27
17.51
+7.12
48.79
+1.44
44.81
− 4.36
Table 2: Main Results on Qwen3-0.6B and Llama-3.2-3B. We report raw scores and the improvement ( Δ ) over the Base Model. Code, Math, and Reasoning are independent single-run experiments from the same checkpoint, each mixed with Alpaca-GPT4 anchor data; MMLU is averaged over the three. Bold: best; underline : second best.
Figure 3: Sensitivity Analysis of Data Proportioning. Performance across Code, Math, and Reasoning domains as mixing ratio γ varies. ECHO matches or outperforms Static Mixing at every ratio in all three domains.
Backbone
Method
Code
Math
Reason
MMLU
Qwen3-8B
Static Mix
64.02
80.89
78.74
61.61
ECHO (Ours)
68.90
81.80
78.88
74.55
Gemma2-9B
Static Mix
51.83
77.79
79.83
69.47
ECHO (Ours)
53.66
78.54
80.63
70.00
Table 3: Performance across Large-Scale Models. We report task-specific accuracy and MMLU scores. Results show that ECHO effectively scales to 8B and 9B parameters across different architectures. All results are from a single run.
Figure 4: Visualization of training dynamics. (a) Entropy trajectories: Ours maintains lower anchor-data uncertainty than Vanilla SFT. (b) Negative entropy difference indicates suppression of forgetting. (c) Adaptive weight λt starts high to protect early stability, then adjusts to balance task learning and retention.
Figure 5: Parameter sensitivity analysis on Qwen3-1.7B. Left: Base Weight λ modulates the static stability-plasticity trade-off. Right: Entropy Scale Kp acts as a dynamic regularizer; increasing Kp restores general capabilities but may constrain new learning if the penalty becomes excessive.
Continual pre-training and fine-tuning in Large Language Models (LLMs) inevitably induce catastrophic forgetting, typically mitigated by replay using often-inaccessible original data. In this data-free regime, we analyze where forgetting occurs and why. Systematic parameter freezing across five settings up to 1.4B reveals that forgetting concentrates selectively in the output embeddings of tokens rarely seen in the new corpus, whereas the same sqrt(v-hat) band of the body is inert and new learning resides elsewhere. This localization is governed by the vocabulary deficiency of the corpus rather than the training mode, allowing pre-retraining risk ranking from token counts alone within a fixed base model. Mechanistically, absent tokens receive persistent one-sided softmax gradients that Adam's second-moment (sqrt(v-hat)) normalization amplifies into full-sized updates. We therefore propose an intervention: raising Adam's epsilon exclusively for the output projection during training. Across eight settings spanning 160M to 12B parameters and four model families, this removes 39.4% to 67.9% of forgetting across all seven stable configurations without degrading target learning or requiring per-model tuning. The defense combines additively or better with replay (79.8% on Qwen/Korean) and rescues released-head LoRA from a 23-fold forgetting surge. Because post-hoc editing of the drifted rows recovers under 5% of forgetting, the intervention must operate during training. Our findings indicate that a single-line optimizer adjustment may serve as the primary defense against catastrophic forgetting where the corpus starves the vocabulary.
Jonghyun Han, Younghoon Song, Jongyoul Park
Seoul National University of Science and Technology · Korea Institute of Land & Infrastructure Safety Technology
We explore catastrophic forgetting in the context of large pre-trained models. By considering forgetting as a geometric problem in the input space of each weight matrix, we uncover a natural retention objective under which updates produced by gradient-based optimizers are suboptimal. Following this observation, we propose Local Support Learning (LSL), a general-purpose framework that augments gradient-based training for retention of prior capabilities without access to prior data. During a new learning phase, LSL pairs two components with distinct roles: a standard weight adapter, trained as usual to minimize the loss, and a gating function that enables the adapter only on input activations from its own training distribution, making the update local to that distribution. The key challenge is that this gate must route data from all learning phases while training only on data from the current one. We address this with a gate based on a Gaussian Mixture Model (GMM), whose likelihood decays rapidly away from its training data, giving it a natural tendency to stay closed on data from prior phases. We show that this post-training approach can resolve forgetting in LLMs of up to 7 billion parameters, retaining both pretrained and finetuned capabilities across multiple training phases, while being efficient in memory and compute, robust to hyperparameter choice, and showing scaling potential.
Large language models (LLMs) acquire new skills through fine-tuning, but it can destroy capabilities they already have: catastrophic forgetting remains a central obstacle to continual learning in LLMs. Recent works connect forgetting to how far, and along which directions, fine-tuning moves the weights. On-policy methods such as reinforcement learning and on-policy distillation avoid updating the principal singular directions of weight matrices and thus forget less. In contrast, SFT concentrates updates along these directions and is susceptible to catastrophic forgetting. In this work, we introduce Subspace Tuning (SST), which restricts each weight update to the bottom singular subspace, eliminating changes along the principal directions. SST is optimizer-agnostic and composes well with fine-tuning recipes including SFT and self-distillation. SST combines tight subspace protection, dense gradient estimation, and a simple refresh mechanism, enabling stronger learning than prior orthogonal fine-tuning methods. With these mechanisms, protecting as much as 99% of the weight subspace substantially improves retention while preserving strong target-task performance. This behavior strengthens with model and data size and nearly eliminates forgetting in the large-model regime. SST also keeps the model close to its base distribution, inducing 2--4× less KL drift than the baseline recipes. Overall, SST advances the learning--forgetting Pareto frontier, making it a practical default for fine-tuning pre-trained language models.