Have we made mitigating catastrophic forgetting more complicated than it needs to be? Continual adaptation often degrades performance on earlier tasks, motivating rehearsal buffers, auxiliary objectives, and adaptive merging procedures. We investigate how far a simpler alternative-periodic parameter interpolation during fine-tuning-can go on its own. We introduce Sequential Fine-tuning with Averaging (SFA) and evaluate it alongside replay-free Lookahead, originally designed for optimization stability to find compelling results. In Qwen3-14B adapter continual learning, fixed configurations of both methods outperform the tested replay and adaptive-merging configurations in mean final accuracy using up to 36.3% less task training time. Furthermore, across language and vision tasks, our results compete with more complex continual-learning methods. Together, these findings suggest that simple in-training interpolation deserves consideration before introducing more elaborate forgetting-mitigation mechanisms.
Figures & tables
Figure 1: Qwen3-1.7B Math → Law: replay-free comparisons over three seeds (17, 42, 123). Both axes show mean ± sample SD. All underlying Law-training runs use learning rate 10−5 . SFA uses the development-selected βend=.5 . Appendix B gives the configurations; Appendix B.1 reports the SFA strength sweep. Table 4 additionally includes seeds 7 and 2026 and uses development-selected sequential fine-tuning at 5⋅10−6 .
Figure 2: Llama 2-7B Math → Law experiments. (a) Intermediate SFA merges recover Math accuracy lost during sequential fine-tuning. (b) The SFA interval sweep is compared with endpoint-interpolation and Task Arithmetic weight sweeps, showing favorable intermediate-merge operating points beyond the equal-weight endpoint. Panel (b) sweeps weights of 0.25, 0.50, and 0.75 on the Law-adapted checkpoint for both endpoint-interpolation and Task Arithmetic. Replay samples from full history.
Method
Final average (%) ↑
Runtime (s) ↓
SFA
78.4±0.8
117.5
Replay (10%)
78.8±0.3
133.0
SFA-R
79.8±0.2
130.7
Table 1: Qwen3-1.7B full-parameter four-task learning at a common total token budget. Final average test accuracy is mean ± sample SD over three seeds; runtime averages two complete-stream training-loop measurements. Replay and SFA-R use approximately 10% replay after the first task. Bold marks the highest accuracy and lowest measured runtime.
Figure 3: Qwen3-14B adapter results under matched current-task exposure. (a) : final four-task accuracy for fixed configurations (three-seed mean and sample SD). Both SFA and Lookahead exceed the tested replay and AIMMerging means. (b) : controlled Amazon-stage training-loop time on one H200 (two repetitions); the measured SFA savings are specific to this stage. Peak GPU memory is comparable.
Appendix figures & tables41 assets
Supplementary material from the paper’s appendix.
Appendix
Method
8B
14B
SFA
243.0
317.6
Replay (buffer)
277.7
389.7
AIMMerging (ported)
350.8
498.4
Appendix
Table 2: Controlled single-stage training-loop time in seconds. Each entry averages two runs on one H200.
Method
Replay-gradient
Monitoring
SFA / Lookahead
0
0
Replay (buffer)
1.20M
0
AIMMerging (ported)
2.51M
4.20M
Appendix
Table 3: Additional training work in the 14B four-task adapter stream. Every method processes 6.01M current-task tokens. Replay and monitoring tokens are distinct from the single-stage timing in Figure 3 .
Method
GSM8K
Law mean
Math-trained start
74.80±0.65
35.63±1.87
Sequential fine-tuning
71.18±0.61
90.07±0.24
Lookahead, β=.5
71.45±0.95
89.74±0.32
SFA, βend=.5
71.83±1.14
90.18±0.43
Appendix
Table 4: Five-seed Qwen3-1.7B Math → Law test accuracy (%, mean ± sample SD; seeds 17, 42, 123, 7, 2026). The starting model is evaluated before Law fine-tuning; bold marks the highest adapted mean. Configurations maximize Math development accuracy while allowing at most a one-point Law reduction relative to reference sequential fine-tuning (Appendix B ). Sequential fine-tuning uses learning rate 5⋅10−6 .
Parameter set
Implementation
SFA
Lookahead
SFA less time (%)
1.7B, full parameters
Per-tensor
9.30
13.13
29.2
Batched
5.09
8.60
40.8
8B, full parameters
Per-tensor
39.91
56.09
28.8
Batched
24.09
40.76
40.9
14B, full parameters
Per-tensor
70.48
98.98
28.8
Batched
43.44
73.55
40.9
Appendix
Table 5: Isolated merge cost and recorded cumulative merging time. All times are milliseconds. SFA and Lookahead each use one auxiliary parameter copy; reductions are relative to Lookahead.
Method
Coefficient / LR
Math
Law
SFA
βend=.25
73.2
91.523
.5
76.4
90.339
.75
75.4
88.722
Lookahead
β=.25
72.2
91.730
.5
76.6
90.471
.75
76.0
88.846
Appendix
Table 6: Development results underlying configuration selection for Table 4 (seed 17; accuracies in %). Bold rows identify the configuration with the highest Math accuracy among those achieving at least 89.843% Law accuracy. These scores determine selection given one seed; the five-seed test results provide the performance comparison.
SFA
Lookahead
Sequential fine-tuning selected LR
Seed
GSM8K
Law
GSM8K
Law
GSM8K
Law
17
71.42
90.22
71.19
89.59
71.11
89.92
42
71.57
90.49
70.96
90.23
70.20
90.39
123
73.77
90.57
73.09
89.61
71.42
90.23
7 (prospective)
71.65
90.12
70.66
89.90
71.87
90.00
2026 (prospective)
70.74
89.49
71.34
89.40
71.27
89.81
Appendix
Table 7: Math → Law per-seed test accuracy (%). Bold indicates the highest accuracy for each task within each seed. Seeds 7 and 2026 are prospective replications of the frozen middle-requirement configurations.
Seed group
Comparison
GSM8K
Law
Seeds 17, 42, 123
SFA minus Lookahead
0.51±0.24
0.62±0.35
Seeds 17, 42, 123
SFA minus sequential fine-tuning
1.34±1.02
0.25±0.13
Seeds 7, 2026
SFA minus Lookahead
0.19±1.13
0.16±0.10
Seeds 7, 2026
SFA minus sequential fine-tuning
−0.38±0.21
−0.10±0.31
All five
SFA minus Lookahead
0.38±0.61
0.43±0.36
All five
SFA minus sequential fine-tuning
0.65±1.19
0.11±0.26
Appendix
Table 8: Paired Math → Law differences in percentage points (mean ± sample SD). Positive values favor SFA. No significance or equivalence test is implied.
Method
GSM8K
Law mean
SFA, βend=.5
72.25±1.32
90.43±0.19
Endpoint interpolation β=.5
72.25±1.09
88.47±0.09
EMA, decay .999
72.48±1.25
87.25±0.47
Lookahead β=.5
71.75±1.17
89.81±0.36
Sequential fine-tuning learning rate 10−5
67.07±1.60
91.30±0.41
Sequential fine-tuning learning rate 5⋅10−6
70.91±0.63
90.18±0.24
Appendix
Table 9: Matched Qwen3 Math → Law averaging and fine-tuning comparison (%, seeds 17, 42, 123, mean ± sample SD). These are the non-replay comparison points in Figure 1 ; Table 10 gives the complete SFA sweep.
βend
Per-merge β
GSM8K
Law mean
Math forgetting
Law gain
Math-trained start
—
74.78±0.86
35.15±0.92
—
—
.25
.069
69.93±0.57
91.22±0.30
4.85±1.42
56.06±0.92
.50
.159
72.25±1.32
90.43±0.19
2.53±0.50
55.27±1.01
.75
.293
73.04±1.26
88.05±0.29
1.74±0.66
52.90±0.82
.90
.438
74.37±0.89
80.98±2.25
0.40±0.04
45.82±1.40
.99
.684
74.96±1.15
54.96±6.02
−0.18±0.31
19.81±5.53
Appendix
Table 10: Qwen3-1.7B SFA strength sweep (three seeds; accuracy in %, changes in percentage points; mean ± sample SD). Positive Math forgetting denotes a decline from the Math-trained start. Law gain is relative to that same starting model.
Input share
Supervised share
GSM8K
Law mean
CaseHOLD
ToS
Overruling
1
≈11
74.50±0.97
89.74±0.22
81.02
93.09
95.11
5
≈38
74.93±0.82
89.01±0.16
80.12
92.34
94.56
10
≈56
75.76±0.85
88.76±0.23
79.67
91.83
94.78
Appendix
Table 11: Qwen3-1.7B bounded-memory replay (three seeds, fixed 500-example reservoir). GSM8K and Law mean show mean ± sample SD; individual Law columns show means. Input and supervised shares refer to different token counts. All accuracies and shares are percentages.
Method
1.7B
8B
14B
32B
Sequential fine-tuning
70.6±0.8
76.2±0.5
77.7±1.1
78.1±1.2
Replay (buffer)
74.6±1.0
77.5±0.3
78.6±0.8
78.7±0.3
AIMMerging (ported)
74.8±0.2
77.8±0.6
78.9±0.6
79.0±0.3
Lookahead, fixed coefficient
72.8±0.6
76.7±1.3
79.6±0.6
79.1±0.4
SFA , fixed strength
72.1±1.9
77.4±0.9
79.9±0.3
79.2±0.4
Appendix
Table 12: Final average test accuracy in adapter continual learning (%, three seeds, mean ± sample SD). Configurations fixed at 1.7B and transferred across sizes, with matched current-task exposure. Bold marks the highest fixed-configuration mean at each size. The 32B runs use activation checkpointing.
Method
Final average (%)
Sequential fine-tuning
79.0±0.2
Replay (buffer)
79.6±0.2
SFA
79.9±0.4
Lookahead
79.3±0.4
AIMMerging (ported)
78.9±1.0
Appendix
Table 13: Qwen3-14B shared-LoRA continual learning with an alternative task order: DBpedia → Yahoo Answers → Amazon → AG News. Final average test accuracy (%, mean ± sample SD over seeds 17, 42, and 123). Methods retain the fixed configurations used in Figure 3 : SFA uses βend=.5 and Lookahead uses β=.5 . Bold marks the highest mean.
Metric
Configuration
DBpedia
Amazon
Yahoo
AGNews
Final accuracy (%)
SFA, βend=.5
97.04±0.09
61.41±0.41
71.11±0.96
90.00±0.30
Lookahead, β=.5 (fixed)
96.24±0.95
60.27±1.22
71.57±0.99
90.28±0.54
Lookahead, β=.75 (selected)
98.06±0.19
61.97±0.64
72.87±0.48
89.90±0.49
Forgetting (points)
SFA, βend=.5
1.37±0.11
3.23±0.58
1.53±0.48
—
Lookahead, β=.5 (fixed)
2.45±0.98
4.79±1.12
1.22±0.68
—
Lookahead, β=.75 (selected)
0.48±0.21
2.36±1.52
1.00±0.21
—
Appendix
Table 14: Task-wise retention after the complete 14B adapter stream, DBpedia → Amazon → Yahoo → AGNews (test, seeds 17/42/123; mean ± sample SD). Accuracy is measured after AGNews, not immediately after learning each task. Signed forgetting is the highest earlier accuracy minus final accuracy; lower is better. The last task has no subsequent stage and hence no forgetting entry. Fixed configurations are those in Figure 3 ; selected Lookahead comes from the equal three-point coefficient study.
Method
βend
DBpedia
Amazon
Yahoo Answers
AG News
Final average
Refreshed SFA
.25
96.7±0.6
58.0±3.8
71.3±0.9
89.9±0.4
79.0±1.0
SFA-Ref
.50
97.4±0.2
61.3±1.6
69.5±1.0
89.6±0.3
79.4±0.7
Appendix
Table 15: Reference selection in Qwen3-14B LoRA continual learning. Both variants continue from an identical post-Amazon checkpoint within each seed and subsequently learn Yahoo Answers and AG News. Values are final test accuracies (%, mean ± sample SD over seeds 17, 42, and 123). Amazon is the designated protected task; its starting accuracy is 64.4±0.7 %. Strengths are selected on seed-17 development data. Bold marks the higher mean in each column.
k (interval)
Δ Math
Δ Law
Merge saving
185
+0.03±0.46
+0.43±0.26
0.015 s (28.9%)
5
+0.14±0.68
+0.46±0.28
0.563 s (28.9%)
1
+0.39±0.51
+0.30±0.23
2.877 s (29.3%)
Appendix
Table 16: Full-parameter Math → Law frequency controls: SFA minus Lookahead in accuracy (points, five-seed mean ± SD) and measured cumulative merge-time savings for SFA on one H200. These pairwise differences diagnose reference-policy and implementation effects; they are not the main comparison to rehearsal-based methods.
Cumulative merging
Training loop
Method
Interval
Rep. 1
Rep. 2
Rep. 1
Rep. 2
SFA
185
0.037
0.037
585.3
586.1
Lookahead
185
0.052
0.053
585.0
586.1
SFA
5
1.388
1.385
583.9
589.9
Lookahead
5
1.960
1.939
585.2
588.1
SFA
1
6.931
6.925
596.2
596.7
Appendix
Table 17: Qwen3-1.7B full-parameter Math → Law fine-tuning: controlled cumulative merge time and complete Law-stage training-loop time (seconds), with two repetitions on the same H200 per merge interval using seed 17. Training-loop time excludes loading, saving, and evaluation. Merge time uses queued CUDA events; loop time uses synchronized wall-clock timing.
Figure 4: Full-parameter Qwen3-1.7B Math → Law across merge intervals. Top: test accuracy (five-seed mean ± sample SD). Bottom left: paired SFA-minus-Lookahead differences; small marks show individual seeds, with seed 17 hollow because it supplied development selection. Bottom right: controlled cumulative merge time in seconds on a logarithmic vertical scale (two repetitions per method). SFA uses βend=.5 and Lookahead uses per-sync β=.5 . Timings cover only merging.
Method
GSM8K
Law mean
Sequential fine-tuning
28.2±4.0
91.1±0.5
Endpoint interpolation, β=.5
75.8±1.1
87.5±0.7
Lookahead
72.9±2.7
89.2±0.6
SFA
71.7±3.4
89.9±0.6
Appendix
Table 18: Direct pretrained-to-Law full-parameter fine-tuning of Qwen3-1.7B. Test accuracy (%, mean ± sample SD over three seeds) uses the standard evaluation prompt, not the worked-solution diagnostic. The pretrained model scores 79.9% on GSM8K and 51.6% on Law.
Method
DBpedia
Amazon
Yahoo Answers
AG News
SFA
96.76±0.11
60.40±0.21
66.63±3.19
89.85±0.22
Replay
97.00±1.26
57.52±1.60
70.15±1.08
90.52±0.39
SFA-R
98.07±0.23
59.13±1.32
72.37±0.81
89.72±0.23
Appendix
Table 19: Per-task test accuracy after the complete Qwen3-1.7B full-parameter stream, DBpedia → Amazon → Yahoo Answers → AG News (%, mean ± sample SD over seeds 17, 42, and 123). Every entry measures final accuracy, rather than accuracy immediately after learning that task. Replay and SFA-R use identical schedules with a 500-example reservoir and approximately 10% replay input tokens after the first task, under the same total token budget as SFA. Bold indicates the highest mean in each column.
Figure 5: Qwen2.5-1.5B Math → Law comparison. SFA at p=.25 retains more Math than the displayed Task Arithmetic and equal-weight endpoint configurations. (Table 24 ).
Figure 6: 20-task vision experiments with ViT-base: Food-101 (top) and CIFAR-100 (bottom). Replay-free SFA improves on the displayed sequential, Task Arithmetic, and endpoint configurations. Dashed lines use replay (full history) at the indicated sampling proportions. SFA-R is a replay-augmented variant of SFA. Multitask reference accuracies are annotated above the plotted range.
Figure 7: A comparison of sequentially fine-tuning ViT (base) on 20 tasks (Food-101) with ( bottom ) and without SFA ( top ). Each new task is introduced with a different colored curve across gradient timesteps (x-axis) resulting in changes to both current and past task accuracies (y-axis). The use of SFA can be seen to improve cumulative past task performance at averaging steps.
Figure 8: A comparison of varying the Task Arithmetic model weights, and β on SFA ( p =1), with SFA (varying p,β=0.5 ) for Pythia (2.8B). We reproduce the results varying p in SFA (orange curve) from Figure 13 and add 2 sweeps showing change in performance on Pythia (2.8B) when the weights for the current and past checkpoints are varied for SFA ( p=1 ) (dashed blue) and the domain-specific models are merged in Task Arithmetic (dashed red).
Figure 9: SFA compared against other continual learning methods, where the two tasks (Task A and B) were created by splitting MNIST by label. The accuracy after single-task training, sequential training, and multitask training is also shown. The lines for EWC and L2 are created by varying the coefficient corresponding to each method (and are the same for the top and bottom plots). (Top) visualizes SFA performance under varying β coefficient, which determines how much weight is being placed on the initial model. (Bottom) visualizes SFA with varying averaging frequency in steps before averaging.
Task/Domain
Eval Metric
Food-101
Food-101 holdout set
CIFAR-100
CIFAR-100 holdout set
Text Simplification (Simpl)
Text Simplification (Simpl) holdout set
Inquisitive Question Generation (InqQG)
Inquisitive Question Generation (InqQG) holdout set
Twitter Stylometry (TwSt)
Twitter Stylometry (TwSt) holdout set
Headline Generation with Constraint (HGen)
Headline Generation with Constraint (HGen) holdout set
Appendix
Table 20: Evaluation metrics for each task and domain used in our work.
Figure 10: An analysis of the negative correlation between accuracy on Math and the L2 distance of the final model (fine-tuned on Math, then Law) from the original model (fine-tuned on Math only). The fine-tuning on Law is done using SFA with varying values of p that determine the merging frequency. For reference we also mark sequential fine-tuning which leads to much higher L2 distance due to no merging, and accuracy just below that achieved with SFA merging once at the end of fine-tuning on law ( p=1 ).
Figure 11: The fine-tuning of T0_3B (3B) and T0pp (11B) on a stream of language generation tasks. Training loss on each subsequent task decreases as the model learns it, while evaluation loss on Simpl continues to increase, indicating that forgetting is present.
Figure 12: The Simpl loss curve of T0_3B (3B) from Figure 11 is compared to a multitask model training on all tasks, and a multitask model training on all tasks except Simpl. As T0_3B (3B) continues to fine-tune on each new task, the loss on Simpl becomes the same order of magnitude as that of a model that is never exposed to Simpl.
Pythia (2.8B)
case_hold
tos
overruling
GSM8K (0-shot)
Pythia (2.8B) Original
0.25
0.85
0.45
0
metamathqa
0.19
0.87
0.48
0.38
law
0.74
0.93
0.97
0
Sequential fine-tuning: metamathqa, Law
0.76
0.95
0.59
0
Endpoint interpolation: metamathqa, Law (p=1)
0.74
0.88
0.49
0.048
Endpoint interpolation: metamathqa, Law (p=1, 0.75 law, 0.25 math)
0.78
0.93
0.52
0
Appendix
Table 21: Results of Pythia (2.8B) models fine-tuning on Math and Law
Pythia (2.8B)
L2-Distance
metamathqa, Law - metamathqa
90.99
metamathqa, Law (p=1) - metamathqa
45.50
metamathqa, Law (p=0.5) - metamathqa
35.38
metamathqa, Law (p=0.25) - metamathqa
24.16
metamathqa, Law (p=0.10) - metamathqa
10.94
Task Arithmetic (0.5 Law, 0.5 math)- metamathqa
101.77
Appendix
Table 22: The L2 distance of Pythia (2.8B) models from previous checkpoints of models fine-tuning on Math and law
Llama 7B
case_hold
tos
overruling
GSM8K (0-shot)
Llama 2 (7B) Original
0.32
0.13
0.49
0
metamathqa
0.21
0.38
0.49
0.42
law
0.81
0.51
0.94
0
Sequential fine-tuning: metamathqa, Law
0.64
0.86
0.93
0
Endpoint interpolation: metamathqa, Law (p=1)
0.61
0.59
0.90
0.0015
Endpoint interpolation: metamathqa, Law (p=1, 0.75 law, 0.25 math)
0.64
0.83
0.94
0
Appendix
Table 23: Results of Llama 2 (7B) models fine-tuning on Math and law
Qwen2.5 1.5B
case_hold
tos
overruling
GSM8K (0-shot)
Qwen2.5 (1.5B) Original
0.47
0.28
0.90
0
metamathqa
0.26
0.19
0.69
0.60
law
0.77
0.91
0.95
0
Sequential fine-tuning: metamathqa, Law
0.78
0.92
0.94
0
Endpoint interpolation: metamathqa, Law (p=1)
0.81
0.88
0.93
0.01
SFA: metamathqa, Law (p=0.5)
0.77
0.89
0.94
0.12
Appendix
Table 24: Qwen2.5-1.5B Math → Law accuracy. These single-run configurations illustrate retention-adaptation trade-offs.
Table 27: Results of Pythia (2.8B) models fine-tuning on Math, Law and Code for 2 orders
Figure 13: A comparison of Pythia (2.8B)’s performance on multiple domains (Math, Law and Math, Code) using various fine-tuning and model merging techniques similar to Figure 2 . On Math to Law, SFA p=0.25 can be seen as having comparable performance to using a data buffer, while outperforming Task Arithmetic. Likewise, in Math to Code, SFA with varying p outperform using a data buffer and Task Arithmetic.
Figure 14: A comparison of Pythia (2.8B)’s performance when training on more than 2 domains (e.g. Math-Law and Code, Math-Code and Law) using various fine-tuning and model merging techniques similar to Figure 13 . On Math-Code to Law, SFA p=0.25 can be seen as having comparable performance to using a data buffer, while outperforming Task Arithmetic. While, SFA with varying p on Math-Law to Code outperforms Task Arithmetic, but performs worse than using a data buffer.
Figure 15: A comparison of varying the Task Arithmetic model weights, and β on SFA ( p =1), with SFA (varying p,β=0.5 ) for Pythia (2.8B) on math then code, similar to Figure 8 . ( Table 25 ).
Figure 16: SFA’s constant parameter-storage requirement compared with growing replay collections in hypothetical CIFAR-100-sized ( left ) and ImageNet-1k-sized ( right ) task streams. Replay retains 10% of each task without a capacity limit. The SFA curve includes both working and reference parameters, while replay curves show retained data only; adding replay’s working model would increase its total storage. Images are assumed uncompressed, and these analytical examples are distinct from the experimental task streams.
Figure 17: Analytical parameter-plus-buffer storage for SFA and CLS-ER with FP16 parameters and uncompressed 224×224 RGB images stored as uint8 pixels. Parenthesized legend values denote the number of retained images. SFA requires one reference alongside the working model, whereas CLS-ER maintains two auxiliary model copies and a replay buffer.
Figure 18: A comparison of SFA with and without using task boundaries to control model averaging and updating frequencies on a sequence of 20 tasks from Food-101 ( left ) and CIFAR-100 ( right ). While SFA is still effective without access to task boundaries, their incorporation enhances performance.
Models trained on a new task typically degrade on prior tasks, a phenomenon known as forgetting. Traditionally, mitigating forgetting has required replaying stored exemplars from prior tasks, which is often impractical. By contrast, language models can sample from their own training distribution, and we show that these self-generated samples serve as effective replay data, nearly eliminating forgetting. We find that forgetting nonetheless persists when the model has little remaining capacity: models pretrained close to saturation cannot absorb new information without overwriting prior knowledge. When capacity is not the limiting factor, low learning rates reduce forgetting but require substantially more training steps. Replay breaks this tradeoff, enabling fast, high-learning-rate finetuning without forgetting.
Continual fine-tuning of large language models (LLMs) is becoming increasingly crucial as these models are deployed in dynamic environments where tasks and data distributions evolve over time. While strong adaptability enables rapid acquisition of new knowledge, it also exposes LLMs to catastrophic forgetting, where previously learned skills degrade during sequential training. Existing replay-based strategies, such as fixed interleaved replay, accuracy-supervised, and loss-driven scheduling, remain limited: some depend on heuristic rules and provide only partial mitigation of forgetting, while others improve performance but incur substantial computational overhead. Motivated by retention dynamics under sequential fine-tuning, we propose Memory-Inspired Sampler and Scheduler Replay (MSSR), an experience replay framework that estimates sample-level memory strength and schedules rehearsal at adaptive intervals to mitigate catastrophic forgetting while maintaining fast adaptation. Extensive experiments across three backbone models and 11 sequential tasks show that MSSR consistently outperforms state-of-the-art replay baselines, with particularly strong gains on reasoning-intensive and multiple-choice benchmarks.
Yiyang Lu, Yu He, Jianlong Chen +1
The Chinese University of Hong Kong, Shenzhen · Nanjing University
Continual learning commonly relies on post-hoc mechanisms such as replay, elastic regularization, or distillation. This work argues that forgetting should instead be modeled directly as interference between tasks. In the frozen-feature regime, forgetting from learning a new task is exactly the interference energy induced on the old task. In deep networks, the same quantity is recovered through path-averaged curvature with minimal additional forward passes. When task supports are disjoint, forgetting can be eliminated structurally and when task supports overlap in conflicting directions, a non-zero distortion floor is unavoidable. The same geometry optimally merges models through task-aware orthogonalization. From this analysis we derive Interference-Gated Functional Allocation (IGFA), a replay-free, Fisher-free method that shares directions when tasks align and protects them when they conflict. Across benchmarks, IGFA achieves lossless retention when tasks are structurally separable and moves unavoidable cost from irreversible forgetting into deferred but recoverable plasticity when they are not. It matches the strongest replay-free structural baselines on dissimilar-task streams and improves on unconditional projection when similarity makes transfer worth preserving.