Large language models (LLMs) struggle to accumulate evidence across multiple rounds of user interactions, failing to update their beliefs in a manner consistent with Bayesian inference. Existing solutions require fine-tuning on sensitive user interaction data, limiting their applicability in privacy-conscious settings. We propose AdaptFuse, a training-free framework that externalizes probabilistic computation entirely from the LLM, where a symbolic module maintains a Bayesian posterior over a discrete hypothesis set, while a frozen LLM contributes semantic reasoning via multi-sample Dirichlet aggregation. The two signals are combined through entropy-adaptive fusion, which automatically weights each source by its predictive confidence, shifting reliance from the LLM to the symbolic posterior as evidence accumulates. We evaluate across three domains: flight recommendation, hotel recommendation, and web shopping; on Gemma2 9B, Llama3 8B, and Qwen~2.5 7B. AdaptFuse consistently outperforms both prompting baselines and fine-tuned Bayesian Teaching models on all tasks, with accuracy improving monotonically over interaction rounds. These results demonstrate that principled inference-time algorithms can substitute for fine-tuning in personalized recommendation, without storing or training on sensitive user data.
Figures & tables
Figure 1: Overview of AdaptFuse. Left: Sequential interactions provide feedback about user preferences. Middle: Frozen-LLM samples and self-reported confidence are aggregated into choice probabilities pL . The Bayesian module updates the preference posterior p(h) and derives choice probabilities pB . Entropy-adaptive fusion combines these into pF , giving greater weight to more concentrated predictions. Right: The highest-probability option is recommended, with flight and hotel panels illustrating potential applications.
Domain
Features / representation
M
Flight
Departure, duration, stops, price
96
Hotel
Distance, price, rating, amenities
112
WebShopping
Title and product description
187
Table 1: Domain-specific inputs and hypothesis support. Flight and Hotel use d=4 normalized scalars; WebShopping uses approximate extraction from free text.
Gemma
Llama
Qwen
Method
First
Final
First
Final
First
Final
Direct
31.3
33.5
30.2
34.6
31.2
34.1
CoT
36.2
38.4
35.1
39.1
34.5
38.6
Self-consistency
40.4
44.7
38.1
43.8
37.2
41.5
Oracle Learning
48.6
59.1
45.1
58.3
40.6
51.7
Bayesian Teaching
54.1
73.4
55.5
74.3
52.5
65.2
Table 2: Flight accuracy (%) after the first and fifth rounds. EMA denotes original positional configuration.
Figure 2: Reported Flight accuracy through five interactions. The plotted methods are Original, Oracle Learning, Bayesian Teaching, and the original AdaptFuse configuration with EMA. CoT, self-consistency, and no-EMA trajectories are not plotted.
Figure 3: Reported final Flight accuracy as the number of attributes varies from two to eight. “Ours” denotes the original EMA configuration. Relative method rankings vary across dimensionalities.
Method
Gemma
Llama
Qwen
Calls
Direct
0.52
0.74
0.63
1
CoT
2.15
2.87
2.42
1
Self-consistency
3.67
3.79
3.68
5
Bayesian Teaching
1.42
1.34
1.05
1
AdaptFuse + EMA
4.35
4.63
4.51
5
Table 3: Reported mean seconds per interaction round on one A100 GPU, Flight. Training cost is excluded. Calls denote LLM invocations, rather than matched generated tokens.
Configuration
Seconds
Accuracy (%)
EMA, N=1
0.91
71.6
N=2
1.77
72.8
N=3
2.63
73.3
N=4
3.49
74.6
N=5
4.35
76.2
Bayesian Teaching
1.42
73.4
Table 4: Sampling trade-off on Flight with Gemma. Other components, including legacy EMA, are fixed. The no-EMA core’s corresponding sampling curve is not measured.
Variant
Flight
Hotel
WebShopping
Fixed fusion
72.7
67.9
55.1
Majority vote
73.1
68.0
56.8
Dirichlet, no EMA
74.0
69.3
57.0
Dirichlet + EMA
76.2
70.5
57.6
Table 5: Gemma cross-domain component ablations: final accuracy (%). Fixed fusion and majority vote replace the named component in the original default; no EMA removes positional smoothing.
Support condition
Fixed fusion
Adaptive fusion
Covered: h∗∈H
72.7
76.2
Mild misspecification
69.2
70.4
Severe misspecification
67.6
67.2
Table 6: Reported Flight final accuracy (%), Gemma, under support misspecification. Both fusion variants retain the original EMA configuration; fixed fusion uses equal source weights.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Field
Content
Title
Men’s Classic Fit Short-Sleeve Crewneck T-Shirt
Description
100% cotton. Machine wash cold. Available in sizes S, M, L, XL, XXL. Relaxed fit. Imported. $24.99.
User goal
Looking for a cotton shirt, machine-washable, size XL, under $30.
Appendix
Table 7: Example product representation in the WebShopping task.
Statistic
Flight
Hotel
WebShopping
User records / trajectories
624
624
990
Rounds per trajectory
5
5
5
Candidates per option set
3
3
3
Hypothesis-support size ( M )
96
112
187
Appendix
Table 8: Dataset statistics and domain-specific hypothesis-support sizes. M counts preference hypotheses, rather than users or trajectories.
Symbol
Parameter
Value
Role
Eq.
β
Softmax inverse temp.
6.0
Likelihood sharpness
( 1 )
α0
Dirichlet prior
1.0
Laplace smoothing
( 4 )
m
EMA coefficient
0.65
LLM variance reduction
( 9 )
N
LLM samples/round
5
Aggregation sample count
( 4 )
εw
Fusion weight floor
10−3
Prevents zero weights
( 5 )
ε
Likelihood floor
10−8
Numerical stability
( 2 )
Appendix
Table 9: AdaptFuse hyperparameters. No parameter was tuned on held-out data.
Figure 4: Interactive preference inference on flight recommendation task. We show accuracy after the first and final (fifth) rounds across different assistants, including original LLMs, models fine-tuned with the Bayesian Assistant, and models fine-tuned with an oracle that provides correct answers (models provided by the Qiu et al. (2026) ). Both fine-tuning approaches improve performance, and our method achieves the best overall results. Error bars denote the standard error over three random seeds.