Table reasoning requires models to jointly perform semantic understanding and precise numerical operations. Most existing methods rely on a single-turn reasoning paradigm over tables which suffers from context overflow and weak numerical sensitivity. To address these limitations, we previously proposed TableMind as a tuning-based autonomous programmatic agent that simulates human-like interaction within a lightweight large language model (LLM). TableMind internalizes planning, action, and reflection through a two-stage training strategy involving supervised fine-tuning (SFT) on filtered high-quality data and reinforcement learning (RL) via a multi-perspective reward and the Rank-Aware Policy Optimization (RAPO) algorithm. While TableMind establishes a solid foundation for programmatic agents, the inherent stochasticity of LLMs remains a critical challenge that leads to hallucinations. In this paper, we extend this foundation to TableMind++ by introducing a novel uncertainty-aware inference framework to mitigate hallucinations. Specifically, we propose memory-guided plan pruning to retrieve historical trajectories for validating and filtering out logically flawed plans to address epistemic uncertainty. To ensure execution precision, we introduce confidence-based action refinement which monitors token-level probabilities to detect and self-correct syntactic noise for aleatoric uncertainty mitigation. Finally, we employ dual-weighted trajectory aggregation to synthesize a robust consensus from multiple reasoning paths. Extensive experiments on diverse benchmarks demonstrate that TableMind++ consistently outperforms previous baselines and proprietary models to validate the effectiveness of integrating autonomous training with uncertainty quantification. Our code is available.
Figures & tables
Figure 1. TableMind++ mimics the human chain of thought by using a multi-turn plan-action-reflect loop to solve table tasks. This foundational loop is augmented with uncertainty-aware guardrails including planning pruning and weighted aggregation during inference to filter errors and guarantee reliable execution.
Figure 2. The overall training pipeline for TableMind. The process begins with Prompt Building and SFT to warm up the model by providing it with a strong initial policy. Subsequently, RFT with RAPO is applied to significantly enhance its generalization capability. The final model is then deployed for Inference and evaluated for accuracy.
Figure 3. The architecture of TableMind++. The framework integrates two-stage policy optimization with an uncertainty-aware inference pipeline. During inference, the system sequentially employs memory-guided plan pruning to filter logical errors, confidence-based action refinement to correct syntactic noise, and dual-weighted trajectory aggregation to derive a calibrated final consensus.
Split
TabFact
TabMWP
WTQ
HiTab
FinQA
Training
3,500
3,500
1,000
–
–
Test (RL)
800
800
800
–
–
Evaluation
12,779
7,686
4,344
1,349
1,138
Table 1. Dataset statistics for training and evaluation. In-domain datasets (TabFact, TabMWP, WTQ) are used for training, where Test (RL) denotes the subset reserved for monitoring performance during the RL training phase. Out-of-domain datasets (HiTab, FinQA) are utilized exclusively for final evaluation.
Models
In-domain Performance
Out-of-domain Performance
Wikitq
TabMWP
TabFact
HiTab
FinQA
Proprietary
GPT-4.1
59.13
90.34
83.94
61.42
6.45
GPT-5
77.42
96.12
90.05
44.52
28.93
Gemini-2.0-flash
72.54
91.56
81.03
76.08
19.62
Gemini-2.5-flash
75.88
95.89
89.65
52.79
33.45
Open-source
Qwen3-8B
50.47
60.86
70.34
63.12
27.83
Table 2. Main results (%) of different baselines over the benchmarks. In each column, the best result is marked in bold and the second-best result is underlined . Our proposed TableMind++ consistently achieves the best performance across both in-domain and out-of-domain tasks, demonstrating exceptional capability in handling complex structural and numerical reasoning.
Figure 4. Performance analysis of core components. (a) SFT initialization serves as a crucial warm-up, yielding higher initial rewards and accelerating convergence compared to Pure RL. (b) Our RAPO algorithm consistently outperforms the GRPO baseline, demonstrating superior sample efficiency and greater training stability throughout the optimization process.
Figure 5. Ablation study on model types and sizes. (a) The instruct-tuned model leverages superior initialization to maintain a consistent performance advantage over the base model throughout training. (b) Reward trajectories exhibit a clear positive correlation with model capacity, where larger parameter sizes consistently yield higher reward scores.
Figure 6. Ablation study on training strategies. We evaluate the contribution of each module by removing them individually from the full training framework. The results demonstrate that SFT, RFT, RAPO, and the auxiliary tool reward ( Rtool ) are all essential for achieving optimal performance, with the RFT stage proving most critical for accuracy.
Epoch
Sample Size
In-domain Performance
Out-of-domain Performance
Wikitq
TabMWP
TabFact
HiTab
FinQA
0
-
50.47
60.86
70.34
63.12
27.83
1
100
52.52
62.49
70.16
62.85
27.41
150
53.65
62.63
71.32
62.40
27.15
200
55.40
68.42
77.15
62.15
26.88
2
100
50.12
60.62
70.12
61.50
26.05
Table 3. Performance trade-off during the SFT stage. The selected configuration (Epoch 1, 200 samples) achieves substantial in-domain gains with minimal loss in OOD generalization. Crucially, this serves as an effective warm-up phase, facilitating faster convergence and better stability in the downstream reinforcement learning process.
Model / Variant
In-domain Performance
Out-of-domain Performance
Wikitq
TabMWP
TabFact
HiTab
FinQA
TableMind++ (Full)
78.07
99.57
93.73
73.69
45.48
w/o Weighted Voting
77.85
99.45
93.25
73.15
44.85
w/o Action Refinement
77.42
99.30
92.80
72.50
43.60
w/o Plan Pruning
77.10
99.15
92.45
72.10
42.95
TableMind (Base)
76.82
99.27
91.85
71.95
42.02
Table 4. Ablation study on inference-time mechanisms. We evaluate the contribution of each module by removing them individually from the full TableMind++ framework. The results demonstrate that memory-guided plan pruning, confidence-based action refinement, and uncertainty-weighted voting are all essential for achieving optimal performance.
Figure 7. Analysis of training dynamics and inference efficiency. The left panel displays the synchronized rise of the tool usage ratio and pass ratio indicating that the agent adopts tools as execution reliability improves. The right panel demonstrates that TableMind++ matches the accuracy of Self-Consistency with significantly lower computational cost.
Figure 8. Qualitative comparison of error distributions between TableMind (a) and TableMind++ (b). The results illustrate a fundamental shift in failure modes: TableMind++ effectively suppresses early-stage structural errors such as Logic Planning and Data Grounding, resulting in a cleaner error profile where remaining failures are concentrated in complex Code Semantics and Syntax, reflecting the intrinsic capability boundaries of the backbone model.
Hyperparameter
Value
In-domain Performance
Out-of-domain Performance
Wikitq
TabMWP
TabFact
HiTab
FinQA
Max Turns
1
74.35
97.23
89.83
68.52
38.15
3
76.82
99.03
92.33
71.95
42.02
5
75.65
98.56
90.55
70.88
40.65
Temperature
0.6
73.35
96.58
88.43
68.12
38.45
0.8
75.51
98.84
91.25
70.25
40.12
Table 5. Hyperparameter sensitivity analysis regarding the Training (RFT) stage. We systematically evaluate the impact of the maximum number of tool-call turns and the rollout temperature on model performance. The results highlight that setting the turn limit to 3 and the temperature to 1.0 achieves the optimal balance between reasoning depth and exploration efficiency.
Hyperparameter
Value
In-domain Performance
Out-of-domain Performance
Wikitq
TabMWP
TabFact
HiTab
FinQA
Memory K
3
77.20
99.65
92.50
72.10
44.20
5
78.07
99.57
93.73
73.69
45.48
10
77.55
99.35
93.10
72.85
45.82
Conf. Threshold τ
0.6
76.90
98.80
91.90
71.50
43.80
0.8
78.07
99.57
93.73
73.69
45.48
Table 6. Sensitivity analysis for Inference-time mechanisms in TableMind++. This table investigates the impact of Memory Retrieval size ( K ) and the Confidence Threshold ( τ ). While K=5 and τ=0.8 are selected as the default settings for their robust overall performance, some specific tasks benefit from alternative configurations.
Figure 9. A case study demonstrating the model’s iterative plan-action-reflect loop. The agent initially retrieves raw data but identifies through self-reflection that the time strings require format conversion. This insight drives a refined plan in the second loop, showcasing its ability to dynamically decompose and solve complex queries.