TypedThinker: Diversify Large Language Model Reasoning with Typed Thinking
Authors: Danqing Wang
Jianxin Ma
Fei Fang
Lei Li
Venue: ICLR 2025 Poster (2025)
Keywords: Reasoning
Large Language Models
Self-training
Primary area: generative models

Abstract: Large Language Models (LLMs) have demonstrated strong reasoning capabilities in solving complex problems. However, current approaches primarily enhance reasoning through the elaboration of thoughts while neglecting the diversity of reasoning types. LLMs typically employ deductive reasoning, proceeding step-by-step from given conditions, which limits their exploration during problem-solving. Our analysis reveals that certain problems are exclusively solvable through specific reasoning strategies like inductive, abductive, or analogical reasoning. However, incorporating diverse reasoning approaches presents two key challenges: identifying the appropriate reasoning type for each problem and exploiting this approach during problem-solving. Therefore, we propose the TypedThinker that predicts suitable reasoning types based on the problem and their previous effectiveness and provides relevant demonstrations to guide LLMs in applying these strategies. Experimental results show significant improvements across multiple benchmarks, with performance gains of 3.4\% for Mistral 7B, 6.5\% for LLaMA3 8B, and 7\% for Qwen 2 7B on logical and mathematical reasoning tasks. TypedThinker enhances LLM reasoning without requiring knowledge distillation from larger models. It can be integrated into more advanced systems like GPT-4o or specialized models like MetaMath to diversify their reasoning approaches and improve their problem-solving capabilities.

Published as a conference paper at ICLR 2025
TYPEDTHINKER: DIVERSIFY LARGE LANGUAGE MODEL REASONING WITH TYPED THINKING
Danqing Wang': Jianxin Ma², Fei Fang', Lei Li'
1 Carnegie Mellon University 2 Qwen Team dangingwecs. cmu. edu
ABSTRACT
Large Language Models (LLMs) have demonstrated strong reasoning capabilities in solving complex problems. However, current approaches primarily enhance reasoning through the elaboration of thoughts while neglecting the diversity of reasoning types. LLMs typically employ deductive reasoning, proceeding step-by- step from given conditions, which limits their exploration during problem-solvine Our analysis reveals that certain problems are exclusively solvable through specific reasoning strategies like inductive, abductive, analogical reasoning. However, incorporating diverse reasoning approaches presents two key challenges: identify- ing the appropriate reasoning type for each problem and exploiting this approach during problem-solving Therefore, we propose the TypedThinker that predicts suitable reasoning types based on the problem and their previous effectiivnness and provides relevant demonstrations to guide LLMs in applying these strategies. Experimental results show significant improvements across multiple benchmarks, with performance gains of 3.4% for Mistral 7B, 6.5% for LLaMA3 8B, and 7% for Qwen 7B on logical and mathematical reasoning tasks. TypedThi i nnke enhances LLM reasoning without requiring knowledge distillation from larger mod- cls. It can be integrated into more advanced systems like GPT-4o or specialized models like MetaMath to diversify their reasoning approaches and improve their problem-solving capabilities.
INTRODUCTION
Large Language Models (LLMs) exhibited promising capabilities in reasoning, such as solving logical reasoning and mathematical problems (Bai et al. [022]] OpenAl (023). Plenty work has been done to improve the reasoning capabilities by adding reasoning thoughts (Wei et al. (022) and making these thoughts more elaborated (Fu et al. 2023 Zheng et al. 2024). However, the exploration of diverse reasoning approaches remains severely limited. LLMs typically rely on a single reasoning pattern-usually deductive reasoning that proceeds step-by-step from given conditions. This narrow focus traps models in fixed thinking patterns, preventing them from solving problems that require different high-level reasoning approaches.
Current research fails create truly diverse reasoning approaches. AlphaCode (Li et al. 2022 Leblond et al. 2023) tries to increase diversity by randomizing problem difficulty and tags. This method has limited scalability because it needs manual curation of attributes. It also works poorly beyond coding tasks. Increasing temperature settings offers another approach. This can generate outputs that appear different on the surface. Yet rarely produces solutions with fundamentally different reasoning strategies. For example, repeated sampling (Brown et al.] 2024) generated 100,000 solutions per problem using temperature 0.6. Their solutions all follow the same basic approach. They start with problem conditions and work forward to deduce answers step-by-step. Humans, however, can use multiple reasoning strategies. One alternative approach is to propose a hypothesis first and then verify this hypothesis within the problem context. Current methods do not capture this diversity of thinking patterns.
Work was done during the internship in Qwen Team. 'Thii results available

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Similarly, encouraging LLMs explore diverse high-level thinking patterns leads more varied solutions. Human cogmitive research (Halpem] 2014: Bronkhorst et al. (0200 reveals multiple problem-solving approaches beyond deduction, including inductive (Flach and Kakas 2000), abduc- tive (Douven 2011), and analogical reasoning (Bartha 2013). These non-deductive strategies offer different directions through the solution space, often leading more effective results. For example, abductive reasoning-propprle proposing hypotheses and verifying them-is more suitable in multiple-choice scenarios. Humans demonstrate remarkable flexibility by switching from deductive abductive reasoning when a free-response problem is reformatted with answer choices, despite unchanged problem content. This adaptive behavior shows how humans intuitively select optimal reasoning strategies for each problem format.
To examine how reasoning types affect L.L performance, we explicitly directed LLMS to apply specific reasoning strategies to problems. For each problem, the model is asked to follow a specific reasoning type and generate multiple solutions. We considered problem "solvable" by reasoning type if at least one of these solutions is correct. We calculate the percentage of problems solvable exclusively by one particular reasoning type. These represent cases where lacking the right reasoning approach makes problems nearly impossible to solve. We tested Mistral 7B instruct (Jiang et al. 2023 across four benchmarks: LogiQA (Liu et al. 2023a), BBH (Suzgun et al. 2022). GSM8k (Cobbe al., 2021), and MATH (Hendrycks et al. (021). Results in Figure [ reveal that each reasoning type uniquely solves certain problems that other approaches cannot. This demonstrates that incorporating diverse reasoning strategies effectively expands the range of solvable problems. More detailed
analysis is put in Section 4.2
However, incorporating reasoning types into LLM problem-solving faces two major chal- lenges. First, identifying the right reason- ing type is difficult. Figure [ shows that in- correct reasoning types mislead L.LMs with wrong thinking directions. Second, ensuring the model follows the chosen reasoning type during problem-solving is crucial. Therefore, we propose TypedThinge nnke to address these challenges. It predicts suitable reasoning types based on previous successful experiences and uses explicit demonstrations to help LLMs effec- tively apply them. TypedThi h nker consists of three key components: the LLM reasoner, the meta-thinker and demonstration collection.
15.0%
Percentage
10.0%
Deductive
Inductive
Analogical
5.0%
Abductive
0.0%
LogQA
BBH
GSMBK
MATH
Figure I: The percentage of problems solvable exclu- sively by one reasoning type.
The meta-thinker is fine-tuned on empirical effectiveness scores of each reasoning type from the training set. We use rejection sampling to collect successful solutions for each type demon- strations, which enhance LLMs' ability to exploit specific reasoning strategies. During inference, TypedThinker uses the meta-thinker to identify the most suitable reasoning type and retrieves relevant demonstrations to guide the LLM reasoner applying this approach to solve the problem.
Experimental results show that TypedThing nker improves Mistral 7B instruct by 3.4%, I.LMA3 8B instruct (Touvron et al. (202)) by 6.5%, and Qwen 2 7B by 7% on two logical benchmarks and two mathematics benchmarks. We further demonstrate that SyppeThinnke can directly be applied to the benchmark Contexthub (Hua et al.) (2024) and outperforms other baselines. Moreover, we show that the meta-thinker can be adapted in much larger LLMs such GPT-40 domain-specifie LLMs such as MetaMath (Yu et al. 2023) and enhance their reasoning.
RELATED WORK
Logical Reasoning Logical reasoning includes various methods to emulate human-like thought processes (Wason and Johnson-Laird 1972 Dowden 2018 Nunes 2012). Deductive reasoning focuses on deriving specific conclusions from general principles or premises, ensuring that conclusions logically follow if the premises true (Johnson-Laird 2010). In contrast, inductive reasoning involves generalizing from specific instances to broader principles, often used to identify patterns and make predictions based empirical data (Flach and Kakas 2000). Abductive reasoning, considered
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more creative and open-ended, involves forming hypotheses to explain observations, often generating the most plausible explanation rather than a guaranteed conclusion (Douven 2011). Analogical reasoning is concerned with the comparison between two more objects and drawing a conclusion based on the similarity (Barthal 2013). Previous LLMs studies on logical reasoning mainly focus on benchmarking its performance in different reasoning types (Bang al. 2023 Dougrez-Lewis et al. 2024, [uo et al.) 20233] Yu et al. (2024) or applying one reasoning type to solve the corresponding reasoning problems. such as using inductive reasoning for inductive reasoning problems (Wang et al. 2023a Shao et al., 2024; Yang et al., 2024). Instead, this paper mainly focuses on the selection and application of the appropriate reasoning type when solving a general logic or math problem.
Reasoning in Large Language Models Plenty of studies have been done to enhance the reasoning capability of L.MMs. Chain-of-thoughts methods focus on creating better instructions to improve the quality of the reasoning process, such as Complex CoT (Fu et al., 2023), Tree of Thought (ToT) ( Yao al. 2023) and Graph of Thought (Besta et al., 2024). Refinement-based methods revise LLMS
solutions by the feedback from themselves or others model (Akyürek et al. 2023 Wang and Li
2023). Search-based methods use the reward model to search the best reasoning path (Lightman et al.
Liu et 2023b Hao et al., 2023). While most focus creating high-quality reasoning paths, the diversity of thinking attracted more attention recently. Studies have investigated the diversity brought by repeated sampling (Brown et al. 2024) or multi-agent discussion with different prompts (Du ct al. 2023] Liang et 20023 Suzgun and Kalai (024). Our paper aims to diversify thinking by incorporating suitable reasoning types for each instance.
Self-improvement and Sell-training in LLMs Recent works explore the self-improvement capability of LLMs, by finetuning LLMs on their high-quality generations (Wang al. 2023b Huang et al.)
2023 Toshniwal et al.
2024). This process can be extended to multiple iterations Gül Gülçehre et al.
(2023) ; Aksitov et al. Benefiting the LLMs' ability follow instructions, researchers also ask LLMs
to provide feedback themselves and improve their responses without finetuning (Peng et al., 2023
Shinn et al. 2023). This can be further enhanced by using their own feedback as the reward model to provide hetter signals for finetuning (Yuan et al.) 2024 Kumar et al.) (024). In this paper, we focus on stimulating their capabilities to conduct various reasoning types and use these experiences to diversify their thinking in reasoning type selection and following.
3 TYPEDTHINKER: DIVERSIFY THINKING WITH TYPED REASONING
In this paper, we focus on four logical reasoning types: deductive, inductive, abductive, and analogical reasoning defined in (Nunes) 2012). For each reasoning type, we provide a short definition and simple example to demonstrate the inference rules, which are listed in Table the Appendix. Based on that, we introduce a reasoning framework TypedThinke: to diversify LLMs' thinking with different reasoning types. As shown in Figure there are three components in TypedThinkez: the meta-thinken to select reasoning type, explicit collection for demonstration, and the LLM reasoner to exploit one particular reasoning type. TypedTh i nker optimizes the implicit policy of the meta-thinker and updates the explicit collection of demonstration based on previous experiences.
3.1 TYPING REASONING WITH IMPLICIT POLICY AND EXPLICIT DEMONSTRATION
Let D ((x1 (i),,,)),"" "..,.... (WN, } be set of N problems, where æ; and yi is the problem and the ground-truth answer of the i-th instance. We define a reasoning type space J that includes an empty type and four types of reasoning: deductive, inductive, abductive, and analogical. The goal is to model the selection and implementation of various reasoning types as implicit and explicit collection of demonstration, thus enhancing L.MMs' performance in reasoning tasks.
Meta-thinker for the reasoning type identification. Given problem x. the goal of the meta-thinker is to select appropriate set of reasoning types solve the problem. Specifically, it predicts an effectiveness score 8& E [0, 1] for each reasoning type fa E F. which can be represented as 8n,k (x, ft). 82,4 0 indicates that the problem can hardly be solved by the reasoning type fı with limited sampling times I Note that the effectiveness scores of different types independent of each other and their sums are not necessary to be 1. The most effective reasoning
type is defined as f*() arg maxf EF k. Meanwhile, we can obtain set of reasoning types
II this paper, we sample most 10 times for one problem.
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Explicit Collection of Demonstration Experience 1: (Problem 1, Deductive, Solution 1)
Inttaalze
Somple rensoning types
Experience N: (Problem N, Abductive, Solution N) Implicit Policy of Reasoning
Abductive Experience
incorrect trajectories Filter ineffective types
Problem
Deductive
Inductive
Abductive
Analogical
Abductive Reasoner
Finetune
Meta
Store
Rassorer
thinker
Reasoner
Empirical
Finetune
Score
Figure 2: TypedThinkes consists of three components: the meta-thinker to select the reasoning types, the explicit collection of demonstrations to re- trieve relevant experience, and the reasoner to conduct the specific reasoning. The meta-thinker fine-tuned predict an effective score E [0, 1] for each reasoning type.
Expicit Memory
Meto thinker
Figure 3: Learning the implicit policy and explicit memory by self-training.
with non-zero effective ratio, which we call the effective set: F(x) (fulsa,k > 0}. We initialize Ty with a pre-trained LLM. The prompt listed Appendix A.
Explicit collection of demonstration TypedThinker collects set of demonstration M Uner Mr for each type of reasoning. For each problem in the training set, we keep one cor- rect solution per reasoning type if applicable, resulting in a set of at most [D] x [J] solutions. multiple solutions exist for one problem, we keep the longest get more detailed context. The entry in the collection of demonstration MM& is represented as a tuple of (ar sol+). Here sol is the concrete reasoning process of the reasoning type Ss. including the predicted answer. During inference stage, given a new problem æ and its reasoning type fk. it retrieves set of relevant experience d = [(+ h solş) My L(x x) 8). L is the distance function measuring relevancy between two problems and 8 E [0, 1] is the relevancy threshold. We use the cosine similarity between the semantic embeddings as the distance function. The retrieved experiences are used as the few-shot examples of the reasoner.
Reasoner to perform the reasoning according the type. The reasoner applies the reasoning type Sa to the problem æ and provides a detailed reasoning path for its predicted answer ÿ. The reasoner based on L.M to conduct reasoning and the instruction is composed of (ær, fú. dd where the dl the retrieved relevant successful experience. The reasoner can be further optimized via instruction tuning to enhance the capability of conducting a specific type reasoning.
To conclude, TypedThinker r enhances LLMs' reasoning by estimating the effectiveness of each reasoning type and guiding the LLM reasoner with the demonstration of this reasoning type. Specifi- cally, the veta-thinker Ty predicts then retrieves the most relevant reasoning demonstration d² from the fixed explicit collection cor- responding the reasoning type St. Finally, the reasoners conduct the specific type of reasoning fa with the guidance of demonstration. In our experiments, we use two approaches to decide the reasoning types used in the gobblem-solvingg One is to greedily resample several times based on the most effective reasoning type f* and use self-consistency (Wang et al. 2022) to enhance the answer; the other is to sample solutions for all effective reasoning types F, and apply a weighted vote with the effective score as the coefficient. By default, we use the greedy approach for Tnkee,hinker, and we discuss the weighted vote Section 4.4
effective score Sę for each reasoning type. TypedThinken
3.2 OPTIMIZE IMPLICIT POLICY FOR REASONING TYPE SELECTION AND EXPLOITING
We optimize the meta-thinker Th and the reasoner while updating the explicit collection of demonstra- tion with the collected experience. The pipeline is demonstrated in Figure The green lines represent the parametric optimization process, while the blue line represents the parameere update.
Diversify Reasoning Experiences with Types To inspire LLMs' knowledge of solving problems with different reasoning types, the definition (Table g) and wrritlly-written few-shot examples with detailed reasoning paths (Table 16) used for prompting solutions for each reasoning type. For
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each problem in the training set, type. These solutions are then filtered by the correctness of the final answers. To guarantee that these solutions belong to their reasoning type, we apply reverse check on the remaining solutions. For the experience (æt, sol, y) of the reasoning type fk. we prompt the model to predict its reasoning type fs. If f = fr. we think this experience indicates the methodology of this reasoning type and keep it. Otherwise, will be removed. Finally, we collect an experience dataset with multiple types of reasoning. The experiences are grouped by their reasoning type and are stored in the explicit collection of demonstration M.
temperature of 1 to sample 10 solutions per reasoning
Optimize the Implicit policy of Meta-thinker and Reasoner Given problem æ. the meta-thinker
Te predicts a score sy.k to indicate how likely this reasoning type can solve this problem. This can be estimated by the experience in the training set. We assume that if one reasoning type is more effective in solving this problem, it will generate more correct solutions among the same sampling times. Therefore, given there n& successful experiences of the reasoning type fx among m samples, we define the empirical effectiveness score based on its success rate: Sa,k- = -i//m. This empirical effectiivnnes score calculated on the experience dataset D is then used for finetuning the meta theaerhinnkrr We reconstruct the tuple (xr, 32, into the instruction-followii 1. for supervised finetuning, Meanwhile, we finetune a reasoner with the experience to enhance its capability to conduct a specific type of reasoning.
pair via the prompt in Section
4
EXPERIMENTS
4.1 EXPERIMENT SETUP
We investigate two spen-source LLMs Mistral 7B instruct (hang et al.) 2023) and LLaMA3 8B instruct (Touvron et al. 2023) and Qwen 2-7B-Instruct (Bai et al. 2023) on two logical benchmarks (LogiQA, BBH) and two mathematics benchmarks (GSM&K and MATH). For each LLM,, we set up the following baselines: (i) Few-shot baseline with 3 in-context examples. We use the few-shot examples provided in Suzgun et al. (022)) for BBH, and text-based few-shot examples in Toshniwal et al. (2024) for GSM8K and MATH since we do not consider the code interpreter in this paper. We also manually write few-shot examples for LogiQA, (ii) CoT Selection: Select the best reasoning type by prompting. We let the LLM identify the best reasoning type and then apply the selected type to the problem. (iii) Self-Discover (Zhou et al.) 2024) generates a task-level reasoning structure by prompting L.MSs select relevant modules from a list of seed modules and adapt the selected module to task-specific descriptions. We follow their official implementation F1 and use the backbone LLMs to generate one reasoning structure from an exemplar training instance of each task. This reasoning structure is then applied to all instances in this task. (iv) Zero-shot Mixture of Reasoning (MoR): apply all possible reasoning types and use the majority vote to get the final answer 3 The LLM is instructed with the definition and demonstration in T (v) Few-shot MoR: Similar to the zero-shot MoR except for each reasoning type, 3 few-shot examples are provided in the prompt. (vi) TypedThinker: use the most effective reasoning type f*. The +SC baselines indicate the majority vote over responses.
The temperature is set to 0.7 for all baselines suggested by Wang et al. (2022). The maximum output length is set to 1000 tokens. We use CentenceTransfoon to retrieve top-3 similar experiences and the threshold is set to ó 0.5. We use accuracy as the measurement of task performance. The model response is compared with the ground truth based on the exact match for logic problems. The script in Toohniwal et al. (2024) calculates the mathematical equivalent of mathematics benchmarks. The training details are put in Appendix A.3
Reimers and Gurevych, 2019)
4.2 HOw DO REASONING TYPES ENCOURAGE DIVERGENT THINKING DURING GENERATION?
We first investigate the role of reasoning types in LLMs' self-training. We group problems of the collected experience dataset D) based on their empirical effective set F(x)) = {sx &r.kk > 0). and the empirical effectiveness score is defined in Section 3.2 The problems in the same group can be solved
"For answers with the same votes, we choose the first one in alphahetical order. https://wwwsbbrtt.m
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with the same set of reasoning types. We focus on the effective set with only one reasoning type and count the size of these groups. The size indicates how many problems that can only be solved by one specific reasoning type. showing the advantage of including this reasoning type. We illustrate their percentage on the whole dataset in Figure[] We find that even if we use temperature = 1 to sample 10 times diversify the solutions, lot of problems still have only one effective reasoning type. It indicates that given an inappropriate reasoning type, the diversity brought by repeated sampling with a high temperature cannot help the LLM solve this problem.
Meanwhile, although these reasoning types have similar performance on the whole dataset (shown in Table 6 in Appendix), the problems they can solve do not completely overlap. None of the percentages of the reasoning type is zero, indicating that for each reasoning type, there is a unique set of problems that can only solved by it. It indicates that these reasoning types have their advantages over different problems, highlighting the importance of considering the appropriate reasoning types during poblemmsslvving
We further compare the diversity of the solutions before and after adding the reasoning types in Table of Appendix A.44 We can find that introducing different reasoning types can bring more diversity to the solution set than repeated sampling with a high temperature.
Table I: TypedTh h whhiinn inker achieves the best performance in both single response and the majority vote setting on two logical benchmarks and two math benchmarks. @5 indicates the result is based on the majority vote over 5 responses. +SC indicates the self-consse self-consistency method. MoR indicates the Mixture of Reasoning, which employs all reasoning types (including an empty type) and votes for the final output. Avg. indicates the average accuracy over four benchmarks. Owen's results are put in Table 11
Mistral 7B
LLaMA3 8B
LogiQA
BBH
GSM8K
MATH
Avg.
LogiQA
BBH
GSM8K
MATH
Avg.
Few-shot
0.485
0.346
0.369
0.074
0.318
0.581
0.359
0.581
0.193
0.428
+ SC @5
0.532
0.441
0.444
0.136
0.388
0.579
0.391
0.769
0,250
0.497
COT Selection
0.474
0.361
0.372
0.095
0.325
0.564
0.392
0.556
0.181
0.423
+ SC @5
0.503
0.429
0.466
0.132
0.382
0,562
0.426
0.785
0.222
0.499
Self-Discover
0.386
0.340
0.141
0.056
0.231
0.493
0.425
0.587
0.200
0.426
SC @ 5
0.476
0.391
0.208
0.082
0.289
0.540
0.543
0.701
0.278
0.516
Zero-shot MoR @S
0.528
0.414
0.313
0.108
0.341
0.556
0.463
0.666
0.189
0.468
Few-shot MoR @5
0.509
0.456
0.460
0.127
0.388
0.599
0.543
0.585
0.195
0.481
TypedThinker + +SC @5
0.554
0.423
0.386
0.092
0.364
0.599
0.543
0.585
0.195
0.481
0.570
0.469
0.500
0.149
0.422
0.637
0.591
0.753
0.267
0.562
4.3
WHAT KINDS OF BENEFITS CAN TYPEDTHINKER BRING?
As see in Table T our TypedThinker achieves the best performance among baselines. The improvement is more obvious in LLaMA3 8B, which is more powerful than Mistral 7B. It shows that L.MMs with better capability in reasoning and instruction-follwiii the self-training of inkke.. Additionally, there are several key insights from the detailed comparison with different baselines.
can benefit more from
Appropriate reasoning types improve the reasoning performance. The main difference between Fewshot and CoT Selection without the majority vote is the reasoning type selection. For CoT Selection, the model is first prompted to predict a reasoning type and then apply it, while the Fewshot baseline directly solves the problem. However, we find that the CoT Selection struggles with the reasoning type selection. Given the option to choose from four reasoning types or none, it chooses none over 60% of the time. The rest of the time, it selects more than 50% deductive, while only 34% of them can be effectively solved by deductive reasoning during the sampling. The mismatch in reasoning types results in poor performance. Facilitating with a trained meta- thinker, TypedThing TrpedThinkkss is more accurate in selecting the reasoning type, which helps it improve performance under the single response setting. Deff--Disooee, which uses a shared reasoning structure for all instances of the task, performs poorly, especially for the weaker model Mistral 7B. This may be due to the difficulty these models face in identifying reusable shared high-level reasoning structure for diverse instances, especially in datasets like LogiQA, where reasoning structures are highly varied.

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Precise prediction is more effective than an inappropriate mixture. The zero-shot MoR and few-shot MoR apply all types of reasoning to the given problem and use a majority vote to get the final answer. Compared with the other two majority vote baselines Few-shot SC @5 and CoT Selection + SC @5, these methods fall behind on several benchmarks, especially on MATH. We find that the performance drop typically happens when there are only one or reasoning types that are effective for this problem. In such cases, the majority of incorrect answers dominate, resulting in fewer votes for the correct one. As we can see in Figure I plenty of problems on the MATH benchmark can only be solved by inductive reasoning, In such cases, if the CoT Selection correctly predicts the inductive reasoning for them, the CoT Selection SC @5 can benefit from the majority vote and have better performance. This highlights the importance of predicting the effectiveness of reasoning types before aggregating them.
Experience of how to conduct specific type of reasoning is important. The performance difference between zero-shot and few-shot MoR illustrates the impact of the reasoning demonstration. When prompted solely with the definition, LLMs struggle to understand how to apply the reasoning type to specific problems.
can be improved by human-written few-shot examples in few-shot MoR. However, it still falls behind the non-parametric retrieval and the parametric reasoner in TypedThinkex. both of which enhance the capability of conducting a specific reasoning type. Additionally, poor performance in Self-Discover also indicates that, without demonstration, the complex reasoning structures will introduce excessive complexity, confusing the models.
Table 2: Ahlation Study on the Mistral 7B based Thped rker's components. We remove one component each time. The results are based on the best reasoning type and calculated for the single response per query. The negative scores indicate the performance drop, and the largest scores shown in bold.
LogiQA
BBH
GSM8K
MATH
TypedThinker
0.554
0.423
0.386
0.092
w/o Finetuned Reasoner
-0.076
-0.041
-0.102
-0.018
w/o Meta-thinker
-0.025
-0.036
-0.152
-0.024
w/o Memory
-0.082
-0.051
-0.033
0.013
4.4 WHAT CONTRIBUTES TO TYPEDTHTNKES EFFECTIVENESS?
We conduct several investigations to enhance the understanding of our proposed method.
Ablation study The ablation studies are conducted on three key components in TypedThinker Each time one component is removed. It includes (i) w/o Fine-tuned Reasoner: it is replaced with the base LLM (ii) w/o Meta-thinker: it is replaced with a CoT selection (iii) w/o collection of demonstration: the explicit collection is replaced with the human-written few-shot examples of each reasoning type. In Table 2 we can find the meta-thinker is the most important module for the math benchmarks, while the explicit collection is more effective two logical benchmarks. The fine- tuned reasoner also contributes a lot to the performance improvement. We also observe that explicit collection does not always bring benefits: the performance on MATH even increases when remove it. We find that the retrieved examples usually have similar context but different numbers. The math calculation in the retrieved with the observations of Toshniwal et al. (2024) that the solutions with masked computations are more beneficial to the math problems. For logical problems, there are fewer calculations and the retrieved solutions focus more on the reasoning process.
solutions will mislead the reasoner. This is consistent
predictions achieve high correlation with the empirical effectiveness score. We evaluate the performance of the meta-thinker by the correlation between the predicted effectiveness score and the empirical one (which we view as the ground truth). We split the collected experience dataset D by problems and use 0.9 of them to train the meta-thinker and 0.1 for testing. We use Kendall's т coefficient to evaluate the correlation. It measures rank correlation, essentially assessing the similarity of orderings when data is ranked. A higher Kendall's coefficient indicates that when the ground truth assigns a high effectiveness score to a reasoning type, the meta-thinker also ranks high, thereby validating the reliability of the predicted scores. We compare the performance under three settings: the meta-thinker trained only on the logical domain, only in the math domain, and jointly trained the unified domains (including both logic and math data). The meta-thinker trained
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0.40
0.80
Kendall's coefficient
0.35
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Accuracy
0.40
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Deductive
Inductive
Analogical
Abductive
LogiQ4
BBH
GSMBK
MATH
Logic Domain
Math Domain
Unifled Domains
s Logic Domain
s Math Domain
Unified Domains
Figure 4: Kendall's coefficient between the predic- tion confidence score with the ground truth. All results have the p-value < 0.05. The unified policy shows the best correlation on all reasoning types.
Figure 5: Task performance of SypedTh inker with meta-thinkers trained on different domains. The uni- fied one performs best in most except the MATH benchmark. where the pure math setting dominates.
on the unified domain achieves the highest correlation. This suggests that training on dataset with multiple domains enhances the meta-thinker's ability to accurately rank and predict suitable reasoning types. thereby improving its overall performance. We also calculate the accuracy between the predicted optimal reasoning type and the empirical one for the unified setting. The average accuracy on four benchmarks is 68.3% (LogiQA 75.4%, BBH 75.6%, GSM8k 72. %, and MATH 47.7%). Note that the meta-thinker can predict an incorrect optimal reasoning type fa while still generating a correct solution. It is because the predicted reasoning type can belong to the effective set F {fx s 0}, indicating the reasoning type also help solve the problem.
Unified meta-thinken perform well in most cases. We further investigate the effectiveness of these policies by facilitating TypedThinker with these meta meeta-hhinkers. The results are based on the Mistral 7B TypedTh nker without SC. The results in Figure 3 that the unified meta-thinker has the best performance in most cases. However, in the more difficult MATH dataset, the specific meta-thinker trained the math domain can help it be more powerful. To conclude, the unified meta-thinker has reasonable performance in all its domains, while for difficult problems it may slightly underperform the specific meta-thinker trained in this domain.
Table 3: TypedThinkez's performance with the most ef- fective reasoning type f" v.s. weighted votes the effective sct F.
Table 4: TypedThinkk inner performs best on the unseen benchmark Contexthub, Here the results are based the majority vote over responses (+SC @5).
LogicQA BBH GSM8K
Math Average
Mistral 7B LLaMA3 8B
Mistral 7B
Few-shot
0,419
0.378
SC @5 on f weighted on F
0.570
0.469
0.500
0.149
0.422
CoT Selection
0.415
0.390
0.581
0.453
0.501
0.127
0.416
Zero-shot MoR
0.415
0.403
LLaMA3 8B
Few-shot MoR
0.432
0,390
Self-Discovar
0.332
0.365
SC @5 on f 0.637
0.591
0.753
0.267
0.562
weighted on F 0.619
0.587
0.738
0.245
0.547
TypedThinker
0.452
0.423
Optimal reasoning type v.s. weighted vote the effective set In the main experiment, we the optimal reasoning type f which has the highest effectiveness score for reasoning. As discussed in Section 3.1 we can also use majority vote on the effective set F' with the effectiveness score as the coefficient. Specifically, if one solution is based on reasoning type with a higher effectiveness score, its vote gets a larger weight. The results are shown in Table We can see that the weighted vote can balance different reasoning types on LogiQA and GSM8K for the Mistral-7B-hant BB-aeeed model. However, on the other two benchmarks, the TypedThinkes nkerr SC @5 has a better performance. It indicates that accurate selection is more important if one or two reasoning types dominate the benchmark. For example, as we have shown in Figure there are a lot of problems that can only be solved by inductive reasoning, indicating the other types will mislead the final answer. In such cases, the cenf-consis of inductive reasoning is more powerful than the weighted vote. However, when we have more accurate meta-thinker that can identify the correct reasoning type and more
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powerful reasoner that can follow the specific reasoning type, for example, models initialized by LLaMA3, the advantage of TypedThinker + SC more obvious.
4.5 CAN TYPED BE APPLIED TO NEW DOMAINS OR NEW LLMs WITHOUT FINETUNING?
is essential evaluate the generalization capability of TypedThinker: We assess from two aspects: (i) "ypedThinken 's performance new domains; and (ii) other LLMs' performance after facilitated with our finetuned meta-thinker and the explicit collection of demonstration.
TypedThinken inke generalizes well to the unseen domain. We use new propositional logic benchmark Contexthub (Hua et al., 2024) for evaluation. is a recently released dataset, which has never been seen by Mistral and LLaMA3 models during the pre-training. It contains problems from 12 categories with levels of difficulty. We select the difficulty of level 4 to test the complex logic reasoning capabilities. We use the experiences collected from LogiQA the explicit collection of demonstration. The meta-thinker and the reasoner are fine-tuned on four training benchmarks. The results in Table 4 show that TypedThi niker outperforms other baselines this unseen domain as well, indicating that it can generalize well to new domains. One interesting thing is Mistral 7B baselines significantly outperform LLaMA3 8B on this benchmark and its superior capabilities make it benefit more from our TypedThinker.
Facilitating LLMs with TypedThinker makes them more powerful. Our TypedThinken framework is orthogonal to the backbone LLMs and can be adapted to new LLMs. There are two ways to use a new LLM in the TypedThinker framework: one is conduct the self-training process, like the two LLMs used in our main experiments (Mistral 7B and LLaMA3 8B); the other is use our fine-tuned meta-thinker for reasoning type selection and the explicit collection of demonstration for retrieval while using the new LLM as the reasoner without finetuning. The first way can make the LLM more powerful (as shown in the performance comparison between TypedThinker and TypedThinker w/o Finetuned Reasoner in Table 2). but the latter one is more flexible. Here we use the second way to evaluate the direct transferability to new LLMs. We choose one of the most powerful LLMs GPT-4o and one math-specific 7B model MetaMath (Yu et al. 2023). MetaMath is Mistral-7B-basee data distilled from GPT-3.5-Turbo. We randomly sample 100 examples from each benchmark for GPT-4o. For MetaMath, we use the whole test set. The results are shown in Table and Table 6 Compared with Mistral 7B in Table [ the high-quality and large scale of synthesized data from GPT-3.5-Turbo enhances MetaMath's capabilities in math problems. TypedThinker can further improve its performance by reasoning type selection and explicit collection. Meanwhile, although the superior performance of GPT-4o on two math datasets leaves little space for improvement, the results on logic benchmarks (LogiQA and BBH) demonstrate that the meta-thinker trained with the small 7B model also enhances its performance. These findings confirm that our approach is not only effective in improving smaller LLMs but also transferable to larger models, further validating the generalization capability of TypedThinker.
model trained with more than 400k synthesized math
Table GPT-4o's performance is improved with our meta- reasoner. use the finetuned Mistral 7B meta-thinker to predict the reasoning type.
Table TypedThinker can also en- hance the performance the math-specific 7B model such as MetaMath.
LogiQA
BBH
GSMSk
MATH
GSM8K MATH
GPT-4o
0.76
0.84
0.97
0.89
MetaMath
0.690
0.209
SC
0.80
0.85
0.98
0.90
SC @
0.704
0.220
TypedThinker
0.80
0.86
0.95
0.88
TypedThinker
0.696
0.220
SC @5
0.81
0.90
0.96
0.91
SC @
0.736
0.246
4.6 CASE STUDY
Here is example of TypedThinker the LogiQA benchmark in Table 7 This problem states phenomenon that a higher altitude leads to a lower atmospheric pressure. Based on this observation, it is easy for humans to inductive reasoning and get general conclusion about the

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inverse cause-and-effect relationship. It also natural for humans to use analogical reasoning and find the most similar options. The meta-thinker gives the highest effectiveness score for inductive reasoning, which is then chosen as the optimal reasoning type f inductive. Effectiveness scores are all larger than O, so the effective set is all reasoning types. The reasoner gets the correct answer for deductive and inductive reasoning while doing wrong on the other reasoning types. If we use the majority vote over five answers, (A) and (C) will have the same votes, indicating that there is 50% chance to be correct [ However, with the effectiveness score predicted by the meta-thinker, SpedThinkes can get the correct answer either by applying the optimal reasoning type or using the weighted vote on the four answers. Besides, without a specific reasoning type (which 'Empty') ), the model cannot arrive at the correct answer. This shows the limitation of the common few-shot baselines. It shows that TypedThi inker improves the reasoning performance by the introduction of diverse reasoning types and the capability of selecting the appropriate type to apply.
Table 7: One example from LogiQA. The correct answer and the reasoning type with the highest effectiveness score are underlined. MoR is the few-shot MoR baselines, which use the majority votes among reasoning types.
Problem
The higher the altitude, the smaller the atmospheric pressure. Because the altitude of Place A is higher than that of Place B, the atmospheric pressure of Place A is lower than that of Place B. Which of the following examples shows the same pattern of reasoning?
(A) In a highly competitive market, the better the product quality and the more advertising investment, the greater the product sales. Company A invests more money in advertising than Company B. So Company A sells more products than Company B.
(B) The older person is, the more mature he becomes. Person A older than his son, so Person B is more mature than his son.
(C) The older a tree is, the more rings it has. The age of the locust tree in A's yard is older than that of B's family, so the locust tree of A 's family has more rings than B s.s.
(D) The greater the vocabulary of language, the more difficult is learn. English harder to learn than Italian, so English has a larger vocabulary than Italian.
Ground Truth
(C)
Predicted scores
Deductive: 0.4; Inductive: 0.5; Analogical: 0.4; Ahductive: 0.4; Empty: 0.4
and their answers
Deductive: (C); Inductive: (C); Analogical:(A); Abductive: NULL; Empty: (A)
Model Output
MoR: (A); TypedThinker with I (C); TypedThinker with F: (C)
CONCLUSION AND LIMITATION
We investigate how reasoning types diversify LLMs' thinking and propose TypedThinker to inspired by human
incorporate different reasoning types into problem-solving. TypedThinker cognition processes during reasoning: it learns implicit policy to select the appropriate reasoning types with the meta thinkeh and to apply the selected type of reasoning with the reasoner. It also maintains an explicit memory retrieve experiences to aid reasoning. The results show that TypedThi nike r enhances the reasoning capabilities of Mistral 7B, L.LMMA3 8B and Qwen 2 7B on four benchmarks. Furthermore. TypedThinkez shows good generalization capabilities in new domains and models.
Despite the promising results, TypedThinker has several limitations that need further investigation. Firstly, one problem may require different reasoning types at different steps, and applying one sole reasoning type can hardly find correct solution. In that case, dividing the problems into multiple reasoning steps, and applying TypedThinkez for each step could make the reasoning more diverse and effective. Additionally, this paper mainly focuses on logical and mathematical benchmarks. Expanding to broader range of tasks, such as code generation and creative problem-solving could deepen the understanding of the role of reasoning types in various problems and provide a more comprehensive assessment of TypedThinker's capabilities.
'In our implementation, answers with the same votes are ranked based on their alphabetical order, (A) will be chosen in this case.
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A
APPENDIX
A.1 PROMPT
We introduce the simple and practical definition of four reasoning types in Table 8 Table 16 lists the few-shot examples of each reasoning type. The full few-shot examples can be found in the supplementary materials. We use the same few-shot examples for the logical problems and create another set of examples for the mathematics problems.
Table 8: Description of different reasoning types. We give informal definitions that easy follow and illustrate simple examples for each reasoning type.
Type
Definition
Example
Deduction
Deduce conclusion based on the gen- eral rules and premise.
From the premises 'all frogs are amphibians and 'no cats are amphibians', we can infer the conclu- sion 'no cats frogs'
Induction
Make broad generalizations from spe- cific observations.
Starting from the empirical observation that 'all ravens have seen far are black', inductive rea- soning can be used to infer that 'all ravens are black'
Abduction
Assume one candidate is correct and check whether it meets the condition in the problem.
Guess that it has rained to explain that the streets are wet. A tsunami could also explain why the streets are wet but this is usually not the best planation.
Analogy
Retrieve several relevant information and draw conclusion of this problem baxed on the similarity.
Infer information about humans from medical periments on animals: (I) rats are similar mans; (2) birth control pills affect the brain devel- opment of rats; (3) therefore they may also affect the brain development of humans.
The prompt used by the meta-thinker is:
Given the question below, please identify the type of reasoning required to provide a solution. You may choose the following reasoning types: Deductive, Inductive, None. None indicates that no specific reason-
Analogical, Abductive Reasoning, ing type is needed for this problem. Please assign an effectiveness score for each reasoning type from 0 to I, where O represents no effective and represents full effective. Please return the reasoning types and their corresponding effectiveness scores in the JSON format.
For instance, if you think the question can be solved using both deductive and inductive reasoning, with effectiveness of 0.5 for deductive reasoning and 0.3 for inductive reasoning, you should return: (["ReasoningType" "Deductive", "Effectiveness": "eel""""RRnnggTyii
"Inductive", "Effectiveness": 0.3), coningTypet "Analogical", "Effectiveness": 0),[ "..["eesonningTppe "Abductive", "Effeectivensss: 0}, CrrasonninTType" "None". "Elfeectivenss"" 0]].
The prompt used by the reasoner listed below. The definition based on Table g
Use [fx] reasoning to solve the given question. [fk]] reasoning is [definition.
A.2 DATASET
A.2.1
DATA PROCESSING
The dataset statistics of the four benchmarks detailed in Table 9 For multiple-choice questions, we calculate accuracy using the exact match criterion. For mathematics problems, we compare the model's 's response with the ground truth using mathematical equality.
LogiQA (Liu et al. 2021, 2023a) is a multi-choice understanding benchmark for logical reasoning. follows the definition of Delanccy (2017) and categorizes the problems into categorical reasoning,
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Table 9: Logical benchmarks and mathematic benchmarks used in this paper. We follow the standard train/test split on LogiQA and follow split in Toshniwal et al. (2024) for GSM8K and MATH. BBH. we randomly split the dataset. The synthesized data described in Section 3.1 BBH includes 16 tasks while MATH includes math problems of categories. Policy indicates the data used to train the meta-reasoner and SFT indicates the instruction-follont in reasoner finetuning.
Benchmark
Empirical Dataset
Task
Train
Val
Test
Total
# Meta-thinker
Reasoner
LogiQA
3757
500
511
4768
-2k
-6k
BBH
16
1904
320
1600
3824
lk
~3.5k
GSM8K
1
6473
1000
1319
8792
-4k
-4k
Math
7
6500
1000
5000
12500
-1k
1kk
sufficient conditional reasoning. necessary conditional reasoning, disjunctive reasoning, and conjunc- tive reasoning. These reasoning categories not orthogonal and one problem can belong to multiple categories. We follow the standard 3 reasoning categories. This makes the problem more diverse and difficult to solve. We take the validation set as the test set and randomly select 500 examples from the training set for validation.
split and only keep examples with more than
BBH (Suzgun et al. 2022) is set of hard problems borrowed from Big Bench (Srivastava al. 2022). They are also formatted as multi-choice problems. We pick the English tasks with more than 2 options, resulting in 16 tasks: date understanding disambiguation qa, geometric shapes, hyperbaton, logical deduction three, logical deduction five, logical deduction seven, movie recommendation, penguins in a table, reasoning color, ruin names, snarks, temporal sequences, tracking shuffled three, tracking shuffled five, and tracking shuffled seven. For each task, we randomly select 100 examples as the test set and 20 examples as the validation. The rest are used training examples.
GSM8k (Cobbe et al. 2021 is commonly used math benchmark to evaluate LLMs' capability in math reasoning. contains 8.5K grade school math word problems, which are split into 7.5k training examples and 1k test problems. Each problem usually takes between 2 and 8 steps to solve. MATH (Hendrycks et al. (02T) is also a popular math benchmark for LLMs. contains 12,500 challenging competition mathematics problems with 7 categories. There are 7.5k training examples and 5k test problems. We follow Toshniwal et al. (2024) to process the dataset.
Contexthub (Hua et al. 2024) is new propositional logic benchmark. It contains abstract and contextualized logical problems from 12 categories with 4 levels difficulty (Zhu et al. 2024). We follow the standard split of the original paper and the subset of difficult level 4 to test the complex logic reasoning capabilities. The abstract logical problems only contain the symbolic variable without natural language description, which be viewed symbolic reasoning problems.
Livebench (White et al. 2024) a recently proposed benchmark with 18 diverse tasks across categories, specifically designed to minimize data contamination. All problems have verifiable, objective ground-truth answers, allowing hard questions to be scored accurately and automatically. We evaluate our models on three tasks (spatial, web of lies v2, zebra puzzle) from the reasoning category, splitting them 0.7/0.3 for training and testing.
A.2.2 DATASET EXAMPLES
We demonstrate example for each dataset below.
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LogiQA
One seminar had 18 participants. It known that :hat::(1) At least young teachers female; (2) At least female teachers are over middle age: (3) least young women are teachers; According to above information, which can be concluded?
Options:
(A) Some young teachers not women
(B) Some young women are not teachers
(C) There are at least 11 young teachers
(D) There are at least 13 female teachers
BBH: logical deduction three objects
following paragraphs each descrihe set of three objects arranged fixed order. The statements are logically consistent within each paragraph. In golf tournament, there were three golfers: Ada, Mel, and Mya. Mya finished helow Ada. Mel finished ahove Ada. Options:
(A) Ada finished
(B) Mel finished last
(C) Mya finished last
GSM8K
meters rope was cut into parts the ratio of 2:3. How long is the shorter part?
MATH: Algebra Level 1
361 + ((1 + 36 = x. Solve for æ.
ContextHub: Abstract Level 2
(wgeq or mnze) - (NOT ttjmx) + kottz.
(kottz or zkx) pofk.
Given pofk is False, what is the value of ttjmx?
LiveBench: reasoning zebra puzzle
There are 3 people standing in a line numbered through 3 in left-to-right order. Each person has set of attributes: Nationality, Music-Genre, Transport. The attributes have the following possible values:
Nationality: spanish, argentine, canadian
Music Genre: punk, rock, reggae
Transport: train, jet-ski, trike and exactly person in the line has given value for attribute.
Given the following premises about line of people:
the person who is argentine avoids getting on train
the person who is spanish is somewhere between the person who listens to punk and the person who
listens rock
person who listens to punk not anywhere to right the person that travels by trike the person who listens to punk is on the immediate right of the person that travels by jet-ski
Answer the following question:
What the nationality of the person who listens rock? Return your single word, in the
following format: *8*x*** where X the answer.
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A.3 TRAINING DETAILS
For self-training of TypedThinker, we use the splits in the original papers for LogiQA and follow the split of Toshniwal al. (2024) for GSM8K and MATH. For BBH, we utilize 16 English multiple-choice tasks and randomly select 100 examples per task as the test set, with 20 examples as the hold-out validation set. The detailed statistics are listed in Table 9 Finally, the curated generation dataset covers 67 67.2% problems on the LogiQA benchmark, 69.7% on BBH, 74.88% on GSM8K, and 36.27% on MATH. We finetune a unified meta-thinker for both math and logical problems, and unified reasoner for all reasoning types. We use Huggingface (Wolf et al. (019) with deepspeed (Rasley et al. 2020). The finetuning is conducted on A6000 GPUs. The batch size is 64 and the learning rate is le- 5. The maximum epoch is 3 for the meta-thinker and for the reasoner.
A.4 ANALYSIS OF TYPED REASONING
Accuracy of Typed Reasoning We calculate the accuracy for each reasoning type on our empirical dataset D, shown in Figure 6 We find that on LogiQA and MATH, the accuracy of different reasoning types is similar. However, deductive and analogical reasoning outperform the other two on BBH while inductive and abductive reasoning are more effective. The results illustrate that after our carefully designed demonstration for each reasoning type, LLM's capabilities other reasoning types achieve comparable performance with deductive reasoning. This ensures the quality and the balance of our collected dataset each reasoning type.
Comparing Figure and Figure we can see that correctly selected, the specific reasoning type can enhance the model performance by handling problems that cannot be solved by other reasoning types, such as inductive on MATH. However, the unsuitable reasoning type can also mislead the model, leading to poor performance.
Deductive
Inductive
Analogical
Abductive
0.60
0.50
0.40
0.30
0.20
0.10
0.00
LogiQA
BBH
GSMBk
MATH
Figure 6: Accuracy of the solutions different reasoning types. It indicates that the effectiveness of reasoning types varies in different problems.
Diversity of Typed Reasoning To further verify whether the reasoning types can make the solutions more diverse, compare the diversity between solutions under different sampling settings in Table
10 We use Levenshtein Distance (Levenshtein 1966) and the n-gram overlaps between sentences evaluate diversity. Specifically, for K generations G {g),". .... 9gK } of the same problem, calculate the distance between each pair and normalize them with the sentence length. Then the average distance over these paired results is used as the distance of these K generations. If denote
the normalized Levenshtein Distance function as fia, this process can be represented as:
K
fiaGG) K(K -
2
Σ
Σ
fill..9)).
(1)
The calculation of the n- n-gram overlap is defined in the same way. For each setting, present the average score over the problems in the test set Table IO A larger Levenshtein distance and a smaller overlap indicate more diverse solution set. The zero-shot setting does not include examples
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in the prompt, and the zero-shot setting types only include the definition of the reasoning type (as listed in Table 8). The fho-shot setting has 5 examples, and the few-shot setting with types has repeated sampling with
different examples for each type. For zero-shot / few-shot @5, temperature for 5 times. For zero-shot/ / few-shot + types, we sample one solution per reasoning
type.
From Table 10 we can see that after adding the reasoning types, the diversity of both zero-shot and few-shot increases significantly. It indicates that the introduction of various reasoning types can make the LLM's reasoning more diverse. We can also find that in most cases, the few-shot with reasoning types has the highest diversity, while in BBH, the zero-shot setting can benefit more from the reasoning types.
Table 10: Adding reasoning types can enhance diversity in both zero-shot and few-shot sampling settings. It significantly increase the distance and reduce the n-gram overlaps between generations. For cach setting, we use Mistral 7B to sample 5 solutions with temperature = 1. @5 indicates repeated sampling times, types indicates sampling one solution per reasoning type. The diversity is averaged over the whole test set.
Benchmark Sampling Setting
Levenshtein Distance Unigram overlap 1 4 g-gaam overlap L
Zero-shot
0.304
0.588
0.537
Zero-shot + types
0.600
0.258
0.186
LogiQA
Few-shot @ 5
0,573
0.232
0.123
Few-shot types
0.644
0.175
0.077
Zero-shot @
0.517
0.310
0.216
Zero-shot types
0.712
0.128
0.050
BBH
Few-shot @ 5
0,599
0.224
0.119
Few-shot + types
0.650
0.175
0.076
Zero-shot
0.624
0.195
0.091
Zero-shot types
0,683
0.151
0.054
GSM8k
Few-shot @ 5
0.498
0.312
0.176
Few-shot types
0.710
0.137
0.048
Zero-shot
0.673
0.157
0.070
Zero-shot + types
0.729
0.112
0.035
MATH
Few-shot
0.659
0.174
0.080
Few-shot types
0.732
0.115
0.038
A.5
MORE EXPERIMENTAL RESULTS
A.5.1 RESULTS ON MORE BACKBONE LLMS
We conducted further experiments using Qwen 2-7B-Instrue (Bai et al. 2023) as backbone LLM. The Qwen series of open-source large language models have demonstrated comparable or superior performance to the Mistral and LLaMA families across multiple tasks. The results are shown in Table [I Our method achieves approximately 7% improvement over the few-shot baseline in both single-generation and majority-vole settings (+SC @5), These results demonstrate that T TypedThinker is general and effective method for enhancing the reasoning capabilities of various LLMs.
Table 11: Qwen 1-7B-Instruct results. The annotations the same with Table
LogiQA
BBH
GSM8K
MATH
Avg.
Few-shot
0.552
0.471
0.646
0.417
0.521
SC @
0.579
0.554
0.763
0.497
0.598
CoT Selection
0.554
0.516
0.772
0.451
0.573
SC
0.560
0.528
0.780
0.497
0.591
Zeroshot MoR
0.573
0.498
0.492
0.407
0.493
Fewshot MoR
0.589
0.581
0.889
0.551
0.652
TypedThin Tniker
0.595
0.534
0.779
0.474
0.596
SC @
0.644
0.584
0.880
0.565
0.668
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Table 12: TypedThinker outperforms other baselines on LiveBench without extra finetuning. Here the results are based the majority vote over responses (+SC @5).
Mistral 7B
LLaMA3 8B
Few-shot
0.178
0.200
CoT Selection
0.244
0.200
TypedThinker
0.267
0.267
A.5.2 RESULTS ON MORE BENCHMARKS
We further evaluate methods on LiveBench (White al. 2024) to test the generalization capability of our method. The experimental settings are the same as described in Section 4.5 The results are shown in Table [2] It demonstrates that TypedThinkez outperforms other baselines, further supporting its generalization capability across diverse tasks.
A.5.3 MORE ABLATION STUDIES
The primary reason for comparing our method with the few-shot baseline is that fine-tuning for specific reasoning types is integral part of our approach. Therefore, evaluate the impact of our fine-tuned reasoner through a separate ablation study. However, comparing TypedThinkes to few-shot baselines without fine-tuning may not fully account for the benefits of fine-tuning. Therefore, we conduct two more experiments to verify the influence of the fine-tuned LLMs.
Comparison with base LLM module Ablation studies in Section 4.4 investigate the contribu- tion of each component by removing one component each time. Here we provide additional ablation results by adding one component the base LLM each time, resulting in two variants: Base LLM + Mheta-thnnker and Base LLM + Collection. For more reliable conclusion, we ran experiments three times calculate the average and std and present the result in Table and 14
Table 13: Mistral 7B results are based on three repetitive experiments. Avg. indicates the average accuracy over four benchmarks.
LogiQA
BBH
GSM8K
MATH
Avg.
Few-shot
0.493 0.007
0.347 1 0.01
0.372 1 0.014
0.071
0.003
0.321
0.006
CoT Selection
0.475 1: 0.009
0.361 11: 0.01
0.377
0.011
0.104 1 0.008
0.329
1: 0.004
LLM Meta Thinker
0.512 + 0.003
0.377 + 0.006
0.379
0.106
0.009
0.343
0.004
LLM Collection
0.519 0.007
0.398
- 0.005
0.363
0.086
0.008
0.342
0.001
TypedThinker
0.553 0.004 0.430 + 0.008 0.390 + 0.012 0.103 = 0.01
0,369 0.006
Table 14: LLaMA 3 8B results are based on three repetitive experimmntt.... Avg. indicates the average accuracy over four benchmarks.
LogiQA
BBH
GSM8K
MATH
Avg.
Few-shot CoT Selection
0.569 0.003
0.319 + 0.006 0.476 0.476 0.004
0.102
0.005
0.366
0.001
0.558 + 0.011
0.376 + 0.007
0.360 + 0.006
0.104
+ 0.009
0.349
0.007
LLM + Meta Thinker
0.538 + 0.005
0,434 + 0.005
0.508 0,005
0.118
- 0.005
0,400
+: 0.001
LLM Collection
0.574 + 0.011
0.497 1 0.004
0.438
+ 0.005
0.109
0.006
0.404
0.001
TypedThinker 0.546 0.004 0.534 1 0.003 0.535 1 0.001 0.203 0.009
0.455 0.002
Results show that the retrieval component improves performance on logical tasks but may mislead models on mathematical datasets. This is consistent with our findings in the ablation study in Table 2 the retrieved solutions with digits may mislead the model. Meanwhile, compared with the ICL reasoner, our finetuned reasoner shows better capability in identifying the suitable reasoning type.
A.6 DISCUSSION ON MORE REASONING PROBLEMS
In this paper. we mainly focus on logical and math reasoning problems. However, our TypedThinke inke also be extended symbolic or commonsense reasoning without extra ef-
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Table 15: TypedTainker performs best the abstract category of Contexthub. Here the results are based on the majority vote over responses (+SC @5).
Mistral 7B
LLaMA3 8B
Few-shot
0.25
0.35
CoT Selection
0.55
0.40
Zero-shot MoR
0.55
0.35
Few-shot MoR
0.45
0.45
Self-Discover
0.25
0.55
TypedThinkes Thinkrr
0.75
0.55
forts. For example, the problems under abstract category in ContextHub can be viewed symbolic reasoning, as shown in A.2.2 Therefore, in addition to the overall performance shown in Table 4 present specific performance
the abstract category of symbolic reasoning in Table [5] As we can see TypedThinke. outperforms baseline methods, even without further fine-tuning the meta-thinker and reasoner for this symbolic reasoning task.
While the LogiQA dataset contains problems requiring commonsense reasoning, the dataset lacks explicit annotations (such specific category) for such tasks. For example, here is that requires commonsense knowledge about manufacturing costs, market dynamics, and consumer preferences.
LogiQA: commonsense reasoning example
Traditionally, the most highly sought cars have been the sports cars similar two-door models. Nevertheless, Zinestone Motors has chosen to eliminate the last two-door models and produce only four-door models. Which of the following would, if true, most help to explain Zinestone Motors' strategy?
Options:
(A) In almost every instance, Zinestone Motors models lead all comparable models of competitors in fuel efficiency and have lower average maintenance costs as well.
(B) After spate of recent additional safety requirements, the cost of frame and doors of Zinestone
Motors' standard two-door models are now three doors.
(C) Many of Zincstone Motors models are exported and sold overseas, including in some countries like Japan, which import significant number of cars into the United States. (D) As American consumers lose access two-door cars occupy smaller and smaller shares of United States car market, American consumers' tastes tend to shift from two-door cars.
manufacturers who produce two-door cars, and
For reasoning problems that significantly differ from the existing domains (logic and math), additional demonstrations tailored to the task are recommended to guide reasoning. For example, inductive reasoning might involve deriving general program from exemplar input-output test in code generation (Shao et al.) 2024) Yang et al.) 2024). In such cases, providing a few task-specific examples conducting light fine-tuning the reasoner further enhance performance.
A.7 IMPACT STATEMENT
This work will enhance current LLMs with better reasoning capability, which can make them more useful problem-solving. There might be some potential societal consequences of our work, none of which we feel must be specifically highlighted here. However, it might be misused as we release all our code and data for reproduction. We will try our best to avoid the potential misuse.
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Table 16; Examples of four reasoning types.
Type
Query
Example
Deduction
Alice, Bob, and Claire are dancers square dance. At the start of a song. they each have partner: Alice is with Lola, Bob with Rodrigo, and Claire with Patrick. Throughout the song, Alice and Bob switch partners; Claire and Bob switch; Finally, Bob and Alice switch. At the end of the dance, Alice is dancing with Options:
(0) At the start: Alice: Lola, Bob: Rodrigo, Claire:
(Itrick.(I) Alice and Bob switch: Alice: Rodrigo, Bob: Lola, Claire: Patrick. (2) Claire and Bob
switch Alice: Rodrigo, Bob: Patrick, Claire:
Lola. (3) Bob and Alice switch Alice: Patrick, Bob: Rodrigo, Claire: Lola, At the end of the dance, Alice is dancing with Patrick, So the answer
is (C)
(A) Lola (B) Rodrigo (C) Patrick
Induction
Students who told lie overestimated how many people could detect it. Volleyhall players performing poorly thought teammates noticed more than they actually did. A student wearing funny T-shirt expected everyone to no- tice. but only few did. Which option best illustrates the statements above? (A) People overestimate how often oth- notice their appearance and behav- ior.
By examining each of the scenarios mentioned, we notice all these examples indicate that individuals overestimate the level and extent of attention their actions, appearances, or behaviors receive from others. This consistency across different contexts illustrates broader psychological phenomenon.
So the answer is (A)
(B) People rarely notice the appearance
or behavior of others.
(C) We less observant of others' ap- pearance and behavior than we think. (D) People are less aware of their ap- pearance and behavior than others are."
Abduction
The integer m is between 30 and 80 and is multiple of 6. When is divided by 8. the remainder is 2. Similarly, when m is divided by the remainder is 2. What is the value of m?
To solve this problem using abductive reasoning, we assume that possible value of m exists that abides by the constraints and check if this assump- tion holds. Fi rst, filter values of m that are mul- tiples of between 30 and 80. 2. Next, apply the condition that when m is divided by 8, the remain- der is 2. Only 42, 66 fit this condition.3. Apply the third condition, that when divided by m should leave a remainder 2. Testing the applicable val- ues so far and find 42 meets the requirement. So the answer is
42
Analogy
John is 24 years younger than his dad.
Retrieval: Question: Lisa is 10 years younger than her mom. The sum of their ages is 70 years. How old is Lisa?
The sum of their ages is 68 years. How many years old is John?
Answer: Lisa is 30 years old and her mom is years old.
These are solved using the same approach as the problem about John and his dad's 's ages, i.e., setting up two equations based the information given and then solving the two variables representing the ages. Therefore, for the given question, John is 22 years old.
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Reviews:
[{"review_id": "clFkvziHnD", "reviewer": "Reviewer_3EVV", "summary": "This work introduces a novel framework, *TypedThinker*, designed to improve the problem-solving abilities of LLMsimplementing that reasoning type effectively. by integrating multiple types of reasoning, including deductive, inductive, abductive, and analogical. It addresses two core challenges: 1) choosing the best reasoning type for a given problem and 2) implementing that reasoning type effectively. Using a meta-thinker to select the reasoning type and a reasoner to execute it, TypedThinker can improve accuracy from baseline: by 3.4% for Mistral 7B and 16.7% for LLaMA3 8B on logical and mathematical tasks.", "questions": "- Q1. Figure 1 shows the percentage distribution of each reasoning types. How was this annotated? Did the dataset come with these groundtruth labels for type of reasoning required?\n- Q2. Have you considered other models? Especially since there are new models that explore reasoning in-depth, e.g. GPT-o1, it would be interesting to see if this results hold for those reasoning optimized models.\n- Q3. This was primarily done with logical reasoning and math. Is there a particular reason for picking those domains? I wonder if this strategy would be more effective with reasoning domains with more ambiguity e.g. natural language reasoning. Though, I can also understand that those domains may be difficult to experiment with/validate due to the nature of NL.", "limitations": "", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- S1. The approach to incorporate multiple reasoning types (deductive, inductive, abductive, and analogical) into consideration for a meta-thinker for LLM reasoning is novel and seems like a generalizable approach for most LLMs.\n- S2. There were clear quantitative gains for this approach.\n- S3. TypedThinker’s ability to generalize to unseen benchmarks is a strength particularly in regards to generalization.\n- S4. The experiments on the two models were very thorough, with various components of the framework ablated (e.g. w/o meta-thinker, w/o finetuning, w/o memory on 4 benchmarks)", "weaknesses": "- W1. Accuracy improvement of 3.4% on Mistral 7B seems rather minimal, though improvements on LLaMA3 was quite notable. Since there were such varied performance improvements, it would have been more beneficial to have more models to convincingly validate the findings on this paper.\n- W2. The individual methods in this paper does not seem novel enough, as strategies for the individual types of reasoning were studied in numerous work (e.g. https://arxiv.org/pdf/2309.05660 for inductive reasoning). However, I do believe that the overall framework has strong potential and is novel by ensembling these existing strategies and methods for prediction. Since there are existing methods for each of these types, it would have been very effective to compare these existing methods with this framework. This could be possibly used to measure effectiveness for/against existing methodologies, and would have made this work a lot more relevant and connected with existing work.\n- W3. While overall performance gain with a unified meta-thinker is a gain, I wonder you could have compared this with a baseline, e.g. if there is a significant difference with simply prompting the model to simultaneously state and explore all these reasoning type for final prediction. If there is not a significant performance gain with respect to this baseline, this seems like an overly contrived framework for marginal gains. If there is a significant performance gain, this work would certainly be more convincing, particularly with regards to needing to differentiate reasoning type for precise prediction rather than having inappropriate mixtures.\n- W4. While it is encouraging to see that there were improvements on a rather new dataset probably outside pretraining, I do not think an experiment on a single dataset on 1 task is evidence enough to claim generalization.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BOXlKuMt9Z", "reviewer": "Reviewer_68w7", "summary": "The paper proposes to solve reasoning by a two-step process. First, select a reasoning type from deductive, inductive, abductive and analogical reasoning. This selector is finetuned. Then historical success cases of the selected reasoning type are retrieved from the memory. These retrieved examples along with the selected reasoning type are used to solve the reasoning problem. The paper conducted experiments on Mistral 7B, LLaMDA 3 8B, GPT-4o and MetaMath, on benchmarks such as BBH, GSM8K, MATH etc.", "questions": "Overall, the basic assumption of choosing one reasoning type from 4 is flawed. The fact that there is almost no gain at all for strong models such as GPT-4o reflects the method is not touching the core of how to improve LLM's reasoning ability.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 1, "strengths": "1. The paper is well written and easy to follow.\n2. The experiments conducted are very thorough to get a whole picture of the impact of each component.\n3. It is clearly motivated that diversity is important for superior reasoning performance in LLMs.", "weaknesses": "1. The paper lacks novelty: the idea of introducing different thinking types is not new at all. For example, Meta-Prompting [1] introduced the concept of applying different experts to solve different tasks. Self-Discover [2] proposed to select and compose different reasoning modules to customize the solving of each reasoning task.\n2. The fundamental assumption of matching each task into one of the 4 reasoning types is flawed. There are many ways of solving reasoning beyond the 4 reasoning types. In addition, each task could involve several different reasoning types at different steps. \n3. The proposed method is unnecessarily complex with a fine-tuned reasoner, a meta thinker and a memory.\n4. Despite the cost of fine tuning a reasoner, the gain compared to Few-shot methods is not impressive at all and doesn’t seem to justify the complexity of the pipeline. For example, on Mistral 8B, the average gain on 4 tasks from Few-shot SC@5 is only 3.4% (Table 1). There is almost no gain at all when TypedThinker is applied to GPT-4o (Table 5) and MetaMath (Table 6).\n5. It is not fair to compare TypedThinker against few-shot methods, since TypedThinker involves fine tuning. Instead, it should be compared against methods such as OPRO [3].\n\n[1] https://arxiv.org/abs/2401.12954\n\n[2] https://arxiv.org/abs/2402.03620\n\n[3] https://arxiv.org/abs/2309.03409", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "MPf6pQzxSX", "reviewer": "Reviewer_axGG", "summary": "The paper presents TypedThinker, a framework that improves LLMs problem-solving ability by integrating multiple reasoning types—deductive, inductive, abductive, and analogical. The authors do this by using a meta-thinker for selecting appropriate reasoning types and a reasoner for execution. Several experimental results demonstrate accuracy improvements over baseline models across various logical and mathematical benchmarks.", "questions": "- Can this method be applied to other types of reasoning (symbolic, commonsense etc)?\n- How quickly can this approach adapt to an unseen task? Would one or two examples from new task be enough to achieve reasonable accuracy? It would be great to give some analysis to the adaptability and continual learning ability of the proposed approach.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The framework is clearly explained and the paper is easy to follow\n- Improved accuracy by leveraging different and multiple types of reasoning allowing the models to approach the problem with a better suited strategy and different cognitive point of view\n- The novelty of the proposed method is a good contribution of the paper which may significantly improve LM's reasoning ability for some tasks.", "weaknesses": "- Scalability and resource requirement due to the maintenance of the memory buffer could increase computational cost.\n- TypedThinker depends on self-training and experience retrieval. How generalizable is the learned experience to other different domains? In sect. 4.5 the authors discuss applicability of typedThinker to ContextHub however this remains a collection of problems for logical reasoning. There is no issue with the proposed framework to be suited only for mathematical and logical reasoning, but then this needs to be specified.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "aJRuBZGtTa", "reviewer": "Reviewer_ncpz", "summary": "This paper proposed a novel TypedThinker to incorporate four diverse reasoning types and enhance LLMs' problem-solving abilities. The proposed framework first selected appropriate reasoning types for given problems with a fine-tuned meta-thinker module, and then conducted the selected type of reasoning with a fine-tuned reasoner module and retrieved experiences as few-shot examples. The authors conducted extensive experiments and demonstrated the effectiveness and generalization of the proposed method.", "questions": "See the Weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The idea of different reasoning types in problem-solving is novel and inspiring.\n2. The authors conducted sufficient data analysis to support the necessity of applying different reasoning types.\n3. The authors conducted extensive experiments and in-depth analysis of the proposed method to demonstrate its effectiveness.", "weaknesses": "1. Although the idea of the paper is novel, the technical contribution seems to be limited. The authors seem to simply fine-tune a model to select the reasoning type and use it to search the examples and specify the prompt.\n2. Some technical details may be misleading. For example, the memory usually refers to data buffers frequently updated in inference, but in this paper it is updated during training and fixed in inference. It would be better to clarify more clearly. Besides, some details used in training and inference are mixed such as the accuracy measurement and memory storage, which makes it somewhat confusing. It would be better to clarify the framework from the input to the output for training and inference.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)