Chain-of-Thought Reasoning Without Prompting

Authors: xuezhi  wang
google  deepmind
denny  zhou
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-13 19:19:10

Abstract: In enhancing the reasoning capabilities of large language models (LLMs), prior research primarily focuses on specific prompting techniques such as few-shot or zero-shot chain-of-thought (CoT) prompting. These methods, while effective, often involve manually intensive prompt engineering. Our study takes a novel approach by asking: Can LLMs reason effectively without any prompting? Our findings reveal that, intriguingly, CoT reasoning paths can be elicited from pre-trained LLMs by simply altering the \textit{decoding} process. Rather than conventional greedy decoding, we investigate the top-$k$ alternative tokens, uncovering that CoT paths are frequently inherent in these sequences. This approach not only bypasses the confounders of prompting but also allows us to assess the LLMs' \textit{intrinsic} reasoning abilities. Moreover, we observe that the presence of a CoT in the decoding path correlates with a higher confidence in the model's decoded answer. This confidence metric effectively differentiates between CoT and non-CoT paths. Extensive empirical studies on various reasoning benchmarks show that the proposed CoT-decoding effectively elicits reasoning capabilities from language models, which were previously obscured by standard greedy decoding.

Main paper: 
 introduction: 
 Large language models (LLMs) have demonstrated remarkable performance on various complicated reasoning benchmarks (Anil et al., 2023; Brown et al., 2020; Chowdhery et al., 2023; Gemini, 2023; OpenAI, 2023; Romera-Paredes et al., 2023) . These reasoning capabilities of LLMs are typically elicited by prompting techniques (Brown et al., 2020) , which can be few-shot prompting with intermediate steps augmented demonstration exemplars (Chen et al., 2023b; Gao et al., 2022; Nye et al., 2021; Wei et al., 2022; Yao et al., 2023; Zhou et al., 2023a) , or zero-shot prompting with specific instructions which ask for showing certain intermediate steps (Kojima et al., 2022; Yasunaga et al., 2023) . The other prevalent strategy for eliciting LLM reasoning is through model training or instruction tuning using a substantial amount of chain-of-thought (CoT) reasoning data (Chung et al., 2022; Cobbe et al., 2021; Ling et al., 2017; Nye et al., 2021) .Prompting techniques, while effective, often encode task-specific human priors, thereby making it difficult to assess a language model's intrinsic reasoning abilities. Ideally, a well-trained language model should be capable of independent reasoning and delivering optimal responses, without requiring humans to tweak the prompts or refine repeatedly when the initial response is unsatisfactory. Modeltuning can be expensive and requires a substantial amount of supervised data. In this work, we explore a different perspective and ask: Can LLMs reason effectively without prompting? And to what extent can they reason? We find that, perhaps surprisingly, there exists a task-agnostic way to elicit CoT reasoning from pre-trained LLMs by simply altering the decoding procedure. Figure 1 illustrates this phenomenon: given a reasoning question, the LLM generates a wrong answer via the standard greedy decoding path, yet alternative top-k token inspection unveiled inherent CoT paths (e.g., decoding paths 2 and 4), which accurately resolved the query. This decoding modification bypasses prompting and is entirely unsupervised without the need for model tuning. I have 3 apples, my dad has 2 more apples than me, so he has 5 apples. 3+5=8. We have 8 apples in total.We have 5 apples in total.You have 3 apples, your dad has 2 more apples than you, so he has 5 apples. 3+5=8. You have 8 apples in total.The answer is 5.Question in standard QA format Figure 1 : Illustration of CoT-decoding. Pre-trained LLMs are capable of inherent reasoning without prompting by considering alternative top-k tokens, rather than solely relying on the top-1 greedy decoding path. Moreover, these models tend to display higher confidence in decoding the final answer (indicated by a darker shaded color) when a CoT reasoning path is present.In more details, we formulate the input using the standard question-answer (QA) format: "Q:[question]\nA:". 1 While most existing work suggest that LLMs falter in such direct-QA scenarios on reasoning (Cobbe et al., 2021; Kojima et al., 2022; Nye et al., 2021; Wei et al., 2022) , our findings reveal a nuanced picture. We observe that LLMs indeed struggle with reasoning when relying solely on greedily decoded paths. However, when we consider alternative paths among the top-k tokens, CoT reasoning patterns emerge naturally within the decoding trajectories of LLMs. In addition, we have observed an interesting pattern: the model demonstrates increased confidence in the final answer when a CoT reasoning path is present in the decoding process. As illustrated in Figure 1 , this is evident where paths 2 and 4 show heightened certainty in arriving at the correct answer "8", contrasting sharply with the high uncertainty in paths that lead to the incorrect "5". Leveraging this phenomenon, we develop a method to sift through the top-k decoding paths, which we refer to as CoT-decoding, thereby isolating the most reliable paths for model output.Our contributions are summarized as follows:• We present a novel finding that LLMs can reason by simple decoding changes, without the use of prompting. In contrast to prior research that focuses on refining prompts to elicit reasoning from LLMs, our work, for the first time, shows that the reasoning process can be readily elicited by simple decoding changes. Moreover, we challenge the prevailing notion in the literature that LLMs are inherently incapable of effective reasoning without prompting. We show that this belief is an artifact of considering only the greedy path during decoding, and the model's reasoning paths can be revealed by traversing the alternative decoding paths.• Our method enables a better understanding of LLMs' intrinsic reasoning capabilities without imposing human priors. The employment of intricate prompting techniques often introduces various human priors, making it difficult to distinguish between the extent of "human teaching" and the degree to which LLMs can reason independently. Our approach bypasses the confounders introduced by prompting, enabling a more truthful assessment of the models' intrinsic reasoning abilities. Our study reveals that pre-trained language models inherently possess reasoning capabilities for many tasks including math and commonsense reasoning, and existing prompting approaches mostly serve the role of bringing those inherent reasoning paths forward as the top decoding paths. In contrast, the CoT-paths are less prevalent in complex and highly synthetic tasks, where the few-shot CoT demonstrations play a "teaching" role in guiding how models solve a task, with models primarily mimicing the format of these prompts to generate accurate reasoning paths.• We further propose CoT-decoding that reliably selects CoT-paths based on answer confidence. We find that the language model's confidence in its final answers increases when a CoT is present in its decoding path. Leveraging this increased confidence, we propose CoT-decoding to select more reliable decoding paths, demonstrating significant improvements over greedy decoding across various reasoning benchmarks.2 Chain-of-Thought (CoT) Decoding 
pre-trained language models can reason without prompting: 
 We investigate whether pre-trained language models inherently possess reasoning capabilities, without explicit prompts or human intervention. In Table 1 , we show example decoding paths across math (GSM8K, Cobbe et al. (2021) ) and commonsense reasoning (year parity, Allen-Zhu and Li ( 2023)).We employ the pre-trained PaLM-2 large model (Anil et al., 2023) to compare its greedy decoding path (k = 0), predominantly used in state-of-the-art LLMs for reasoning tasks, with alternative decoding paths (k > 0), where k represents the choice of the k-th token at the first decoding step.[GSM8K] One glass costs $ LLMs indeed cannot reason if we only consider the greedy decoding path. First, we observe that models employing greedy decoding often does not contain a CoT path, opting to solve problems directly. This tendency may stem from the model's skewed perception of problem difficulty, shaped by its pre-training on predominantly simpler questions. Consequently, the model is predisposed to immediate problem-solving. This observation aligns with findings in (Cobbe et al., 2021; Kojima et al., 2022; Nye et al., 2021; Wei et al., 2022) , which show that direct-answer prompts generally result in low accuracy on reasoning tasks even for large language models.LLMs can reason if we consider the alternative decoding paths. Contrastingly, an intriguing phenomenon emerges when exploring alternative top-k (k > 0) tokens at the first decoding step.Continuing with greedy decoding from this point reveals natural CoT reasoning in many cases. These findings suggest that large language models possess inherent reasoning capabilities for numerous tasks following pre-training, but these abilities are obscured by the predominant use of greedy decoding. These reasoning paths can be easily uncovered by incorporating alternative decoding paths.For instance, in the GSM8K question (Table 1 ), a valid CoT emerges at k = 9. Similarly, in the year parity task, greedy decoding attempts to directly answer the parity question at k = 0, leading to a random choice between "even" and "odd" which often results in an incorrect answer. However, when exploring k > 0, the model naturally generates CoT paths at k = 3 and k = 7, where it first determines the year before resolving the parity.In this section, we further show how we can reliably extract those CoT-paths during the decoding process. We observe that CoT paths do not consistently outrank non-CoT ones in the model's probability assessment. Moreover, they often do not represent the predominant answer among all paths, rendering methods like self-consistency (Wang et al., 2023a) inapplicable. For instance, in the GSM8K question, the prevalent answer "60", which aligns with the greedy decoding result, fails to serve as a reliable indicator for identifying the correct path.Interestingly, upon examining the model's logits, we found that the presence of a CoT path typically leads to a more confident decoding of the final answer, characterized by a significant probability disparity between the top and secondary tokens:∆ k,answer = 1 |answer| xt∈answer p(x 1 t | x <t ) -p(x 2 t | x <t ).Here x 1 t and x2 t represent the top two tokens at the t-th decoding step in the k-th decoding path, chosen for their maximum post-softmax probabilities from the vocabulary, given x t being part of the answer tokens. This uncertainty measure is similar to the minimum-margin approach in (Jiang and Gupta, 2019) and in our case, the model's overall confidence in decoding the final answer is approximated by averaging these probability differences for all relevant answer tokens x t . For example, for the GSM8K question in Table 1 , given the answer "60", we average the probability differences for all tokens in that answer, i.e., "6" and "0". 2 This method, referred to as CoT-decoding, extracts such CoT paths among the decoded paths from the model. As illustrated in Table 1 , each decoding path is marked with its corresponding ∆ value in blue (the answer tokens are bolded). It is evident that paths with a CoT component exhibit a significantly higher ∆, highlighting the model's increased confidence, as opposed to paths without CoT. We also did a quantitative analysis by manually examining the first 100 questions in GSM8K, and among those, if we take the decoding path with the highest answer confidence among the top-10 decoding paths, 88% of them contain CoT paths. This shows an overwhelmingly high correlation between the model's answer confidence and the CoT paths.Comparing different CoT-path extraction approaches. In Table 2 , we compare different ways to extract the CoT-paths out of the top-10 decoded paths. It is easy to see that the model's own probability measure does not serve as a reliable indicator, nor does the model's length-normalized probability (since an intuition could be a CoT-path should usually be a longer decoding path, which is not always the case, e.g., on the year parity task). In contrast, CoT-decoding can reliably extract the CoT-paths, yielding a significant boost on the model's reasoning performance. .Identify the answer spans. Computing ∆ requires identifying the answer spans in a model's response. One common approach used for public models is to extract the last numerical value in math reasoning tasks, or the final option in set-based reasoning tasks, as the answer, following the Tülu evaluation (Ivison et al., 2023; Liu et al., 2024; Wang et al., 2023b) . Alternatively, similarly to the method used in Kojima et al. (2022) , we can extend the model's output with the prompt "So the answer is", and then align these continuations with spans in the model's decoding path as the answer. A natural question arises: can sampling achieve a similar effect and unveil the CoT reasoning paths? We found that, although sampling works well under few-shot CoT prompting (Wang et al., 2023a) , it does not exhibit the desired behaviour without the prompts. In Table 3 , we show that when no CoT prompt is used, CoT-decoding is much more sample-efficient than sampling-based approaches like self-consistency. The ineffectiveness of sampling stems from the model's skewed distribution towards the direct answer tokens, hence the first token tends to have less diversity compared to CoT-decoding. In contrast, CoT-decoding works by explicitly encouraging diversity at the first decoding step.Branching at other decoding steps. Another natural question is whether branching is viable at later decoding stages, comparing to only branching at the first decoding step. In Figure 2 , we highlight the impact of alternative token consideration in subsequent decoding steps. It is evident that early branching, e.g., at the first decoding step, significantly enhances the diversity of potential paths. Conversely, later-stage branching is significantly influenced by previously generated tokens. For instance, initiating with the token "5" greatly decreases the likelihood of rectifying an erroneous path. Nonetheless, the optimal branching point may vary with the task; in the year parity task, for instance, mid-path branching can effectively yield correct CoT paths. an even year.even.was born in an even year. is 55 years old.Was Nicolas Cage born in an even or odd year? step 1. \nCage was born in was born in an even year.an odd year. 1964, which is an even year.Figure 2: We present an analysis of the decoded paths by considering alternative tokens at various decoding steps. Task-dependent challenges arise: at times, the model encounters difficulty recovering from incorrect paths when branching at later tokens. For certain tasks, multiple branching positions may exist, all leading to the correct reasoning path.Aggregation of the decoding paths. Since we already decode the top-k paths, one natural extension is to aggregate the answers over all those paths, similar to self-consistency (Wang et al., 2023a) but without the use of prompts. The rationale behind this aggregation is to mitigate sensitivity to small differences in the model's logits, particularly when relying solely on the path with the maximum ∆.The examples in Table 1 show that the majority answer is unlikely to be the correct one. Instead, we propose a weighted aggregation method, i.e., we take the answer that maximizes ∆a = k ∆ k,a where ∆ k,a is the k-th decoding path whose answer = a. We found that adopting this approach enhances the stability of the results, and further analysis is presented in Section §3.3. 
experiments: 
 We evaluate CoT-decoding across a range of reasoning benchmarks, demonstrating its capability to successfully recover CoT reasoning paths during decoding, all without the need for specialized prompting.Experiment Setup. For all experiments, the default input to the model is the standard QA format of Q: [question]\nA:, where [question] is filled with the actual question depending on the task, and we ask the model to continue the generation given that prefix. During decoding, we use k = 10 as default for the alternative top-k tokens at the first decoding position, and continue greedy decoding afterwards. We show ablation studies with respect to the different choice of k in Section §3.1.For mathematical reasoning, we use the Grade-school math problems (GSM8K; Cobbe et al., 2021) and the multi-step arithmetic dataset from (MultiArith; Roy and Roth, 2015) . For commonsense reasoning, we investigate the "year parity" task where recent literature finds large language models still struggle with. The task is to query the model with "Was [person] born in an even or odd year?" where "[person]" is filled by a random celebrity name. 3 Existing work (Allen-Zhu and Li, 2023; Berglund et al., 2023) shows that even SoTA models like GPT-4 struggle with such tasks, achieving at-chance accuracy (∼50%) when prompted directly. Additionally, we investigate symbolic reasoning tasks from Big-Bench-Hard (bench authors, 2023; Suzgun et al., 2022) .Models. We use three public models: (1) PaLM-2 (Anil et al., 2023) with different scales, ranging from X-Small, Small, Medium, and Large; (2) Mistral-7B (Jiang et al., 2023) , and (3) Gemma-7B (Team et al., 2024) . Our experiments primarily focus on pre-trained models, but we also include experiments with instruction-tuned models (denoted as "inst-tuned" or "IT").Table 4 : CoT-decoding is the only decoding strategy that can effectively elicit language models' reasoning. CoT-decoding is the only decoding strategy that effectively elicits language model reasoning. In Table 4 , we present results from popular decoding baselines on the Mistral-7B pre-trained model, including temperature sampling (Ackley et al., 1985; Ficler and Goldberg, 2017) , top-k sampling (Fan et al., 2018; Holtzman et al., 2018; Radford et al., 2019) , nucleus sampling (Holtzman et al., 2020) , and beam search. We can see that CoT-decoding is the only decoding strategy that effectively enables language models to reason, while some of the decoding methods even hurt model's reasoning ability compared to greedy decoding.CoT-decoding effectively elicits reasoning across language models. In Figure 3 , we show that across three language model families, PaLM-2, Mistral and Gemma, CoT-decoding yields consistent accuracy gains on both math and commonsense reasoning tasks, sometimes doubling or even tripling the performance compared to greedy decoding.PaLM-2 Large Mistral-7B Gemma-7B CoT-decoding partially closes the reasoning gap between pre-trained and instruction-tuned models, without using any supervised data. Intriguingly, we observe that CoT-decoding enables a pre-trained model to achieve a similar performance of an instruction-tuned model: in Figure 4 (left), CoT-decoding achieves 63.2% accuracy on the pre-trained PaLM-2 Large model, close to the performance of the instruction-tuned model of the same scale at 67.8%. The results demonstrate that instruction-tuning with sufficient CoT data (Chung et al., 2022 ) can be partially achieved by modifying the decoding procedure within pre-trained models. More interestingly, we observe that CoTdecoding can further improve the instructiontuned model (Figure 4 (left) and Table 5 ). The instruction-tuning procedure (Chung et al., 2022) incorporated a large amount of CoT annotations during the fine-tuning process. Consequently, the model is expected to inherently generate CoT paths when addressing reasoning tasks. However, upon analyzing specific examples, we found that even after instruction-tuning, the model occasionally persists in attempting to directly address a question. In contrast, CoTdecoding can enhance the exploration of alternative paths by triggering a CoT first, consequently leading to more accurate answers.Choice of k. In Figure 5 , we illustrate how the choice of k, representing the number of top alternative tokens considered, influences the overall accuracy. Overall we found that higher values of k typically result in improved model performance, suggesting that in many cases, the correct CoT paths may indeed exist but are often ranked lower during model's decoding. For instruction-tuned models, the effect of k is less significant, indicating that the process of instruction-tuning effectively brings forth the majority of CoT-paths to the first few decoding paths. Compared to existing works that improve model's reasoning via better human-written prompts, a key distinction of our proposed approach lies in the complete elimination of human-provided prompts. This modification enables a more truthful assessment of a language model's intrinsic reasoning capabilities. In the previous section, we show that language models inherently possess reasoning capabilities for grade-school-level math problems and simple commonsense reasoning tasks. In this section, we will systematically vary the difficulty levels of synthetic tasks to gain a more comprehensive understanding of language models' inherent reasoning abilities via CoT-decoding.We consider the following symbolic reasoning tasks: (1) the Coin Flip task from (Wei et al., 2022) , with 2, 3, 4 rounds of potential flips; and two tasks from Big-Bench-Hard (bench authors, 2023; Suzgun et al., 2022) : (2) Web of lies, with 3, 4, 5 truth/lie statements, and (3) Multi-step arithmetic with various depth level d and length l. For each task, we produce 100 examples for each difficulty level, except for Web-of-Lies (5) we use the existing dataset from (Suzgun et al., 2022) . We also include two natural-language-based but synthetic tasks from Big-Bench, Sports Understanding and Object Counting, to probe model's intrinsic abilities in solving synthetic tasks.Web of lies Multi-step Arithmetic Sports Und.Object Count Table 6 : The model's intrinsic reasoning ability varies depending on the task difficulty levels.The presence of correct CoT paths depends on the task difficulty levels and correlates with task prominence in the pre-training distribution. The results in Table 6 (on PaLM-2 L) show that despite CoT-decoding helps elicit better reasoning across almost all tasks, the gains vary significantly depending on the task difficulty level: the simpler the task is, the better chance that a correct reasoning path can be found. We also looked at the model's top-k decoding paths, and found that models can generate the correct CoT paths when the solution involves at most 1 or 2 step knowledge manipulation, and the model starts to struggle with generating the correct CoT-paths when the steps become 3 or more. See Figure 5 (right) where the model's accuracy improves only for larger k's as task complexity increases (higher d and l's). This phenomenon suggests that the correct CoT-paths become harder to find when the task becomes more synthetic. This mirrors the finding in (McCoy et al., 2023) , where the authors show language models are highly influenced by the distribution they have been trained on.CoT-decoding unveils model's intrinsic vulnerabilities in reasoning. Our results also unveil the specific areas where language models still struggle with: for example, on Coin-Flip and Web-of-Lies, we observe that the model can generate CoT paths that simulate the process step-by-step, but it can easily lose track of the states, especially when the task complexity increases. This reveals model's intrinsic vulnerability in performing accurate state tracking. On Multi-step Arithmetic, we observe that the model tends to perform calculations from left to right in the CoT-decoding paths, rather than following the correct mathematical order. These observations point to future directions where we should improve the models on.In addition, over these synthetic tasks, we found that existing CoT prompts on Big-Bench-Hard (Suzgun et al., 2022 ) play a larger "teaching" role in guiding the model to solve such tasks, and in most cases the model just mimics the patterns in the CoT prompts to generate the correct response: e.g., the few-shot CoT prompts teach the model to perform explicit state tracking in each step for Web-of-lies. On the Sports Understanding task, CoT-decoding can better reveal LLMs' intrinsic strategy in solving a problem (see Appendix A), without being influenced by the external prompts which could be biased by the prompt designers. In contrast, few-shot CoT prompting constrains the model to follow an artificial strategy curated through human knowledge and intervention.Mistral We further show that CoT-decoding can be easily combined with CoT-prompting, yielding even larger reasoning gains over multiple language models (Table 7 ). CoT-decoding maintains a strong performance compared to self-consistency (Wang et al., 2023a) when both are combined with CoTprompts. Since self-consistency aggregates over multiple paths, we also show the performance based on our path aggregation algorithm, which significantly improves the model's reasoning at a similar cost. For a fair comparison, we use k = 10 for all methods that require multiple decoding paths. 
related work: 
 Chain-of-thought reasoning in large language models. Existing work enhancing the reasoning abilities in large language models predominantly involve proposing better prompting techniques to better elicit CoT reasoning paths from the model (Kojima et al., 2022; Nye et al., 2021; Wei et al., 2022; Yao et al., 2023; Yasunaga et al., 2023; Zhou et al., 2023a) . Despite achieving high performance, few-shot prompting techniques are often task-specific, requiring prompt designs tailored to each task. This limits their generalizability across tasks. Advanced prompting techniques often require manually intensive prompt engineering, and their effectiveness varies depending on the choice of prompts, resulting in inconsistent performance outcomes (Wang et al., 2022; Ye and Durrett, 2022; Zhou et al., 2023b) . Efforts to discover improved prompts (Yang et al., 2024; Zhou et al., 2023b) further entail model-specific and task-specific tuning.In addition, these prompting techniques can subtly alter the vocabulary's posterior distribution in ways that remain largely elusive (Min et al., 2022; Webson and Pavlick, 2022) . Specifically, prompts may assist in task decomposition, induce the model to generate additional tokens, or directly "teach" the model the exact underlying procedure to solve particular problems via manually crafted few-shot demonstrations. Dissecting the distinct influence of each aspect, however, presents a significant challenge. In contrast, our work explores a different perspective within the decoding stage, demonstrating that, even without explicit prompting, the model inherently holds the capability to generate chain-of-thought reasoning paths across a wide set of tasks.Recent work proposes to improve the CoT generation process via better controlling and verifying the steps generated, e.g., step-by-step verification (Lightman et al., 2023) , process-based feedback (Uesato et al., 2022) , self-evaluation guided beam search (Xie et al., 2023) , and PathFinder (Golovneva et al., 2023) . Note all these works still require CoT prompting in order to generate the CoT reasoning paths, while our work completely removes CoT prompting. In addition, these works focus on searching and verifying the "steps" produced by the language model, while our work purely searches in the decoding space on the token-level and utilizes the confidence scores when decoding the answer.Additionally, recent works (Feng et al., 2023; Li et al., 2023b; Prystawski et al., 2023) . McCoy et al. (2023) ; Razeghi et al. (2022) demonstrate a similar phenomenon where the pretraining distribution heavily influences the model's performance in few-shot reasoning.Instruction-tuning to elicit CoTs in language models. When supervision is allowed, techniques such as instruction-tuning or distillation offer another way to elicit reasoning paths from language models without explicit prompting (Chung et al., 2022; Huang et al., 2023; Magister et al., 2023) . However, these approaches typically involve resource-intensive fine-tuning over large language models and require a large set of examples annotated with CoTs, which may not be readily available. Liu et al. (2024) show that a language model can be tuned by a proxy. Their method requires a few additional models, and implicitly assumes that the tuned model is well-optimized, e.g., on reasoning benchmarks the model needs to be tuned with CoT paths to enable contrasting logits with respect to the base untuned model. In contrast, our approach is entirely unsupervised and examines a model's intrinsic ability in generating CoT paths, without resorting to fine-tuning or any additional models.Decoding algorithms for language models. The predominant focus in existing literature on decoding for language models revolves around aspects such as fluency, coherence, reduction of repetitiveness, and diversity in responses. Popular decoding algorithms used for language models include greedy decoding, temperature sampling (Ackley et al., 1985; Ficler and Goldberg, 2017) , top-k sampling (Fan et al., 2018; Holtzman et al., 2018; Radford et al., 2019) , and nucleus sampling (Holtzman et al., 2020) . Additionally, there exist refined algorithms such as minimum Bayes risk decoding (Eikema and Aziz, 2020) , and typical decoding (Meister et al., 2022) . Diverse beam search (Vijayakumar et al., 2018) is another way to explore alternative paths in a model's generation. However, it emphasizes generation diversity rather than accuracy.There is relatively little research dedicated to enhancing decoding algorithms specifically for reasoning tasks. Wang et al. (2023a) improves upon CoT prompting by sampling and aggregating over multiple generated responses to improve reasoning. Contrastive decoding (Li et al., 2023a) is another way to improve model's generation quality by penalizing the logits from smaller models, and recent work (O'Brien and Lewis, 2023) shows that contrastive decoding can contribute to enhancing reasoning performance. Shi et al. (2023) propose context-aware decoding to improves the faithfulness of language models. These approaches typically require additional information, such as employing additional models to generate contrasting logits or incorporating additional contexts. In contrast, our work relies solely on a single model without the need for supplementary knowledge.Decoding algorithms for efficiency. In addition to decoding algorithms for improving quality, there is a substantial body of research dedicated to improving decoding efficiency, e.g., speculative decoding (Chen et al., 2023a; Leviathan et al., 2022; Zhou et al., 2024) . This line of work is orthogonal to our work as their primary focus is not on improving a model's reasoning performance. However, these techniques could potentially be leveraged to improve the efficiency of CoT-decoding. 
conclusion and discussion: 
 We investigate the inherent capabilities of language models in generating CoT reasoning paths during decoding, abstaining from any specialized prompting. Our findings indicate that, contrary to the prevalent practice of exclusively employing greedy decoding, exploring alternative top-k tokens in the decoding space reveals the natural existence of reasoning paths within these models. Furthermore, our empirical observations highlight that the presence of a CoT reasoning path correlates with increased model confidence in decoding its final answer. Based on this observation, we introduce CoT-decoding to extract more reliable decoding paths from language models, thereby enhancing their overall reasoning performance.Discussion and Limitations. The exploration of alternative decoding paths incurs additional computational costs. Future work could leverage the CoT-decoding paths to fine-tune the model to further enhance its reasoning capabilities. Additionally, in cases where the answers are more open-ended, utilizing the probability differences of the top two tokens as an indicator of how models prefer one answer over another could be less precise. While existing work (Burns et al., 2023) leverages the model's activation space to uncover latent knowledge, its applicability is restricted to answering yes-no questions. We hope that future research can address this limitation by delving deeper into the model's internal representation across a broader, more open-ended answer space.Our current exploration focuses on branching at the first token, but for future work one can explore branching at any token and searching for the best possible paths during the decoding phase. The computational cost will be substantially higher though, and how to reliably identify the best token during the search will be an interesting direction to explore. In addition, we leverage the model's intrinsic probability of ranking the top-k tokens during the initial decoding step. For more complex or nuanced tasks, however, if the model is inadequately trained, it is possible that none of the top-k tokens will yield relevant paths. This limitation can, in turn, help identify specific areas of model weakness, indicating the need for additional data coverage during training or for explicit guidance via expert knowledge during inference to successfully address these tasks. 
experimental setting/details: 
 Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?Answer: [Yes] Justification: We provide details in the experiment section as well as in the appendix.Guidelines:• The answer NA means that the paper does not include experiments.• The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. • The full details can be provided either with the code, in appendix, or as supplemental material. 
experiment statistical significance: 
 Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?Answer: [NA] Justification: Our results are deterministic (top-k tokens used at the first decoding step, and then continue with greedy decoding), so there is no variance involved. We perform experiments over multiple public language models and the results can be easily reproduced.Guidelines:• The answer NA means that the paper does not include experiments.• The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.• The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). • The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) • The assumptions made should be given (e.g., Normally distributed errors).• It should be clear whether the error bar is the standard deviation or the standard error of the mean. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 10. Broader Impacts Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? Answer: [Yes] Justification: We discuss in the last section on both the positive societal impacts (we can better inspect models' intrinsic reasoning capability) as well as negative societal impacts (the method incurs higher computational costs). Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. • The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
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 Appendix: In Table 8 , we present qualitative examples illustrating the distinctions in the generated CoTs for each method. Overall we observe that CoT-decoding exhibits a more "free-form" CoT generation in comparison to alternative CoT prompting methods. This divergence may be attributed to two factors:(1) we encourage the diversity at the initial decoding step, and ( 2) the absence of explicit constraints imposed by prompting.Another noteworthy observation is that CoT-decoding can better reveal what LLMs' intrinsic strategy in solving a problem, without being influenced by the external prompts which could be biased by the prompt designers. Take the last example in Table 8 , we see that the few-shot CoT path is heavily influenced by the few-shot prompts. Specifically, the few-shot prompts, sourced from (Suzgun et al., 2022) , consistently follow a standard analytical approach -first assessing the person's profession, followed by an evaluation of whether the profession aligns with the action. This aligns with the standard method of solving this particular task. 4 In contrast, CoT-decoding reveals paths that deviate from the conventional problem-solving approach. Despite yielding an incorrect final answer according to the ground truth in some cases, the CoT paths remain to be valid.[GSM8K] Claire makes a 3 egg omelet every morning for breakfast. How many dozens of eggs will she eat in 4 weeks? Greedy: 3 CoT-decoding: A dozen is 12. 3 eggs per day for 4 weeks is 84 eggs. 84/12 = 7. 7 dozen eggs.Few-shot CoT: There are 7 days in a week. 4 weeks is 4 * 7 = 28 days. She eats 3 eggs each day, so in 28 days she eats 28 * 3 = 84 eggs. 1 dozen is 12 eggs. 84 eggs is 84 / 12 = 7 dozen eggs. The answer is 7.Zero-shot CoT: First, how many eggs does she eat in a week? 7 days in a week, 3 eggs per day, so 7 x 3 = 21 eggs per week. Now, how many eggs does she eat in 4 weeks? 4 x 21 = 84 eggs. Now, how many dozens of eggs is that? 84 / 12 = 7 dozens.[Year Parity] Was Nicolas Cage born in an even or odd year? Greedy: Nicolas Cage was born in an odd year.CoT-decoding: Cage was born in 1964, an even year.Zero-shot CoT: 1. Nicolas Cage was born in 1964.2. 1964 is an even number.3. Therefore, Nicolas Cage was born in an even year.[ Table 9 provides an example where the Mistral-7B model attempts to directly solve the question with greedy decoding. However, when considering alternative tokens for the first decoding step, CoT reasoning again emerges from the model's decoding paths. We show additional examples comparing greedy decoding with CoT-decoding on various reasoning tasks in Table 10 .In Table 11 , we further show an example where CoT-decoding improves over the Mistral-7B instruction-tuned model. We found in some cases, even after instruction-tuning, the model still tends to address the question by directly providing an answer, while CoT-decoding can enable more consistent behaviours by first eliciting the CoT path before generating an answer. For this example, another interesting observation is that, the model generates a CoT after an initial answer "16" is Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?Answer: [Yes] Justification: We use public datasets (with citations and links) and we provide code in supplementary materials.Guidelines:• The answer NA means that paper does not include experiments requiring code. • Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted.The QA format is only needed because without it a pre-trained language model will continue the question instead of answering. It is also the most basic formatting employed in existing works for pre-trained models.We also considered other popular choices for measuring the model's uncertainty(Settles, 2009), e.g., using the model's probability on the token itself (i.e., p(x 1 t | x<t) only), which performs slightly worse compared to the min-margin approach. In addition, an entropy estimate is not accurate due to the large vocabulary size in LLMs and the common use of vocabulary truncation.We curate a list of the top 100 celebrity names from(Berglund et al., 2023): https://github.com/ lukasberglund/reversal_curse/blob/main/data/celebrity_relations/top_celebrities.txthttps://github.com/google/BIG-bench/tree/main/bigbench/benchmark_tasks/sports_understandinghttps://huggingface.co/mistralai/Mistral-7B-Instruct-v0.1 


Decision: This paper investigates whether LLMs can generate CoT paths without any prompting (i.e., only input a question to the model, without additional info).This is in contrast to prior work that focuses on developing different prompts (e.g., few-shot prompts, “let’s think step by step”) to elicit reasoning steps from LLMs. The findings suggest that CoT reasoning paths can be elicited from pre-trained LLMs by simply considering the alternative paths greedily decoded from the top-k tokens at decoding step 0. The authors have added a few more experiments during the rebuttal, which make the results more convincing. Most reviewers tend to agree that the paper introduces a novel approach, very well-written and easy to follow. I would recommend accepting this paper and the authors follow the suggestions and discussions during rebuttal to refine it.

Reviews: review: paper_summary: paper_summary: The paper investigates the intrinsic reasoning capabilities of LLMs without relying on prompting techniques like few-shot or zero-shot prompting. The study introduces an alternative approach by altering the decoding process, specifically by exploring the top-k alternative tokens rather than following the standard greedy decoding path. The proposed "CoT-decoding," reveals that LLMs inherently possess chain-of-thought reasoning abilities that are often hidden by human-involved prompting / conventional decoding methods.
strength_weakness: strength_weakness: - **Extra Computational Cost**: Exploring top-k alternative tokens for decoding paths requires additional computational resources. Compared to CoT/Zero-shot CoT/ComplexCoT/CoT-SC(n) where n is not a large number, CoT-decoding necessitates evaluating multiple decoding paths, which increases computational complexity and time cost, especially when dealing with complex multi-step tasks.
- **Limitations in Open-ended Questions**: This method mainly relies on the model's confidence in specific answers during the decoding process to select reasoning paths. However, for more open-ended questions, this probability difference-based selection method may not be precise enough, making it challenging for LLMs to select the optimal path in a much larger answer space.
questions: questions: Does the limitation of branching only at early decoding stages restrict the flexibility and applicability of CoT-decoding? Would exploring branching at later stages in the decoding process improve overall performance?
limitations: limitations: I do not identify any negative societal impacts in this paper.
paper_summary: paper_summary: The paper investigates an innovative approach to eliciting chain-of-thought (CoT) reasoning from pre-trained large language models (LLMs) without the need for explicit prompting techniques, which typically require intensive prompt engineering and can obscure the model's inherent reasoning capabilities. Instead, this study proposes altering the decoding process by exploring alternative top-k tokens, rather than the conventional top-1 greedy decoding path. This method, termed CoT-decoding, effectively reveals natural CoT reasoning paths within the language model's outputs, leading to more accurate and confident model responses across various reasoning tasks.
Contributions:
1. **Novel Decoding Strategy:** The paper introduces a novel decoding strategy that bypasses the need for prompt engineering by modifying the decoding process to explore alternative token paths, allowing the model to display its intrinsic reasoning capabilities.
2. **Empirical Validation:** Extensive empirical studies demonstrate that this CoT-decoding approach not only enhances the accuracy of LLMs on reasoning tasks but also increases the confidence of the models in their answers, suggesting a higher reliability of the reasoning paths discovered.
3. **Comparative Analysis:** The paper provides a comparative analysis of CoT-decoding against traditional methods, showing significant improvements over greedy decoding and other baseline methods across multiple benchmarks for mathematical and commonsense reasoning tasks.
strength_weakness: strength_weakness: 1. The method involves generating multiple decoding paths and evaluating them to identify the most confident reasoning trajectory, which could be computationally expensive, especially when applied at scale or in real-time applications.
2. The approach heavily relies on the selection of top-k alternative tokens, which may not always yield the most relevant or coherent paths for reasoning, especially in more complex or nuanced tasks.
questions: questions: See weekness.
limitations: limitations: None. Good Paper~
paper_summary: paper_summary: The paper explores the inherent reasoning capabilities of large language models (LLMs) without the need for explicit prompting. By altering the decoding process to consider top-k alternative tokens, the authors reveal that Chain-of-Thought (CoT) reasoning paths can emerge naturally. This approach bypasses the need for task-specific prompt engineering and demonstrates that LLMs possess intrinsic reasoning abilities. Extensive empirical evaluations across various reasoning benchmarks show significant performance improvements using CoT-decoding compared to conventional greedy decoding.
strength_weakness: strength_weakness: - The approach, while novel in its specific application, builds on existing concepts of decoding and model confidence. The novelty is somewhat incremental.
- The scope of experiments could be broadened to include more diverse and complex reasoning tasks. Additional benchmarks and comparisons with state-of-the-art prompting methods would strengthen the paper.
- The paper could benefit from a more detailed comparative analysis with other decoding and prompting strategies to contextualize its contributions better.
questions: questions: - Can the authors provide more detailed comparisons with other state-of-the-art prompting and decoding methods?
- How does the CoT-decoding method perform on more complex and diverse reasoning tasks not covered in the current experiments?
- Are there any potential limitations or biases introduced by relying on top-k alternative tokens for decoding?
limitations: limitations: The authors have addressed some limitations of their work, such as the additional computational costs incurred by exploring alternative decoding paths. However, the paper could further discuss the potential biases introduced by this approach and its applicability to more complex, open-ended tasks.
paper_summary: paper_summary: The paper investigates the inherent capabilities of LLMs to generate CoT reasoning paths. This study introduces CoT-decoding, a method that explores alternative top-k tokens in the decoding space to uncover reasoning paths without any specialized prompting. The findings indicate that the presence of a CoT reasoning path correlates with increased model confidence in its final answer. The paper highlights that CoT-decoding can enhance the reasoning performance of language models by extracting more reliable decoding paths.
strength_weakness: strength_weakness: 1. The primary contribution of the paper appears to be a method for selecting a decoding path from the top-k generated paths. While this approach is useful, it lacks novelty and significant impact.
2. The motivation behind the study is unclear to me for several reasons. Firstly, providing questions alone constitutes a form of prompting instead of no prompting. Secondly, the use of a prompt that inherently challenges the elicitation of CoT reasoning paths via greedy decoding, only to then introduce a specialized decoding method to address this, strikes me as contrived. Lastly, I question the claim that CoT-decoding effectively enhances the reasoning capabilities of language models, as it merely selects from pre-generated paths rather than uncovering new, substantive reasoning processes.
3. The proposed method may face challenges in tasks where identifying correct answer spans is difficult, limiting its practical applicability.
4. The comparison between CoT-decoding and greedy decoding is unfair. CoT-decoding inherently requires multiple reasoning paths to be generated first, which is not a requirement for greedy decoding. The exploration of multiple decoding paths significantly increases the computational cost, which could be a drawback for practical applications.
5. The evidence provided in the paper is restricted to a few reasoning benchmarks and toy tasks. To convincingly demonstrate its utility, the method should be tested across a broader array of datasets, such as the MATH benchmark, and in more complex real-world scenarios.
6. The range of models evaluated in the study is too narrow. Including mainstream models like GPT-3.5, GPT-4, and diverse open-source models like llama3 in various sizes would provide a more robust evaluation of the method's effectiveness.
questions: questions: NA
limitations: limitations: Yes

Comments: title: Thanks for your rebuttal
Official Comment by Reviewer BrnW
comment: Thank you for acknowledging our rebuttal. We will add these additional discussion points to the paper.
Thank you for going through our rebuttal and raising the score. We will move the branching discussion to the main text to make this information more accessible.
Thank you very much for the rebuttal. I found the information I wanted in the appendix. CoT-Decoding is an interesting discovery, and I have raised my score from 7 to 8, leaning toward clear acceptance.
Thanks for your rebuttal, I will keep my positive ratings.
Thank you for carefully reading through our rebuttal and raising your score. We will add these additional discussion points into our paper. We truly appreciate your time in reviewing this work.
Thank you for your thorough rebuttal and for addressing the concerns raised. I believe this work is very meaningful and provides valuable insights into enhancing the model's reasoning capabilities and constructing higher-quality datasets. In light of your detailed response and the efforts made to address these complexities, I have decided to increase my score from 7 to 8.