{"id":"8c920cd5-510e-4926-bb7f-65313ad30a25","arxiv_id":"2508.12265","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"LLM reasoning strategies are organized along fast/slow and internal/external boundaries, and recent adaptive selection methods are surveyed.","lead":"This paper is a review of how large language models choose between quick intuitive answers, step-by-step reasoning, and using external tools. It organizes these choices into a two-by-two framework and surveys recent methods for making the choice adaptively.","discovery_kind":"unification","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Orthogonality of the fast/slow and internal/external axes—formalized as independent thresholds in Eqs. (5)-(6)—is the load-bearing premise; the paper itself concedes the dimensions can interact, and surveyed interleaved methods already suggest coupling.","rationale":"I agree with the reader's identification of the orthogonality assumption as the weakest point; it is the formal underpinning of the claimed 2x2 taxonomy and of the statement that tool-augmented thinking is an external-knowledge dimension rather than a third mode. The paper does not hide the issue: Section 2 explicitly flags possible interaction and calls coupling underexplored. That honesty is a credit, but it does not remove the tension between the abstract's 'orthogonal' claim and the formalization's independent thresholds. The check I propose would settle the concern by testing whether the framework can actually represent a state-of-the-art interleaved reasoning-and-retrieval method without adding a coupling term. If it cannot, the taxonomy remains a useful heuristic but the central claim needs to be softened from 'orthogonal' to 'two interacting boundaries,' and the survey should be positioned as a selection-based abstraction with a known boundary condition. The 'first comprehensive review' claim is secondary: it needs a comparison against ref [5] and other surveys, but that is a completeness issue, not a correctness issue, and it is easy to fix. For these reasons, the reader's CONDITIONAL verdict is appropriate; no adjustment is needed.","tokens_in":17260,"tokens_out":6473,"duration_ms":69487,"concrete_test":"Take R3-RAG [59] (or ARTIST [60]) and write its decision procedure in the notation of Eqs. (5)-(6) using only independent threshold functions. If the derivation requires k_s,t to appear as an input to Φd,t, or if the policy is a joint function of both decision scores, then the orthogonality claim is falsified for a representative surveyed method. This is a direct, low-cost check of the framework's coverage.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that tool-augmented thinking is not a third mode but an external-knowledge dimension that intersects orthogonally with the fast/slow dimension, characterized by two independent threshold crossings in Eqs. (5)-(6) with separate threshold vectors δd and δs. The load-bearing assumption is that these two decisions are independent. The paper itself concedes at the end of Section 2 that 'these two dimensions may still interact' and that explicit coupling is 'underexplored,' proposing only a future extension. This caveat is not peripheral: if using external knowledge changes the optimal reasoning depth (e.g., retrieved evidence resolves uncertainty and reduces the need for CoT, or a code interpreter call introduces planning and verification requirements), then the decision boundary on one axis is a function of the other. Surveyed methods already point in this direction: R3-RAG [59] and ARTIST [60] jointly optimize interleaved reasoning and retrieval, and ReTool [58] treats tool invocation as an action inside a continuous reasoning process. These methods cannot be faithfully reduced to two independent threshold functions without an added coupling term. Because the novelty of the taxonomy and the 'first comprehensive' framing both rest on the two-axis orthogonal structure, this unvalidated premise is the weakest point of the review.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This review paper proposes a taxonomy of LLM reasoning strategies organized along two knowledge boundaries: a fast/slow boundary separating intuitive from deliberative computation, and an internal/external boundary separating parametric knowledge from tool-augmented knowledge. The authors formalize adaptive reasoning selection as a two-stage process of decision-factor extraction (Eqs. 1-2) and threshold-based strategy selection (Eqs. 5-6), and survey recent methods under this framework, grouping them into implicit and explicit selection paradigms and into decision factors of model confidence, task complexity, and utility gain. The paper concludes with future directions including pre-training integration, unified selection, orchestration, multimodal selection, personalization, and robustness. The central claim is that tool-augmented thinking is not a third mode but an external-knowledge dimension that intersects with the fast/slow dimension.","tokens_in":17493,"tokens_out":8248,"duration_ms":81707,"significance":"The taxonomy is conceptually appealing and timely, organizing a rapidly growing literature on adaptive reasoning in LLMs into an interpretable 2x2 structure. The claim that tool-augmented thinking should be treated as a knowledge-source dimension rather than a standalone mode is a useful corrective to the common three-way categorization. The survey covers a wide range of recent methods (roughly thirty) and includes worked examples for MUR, FLARE, and AdaptThink. The paper is honest about the exclusion of fusion-based methods and acknowledges potential interactions between the two dimensions. If the orthogonality concern is resolved, the framework could serve as a common vocabulary for future work. The main weaknesses are the unsubstantiated novelty claim and the unresolved status of dimension coupling in the formal model.","major_comments":[{"comment":"The formalization treats reasoning-depth and knowledge-source decisions as independent threshold crossings with separate threshold vectors δd and δs. However, the paper itself concedes at the end of Section 2 that 'these two dimensions may still interact' and proposes only a future extension. This is load-bearing because the novelty claim rests on the orthogonality of the two boundaries. Interleaved methods surveyed in Section 5.2.2 (ReTool, R3-RAG, ARTIST) jointly optimize reasoning and retrieval, which cannot be faithfully represented by independent per-decision thresholds without an added coupling term. The authors should either provide evidence that such methods can be decomposed into independent threshold decisions per step, or extend Eqs. (5)-(6) with a coupling term (e.g., making δd a function of ks) and soften the 'orthogonal' wording. Without this, the descriptive adequacy of the taxonomy for tool-augmented slow thinking remains unresolved.","section":"Section 2, Eqs. (5)-(6)"},{"comment":"The paper asserts that this is 'the first comprehensive review that systematically examines the adaptive selection among all three major reasoning strategies,' but it does not compare with prior surveys such as ref. [5] ('From System 1 to System 2: A Survey of Reasoning Large Language Models'). Because ref. [5] and other reasoning surveys exist, the novelty claim needs to be substantiated with an explicit discussion of what prior reviews cover and what this review adds. This is important because the contribution is framed around this novelty; if the claim is overstated, the contribution is weakened.","section":"Introduction (contributions list)"}],"minor_comments":[{"comment":"The same FLARE paper appears as both [21] and [51]; these duplicate references should be consolidated.","section":"References [21] and [51]"},{"comment":"The method for reference [28] is referred to as 'MeCo' in the text but 'MetaTrigger' in Figure 3; please unify the naming.","section":"Section 5.2.1 and Figure 3"},{"comment":"The spelling 'ARITIST' should be corrected to 'ARTIST'.","section":"Figure 3"},{"comment":"The acronym 'CRL' for reference [62] is not defined and may be confusing; consider renaming or adding a definition.","section":"Section 5.1.1"},{"comment":"The abstract uses 'two orthogonal knowledge boundaries,' but Section 2 later qualifies that the dimensions may interact; recommend replacing 'orthogonal' with 'distinct' or 'conceptually independent' to avoid overclaiming.","section":"Abstract and Section 2"},{"comment":"Table 1 does not indicate which of the four quadrants (Fast-Internal, Slow-Internal, Fast-External, Slow-External) each method falls into; adding a quadrant column would make the taxonomy easier to use.","section":"Table 1"},{"comment":"There is a formatting issue in Eq. (5) where 'δ d,t' contains an extra space; please ensure the final typeset version is consistent.","section":"Section 2, Eq. (5)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for the journal and the proposed taxonomy has merit. However, the 'first comprehensive review' claim may be challenged by existing surveys, and the orthogonality assumption, which is central to the contribution, is explicitly contradicted by the paper's own caveat. I recommend encouraging the authors to add a related-work comparison and to either justify or amend the independence assumption in Eqs. (5)-(6)."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a solid, well-written survey whose organizing idea—treat tool-augmented thinking as an external-knowledge dimension that cuts across the fast/slow boundary rather than as a third mode—is genuinely useful. It is a review and a framing exercise, not a new empirical result, and it should be evaluated on those terms.\n\nWhat is actually new is the two-axis taxonomy (fast/slow by internal/external) and the decision-factor/selection abstraction in Section 2. The equations are mostly notation, but they serve a purpose: they let the authors map confidence-based early exits, complexity routers, self-reflective RAG, and RL-trained tool use into a common language. The implicit/explicit selection distinction is clear. Credit is due for the paper's honesty about boundary conditions (it excludes fusion approaches like SMaRT) and about calibration failures of confidence signals. The summary tables will be a useful reference.\n\nSoft spots:\n\n1. Orthogonality. The abstract and intro call the two boundaries \"orthogonal,\" and Eqs. (5)-(6) formalize independent threshold crossings. The paper itself concedes in Section 2 that the dimensions may interact and that coupling is underexplored, proposing only a future extension. That is a real tension. Interleaved methods like ReTool, ARTIST, and R3-RAG are not naturally two independent threshold crossings; tool use can change the optimal reasoning depth. This does not sink the taxonomy—two axes can organize a space even if the axes are coupled—but the authors should soften \"orthogonal\" to something like \"two analytically separable dimensions\" or move the caveat into the abstract and intro.\n\n2. Positioning. The claim to be \"the first comprehensive review\" of adaptive selection across fast, slow, and tool-augmented thinking is not defended. The authors should compare against existing surveys, including ref [5] on System 1/System 2 reasoning and the RAG/tool-use survey literature, and state precisely what is added. The claim feels under-supported right now, though I suspect it can be substantiated with a paragraph of careful positioning.\n\n3. Method selection in Figure 3 and Table 1 is not systematic. This is a minor issue for a narrative review, but if they want \"comprehensive,\" they need to state inclusion criteria.\n\nCitation pattern looks fine. A few self-citations appear as legitimate data points, not padding.\n\nWho this is for: anyone starting to work on adaptive reasoning or building routing systems for fast/slow/tool selection. It deserves serious peer review. The taxonomy is useful, and the caveats are addressable, so my recommendation is to send it out, with a request that the authors fix the orthogonality framing and the positioning claim.","headline":"Useful two-axis survey of adaptive LLM reasoning, worth refereeing despite an over-stated orthogonality claim and thin positioning against prior surveys.","tokens_in":18052,"tokens_out":3250,"would_cite":true,"duration_ms":34952,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Fast, slow, and tool-augmented thinking are not three separate LLM reasoning modes but two independent choices: how deeply to reason and whether to draw on external knowledge.","keywords":["LLM reasoning","adaptive reasoning","fast and slow thinking","tool-augmented thinking","chain-of-thought","retrieval-augmented generation","reasoning strategy selection","dual-process theory"],"falsifier":"On the same set of mixed-difficulty, mixed-tool queries, measure whether the optimal fast/slow switching threshold shifts when retrieval is available versus withheld; a systematic shift would mean the two axes interact and the independence assumed by Eqs. (5)–(6) fails.","tokens_in":17033,"feed_emoji":"🧠","tokens_out":7894,"duration_ms":74500,"temperature":0.7,"pith_summary":"This review argues that the three familiar modes of LLM reasoning—fast, slow, and tool-augmented—are better described by two orthogonal boundaries than by three separate strategies. The fast/slow boundary separates immediate intuitive answers from deliberate step-by-step chains; the internal/external boundary separates knowledge stored in model weights from knowledge obtained through tools, retrieval, or computation. Tool-augmented thinking is not a third mode but an external-knowledge axis that can intersect with either depth. The paper also unifies the growing collection of adaptive-selection methods under one two-stage abstraction—extract decision factors, then compare scores against thresholds—and claims to be the first review covering adaptive selection among all three strategies. If the taxonomy holds, reasoning depth and knowledge source become independently tunable levers for routing queries.","feed_headline":"Two axes, not three modes, classify LLM reasoning","feed_subtitle":"A new review maps fast-versus-slow depth and internal-versus-external knowledge onto a single 2x2 grid with one threshold rule.","key_machinery":"The central object is the pair of orthogonal knowledge boundaries that define the 2×2 strategy space: a fast/slow boundary separating intuitive direct responses from deliberative step-by-step reasoning, and an internal/external boundary separating parametric knowledge from tool-augmented knowledge. The argument is carried by the threshold-crossing decision functions of Eqs. (5)–(6): a decision score $\\Phi_d$ or $\\Phi_s$ is computed from extracted factors (confidence, task complexity, utility gain) and compared with a threshold $\\delta_d$ or $\\delta_s$; crossing the boundary flips the strategy on that axis. This mechanism is flexible enough to cover learned implicit policies, where the threshold lives inside the model weights, and explicit routers, where the threshold is a hand-set scalar or a trained lightweight classifier.","core_discovery":"On the paper's own terms, the discovery is a way of organizing an otherwise scattered literature: all LLM reasoning strategies live on a 2×2 grid whose axes are the fast/slow knowledge boundary (computation depth) and the internal/external knowledge boundary (knowledge source). Fast thinking is the direct, step-free answer; slow thinking is chain-of-thought-style deliberation and verification; tool-augmented thinking is any use of external tools, retrieval, or computation, and it can be paired with either fast or slow processing. The paper further claims that every existing adaptive-selection method—implicit ones learned through fine-tuning or reinforcement learning and explicit ones using rules or external routers—can be described by the same two-stage procedure: extract decision factors such as model confidence, task complexity, and utility gain, then cross a threshold on the relevant axis (Eqs. (5)–(6)). This unification lets the field compare methods by which factor they use and where the decision is made, rather than by surface differences in implementation.","pith_inferences":["Editorial inference: if the two axes interact, the natural extension is to make the fast/slow threshold a function of the internal/external decision (feed $k_s$ into the computation of $\\Phi_d$); the paper names this as future work, and a router trained on tool-availability as a depth feature would test it.","Editorial inference: the Fast-External quadrant may be more common in production than in the literature—simple RAG and API-calling systems already do exactly this—so the taxonomy predicts that research attention to this quadrant will grow as latency budgets tighten.","Editorial inference: the 2×2 grid suggests a benchmark design: vary required reasoning depth and required tool access independently across a task suite, then measure a selection policy's accuracy-latency frontier; policies that trace a convex frontier would confirm the two levers are worth tuning separately."],"forward_implications":["Tool-augmented thinking is demoted from a third mode to an axis: retrieval and tools can be combined with either fast direct answers or slow deliberative chains, making Fast-External—simple RAG and function calling—a recognized quadrant rather than an anomaly.","All selection-based adaptive-reasoning methods become comparable within one two-stage pipeline; a reader can ask separately what decision factors a method extracts and how it computes thresholds, which is a cleaner comparison than listing architectures.","Confidence, task complexity, and utility gain are complementary signals; the review implies that combining calibrated confidence with complexity estimates should give more reliable routing than any single factor.","The framework explicitly excludes fusion approaches such as SMaRT that ensemble multiple strategies; any method that aggregates rather than routes falls outside the proposed unification."],"supporting_citations":[{"why":"Supplies the dual-process System 1/System 2 distinction from which the fast/slow boundary is drawn.","marker":"[6]"},{"why":"Defines chain-of-thought, the concrete realization of slow deliberative thinking in the taxonomy.","marker":"[8]"},{"why":"Establishes utility-driven tool invocation, the foundation for the internal/external boundary and the utility-gain decision factor.","marker":"[39]"},{"why":"Momentum-uncertainty threshold instantiation of fast/slow switching; used to illustrate Eq. (5) in the unified framework.","marker":"[22]"},{"why":"RL-trained implicit selection between thinking and no-thinking; illustrates implicit threshold learning for Eq. (5).","marker":"[23]"},{"why":"Confidence-triggered active retrieval; illustrates the sentence-level internal/external decision of Eq. (6).","marker":"[51]"},{"why":"Detects overthinking and early termination via confidence, supporting confidence as a decision factor at the fast/slow boundary.","marker":"[12]"},{"why":"Learned lightweight router over hidden states for mode switching; supports complexity-based explicit selection.","marker":"[18]"}],"fun_headline_variants":["LLM thinking: a 2x2 grid, not a menu","All LLM reasoning fits on two axes: speed and knowledge","2x2 grid: the only map you need for LLM reasoning","Fast/slow and internal/external: the two axes of LLM thought","One threshold rule: how LLMs choose fast, slow, or tools"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The grid assumes that how deeply an LLM reasons and whether it uses external knowledge are independent decisions; if tool use changes the optimal depth of reasoning, the two-by-two taxonomy misrepresents real systems.","fun_headline_variants_meta":{"raw":{"variants":["LLM thinking: a 2x2 grid, not a menu","All LLM reasoning fits on two axes: speed and knowledge","2x2 grid: the only map you need for LLM reasoning","Fast/slow and internal/external: the two axes of LLM thought","One threshold rule: how LLMs choose fast, slow, or tools"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001328,"raw_usage":{"total_tokens":5373,"prompt_tokens":881,"completion_tokens":4492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":497,"completion_tokens_details":{"reasoning_tokens":4397}},"tokens_in":497,"tokens_out":4492,"duration_ms":29126,"temperature":1.0,"reasoning_tokens":4397,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:24:38.888041+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On the same set of mixed-difficulty, mixed-tool queries, measure whether the optimal fast/slow switching threshold shifts when retrieval is available versus withheld; a systematic shift would mean the two axes interact and the independence assumed by Eqs. (5)–(6) fails.","supporting_citations":[{"cited_title":"Thinking, fast and slow","cited_arxiv_id":null,"evidence_quote":"Supplies the dual-process System 1/System 2 distinction from which the fast/slow boundary is drawn."},{"cited_title":"Chain-of-thought prompting elicits reasoning in large language models","cited_arxiv_id":null,"evidence_quote":"Defines chain-of-thought, the concrete realization of slow deliberative thinking in the taxonomy."},{"cited_title":"Toolformer: Language models can teach themselves to use tools,","cited_arxiv_id":null,"evidence_quote":"Establishes utility-driven tool invocation, the foundation for the internal/external boundary and the utility-gain decision factor."},{"cited_title":"Active retrieval augmented gener- ation","cited_arxiv_id":null,"evidence_quote":"Confidence-triggered active retrieval; illustrates the sentence-level internal/external decision of Eq. (6)."}],"review_version":1}