{"id":"e5e660bc-ba8c-4008-8e22-54e81238643a","arxiv_id":"2506.03673","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A prompting method that alternates backward and forward reasoning improves small LLM accuracy on math and search tasks and reduces the number of visited search states.","lead":"This paper introduces Reason from Future (RFF), a prompting method that alternates backward reasoning from a desired final state with forward reasoning steps. On math word problems and Game of 24, RFF reports higher accuracy than chain-of-thought and related baselines while visiting fewer search states.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"RFF's search-space and accuracy gains rest on an unmeasured reverse-step generator; per-step validity of G() is never checked, so the claimed reverse-reasoning mechanism could be an artifact of G() doing the hard decomposition.","rationale":"The reader's weakest_assumption is that G() reliably produces valid pre-target states; I agree that this is the load-bearing premise. My concern is slightly broader: even where G() happens to be correct, the paper has not isolated whether the reverse direction, rather than the extra iterative state accumulation and LLM-based checking, drives the gains. The paper has real supporting evidence—the Pair-vs-Single ablation (Appendix B) and the GSM-Symbolic robustness results (Section 4.5) show the method is not vacuous, and the consistent pattern across math and search benchmarks is hard to explain by pure prompt artifact. Those positives keep the result plausible. But the missing per-step G() measurement and the missing forward-only control mean the central mechanistic claim ('the essence of RFF lies in its reverse reasoning mechanism') is not yet established. This is exactly the kind of missing support that justifies the reader's CONDITIONAL verdict, so my read does not move the verdict; it sharpens the condition: before accepting the claimed mechanism, the authors should report G()'s per-step validity and a matched forward-only control.","tokens_in":13795,"tokens_out":6968,"duration_ms":80440,"concrete_test":"Re-run RFF-T on the 100 Game-24 puzzles and RFF-G on 100 GSM8K problems, logging every G() call: input S_{i-1}, target T_{i-1}, output T_i, and the emitted transition. For every logged tuple, use an exact solver (for Game-24, brute-force all legal one-step reductions; for GSM8K, symbolic arithmetic validation) to label the transition valid/invalid and the proposed pre-target state reachable/unreachable from S_{i-1}. Then compute the per-step validity rate of G() on successful vs failed trajectories, and the final accuracy if G() were replaced by an oracle that always returns a reachable valid pre-target. If the real G() validity is below, say, 80% even on successful runs, or oracle-G accuracy is much higher than actual, then the claimed reverse-reasoning mechanism is not what reduces search space.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Algorithm 2 (RFF-G) terminates only when the LLM-based State Check V(S_i,T_i) outputs True; Algorithm 1 (RFF-T) backs up only after its verifier V() judges a path. Neither the Last Step Generator G() nor the transitions it emits are independently checked. The prompt in Appendix Figure 7 asks G() to output a final operation such as 2×12=24 even when 2 and 12 are not in the current input; the algorithm assumes without measurement that the proposed pre-target state is reachable from S_{i-1}. Table 1's striking state-count reduction (9.9 vs 89.8 at comparable width) is therefore evidence only that RFF spends fewer visited states, not that those states are reached by goal-constrained reverse reasoning rather than by G() guessing the final decomposition, which is the hard combinatorial part. The Limitations section concedes: 'The effectiveness of RFF relies on the model's ability for reverse thinking.' End-to-end accuracy cannot validate this premise, because success could also come from the accumulated-state prompting and LLM-based state/verifier calls. Appendix B's Pair-vs-Single comparison shows alternating direction matters, but it does not include a forward-only planner with the same state-accumulation and checker machinery; the unique contribution of the reverse mechanism is therefore never isolated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes Reasoning from Future (RFF), a prompting paradigm in which an LLM alternates a reverse 'Last Step Generator' G() with a forward stepwise reasoner R(), governed by a state checker C() and a verifier V(). Two algorithmic variants are presented: RFF-T for tree-search tasks such as Game of 24, with backtracking and avoidance of previously failed steps, and RFF-G for tasks modeled as directed acyclic graphs, such as arithmetic word problems and multiple-choice commonsense reasoning. The method is evaluated on Game of 24, GSM8K, SVAMP, ASDiv, MATH-500, CommonsenseQA, LogiQA, and GSM-Symbolic variants, using Llama3-8B-Instruct and Qwen2.5-7B-Instruct. The headline results are higher accuracy than CoT, CR, Least-to-Most, and Give-me-Hint on most math benchmarks (e.g., 83.8% vs 75.6% CoT on GSM8K for Llama3-8B) and dramatically fewer visited states in Game of 24 (e.g., 9.9 visited states at 89% accuracy vs 89.8 states at 19% accuracy for CR on the same model). The paper argues that reverse reasoning narrows the search space by imposing goal-oriented constraints on intermediate steps and thus mitigates error accumulation in forward reasoning.","tokens_in":13984,"tokens_out":6328,"duration_ms":65603,"significance":"If the accuracy and search-space claims hold, RFF is a useful contribution to prompt-level reasoning methods, especially for 7B-8B models where simple CoT is weak. The empirical breadth is a strength: five math benchmarks, two base models, a redundant-variable stress test in Section 4.4, and a GSM-Symbolic robustness analysis in Section 4.5. Appendix C provides the actual prompts for G, R, and C, which substantially aids reproducibility, and the Pair-vs-Single comparison in Appendix B is a useful first step toward understanding the role of alternating backward and forward reasoning. However, the paper's central mechanistic claim, that reverse reasoning is what reduces search space and error accumulation, is not directly tested. The generator G() is never measured separately, and no forward-only control with the same state-accumulation and checker machinery is reported. The empirical results are therefore suggestive but not yet conclusive, and the contribution would be materially strengthened by the missing controls and variance estimates.","major_comments":[{"comment":"The central claim that RFF's reverse mechanism reduces search space rests on G() proposing a pre-target state that is reachable from the current state. The paper never measures the per-step validity of G() or the validity of the transition it emits. The prompt in Appendix Figure 7 explicitly allows 'calculation' numbers that are not in the input, and the algorithm assumes, without verification, that the proposed pre-target state is reachable from S_{i-1}. The LLM-based state checker C()/V() only tests whether S_i matches T_i, not whether T_i was a legitimate predecessor. End-to-end accuracy cannot validate this premise, because success could instead come from the accumulated-state prompting and the checker machinery. I ask for a separate evaluation of G(): for each step, what fraction of proposed targets and transitions are logically reachable from the current state, and what fraction of successful RFF trajectories use only valid reverse steps? An ablation replacing G() with a forward-only or random target generator under otherwise identical machinery would directly test the mechanism.","section":"§3.1, Algorithms 1–2, Appendix Fig. 7"},{"comment":"Table 1 mixes base models in the headline comparison. The text states that 'when the visit-state is around 10, RFF reaches the best accuracy of 89% compared to CR with GPT-4 at 84%' and that 'when the visit-state is around 14, RFF reaches an accuracy of 96% compared to CR with GPT-4 at 94%.' These are cross-model comparisons: the RFF numbers are for Llama3-8B, while the CR numbers are for GPT-4. The same-model comparison, Llama3-8B RFF(n=5) at 89% and 9.9 visited states versus Llama3-8B CR(n=5) at 19% and 89.8 visited states, is not matched in accuracy or compute, so it cannot by itself establish that RFF is more efficient at equal accuracy. The 'visited states' metric is also defined only as counting each branch as a visit state; the paper should specify exactly how RFF's backtracking steps in Algorithm 1, lines 7-14, and CR's sub-question steps are counted, and should report the distribution of visited states, not just the mean.","section":"§4.1, Table 1"},{"comment":"No error bars, confidence intervals, or significance tests are reported anywhere. Game of 24 is run 100 times, but no standard deviation or seed list is given; the math and commonsense experiments are run greedily once per item, so differences on the order of 2-4 points (e.g., Llama3-8B ASDiv RFF 86.7% vs Least-to-Most 84.4%, or CommonQA RFF 77.1% vs Give-me-Hint 76.6%) may be within sampling noise. I request variance estimates, such as bootstrap confidence intervals over items or multiple seeds, and, where possible, paired significance tests for the main accuracy comparisons. This is particularly important for Table 2, where several leading entries are separated by only a few percentage points.","section":"§4 (experimental protocol)"},{"comment":"The Pair-vs-Single comparison in Table 5 is the only ablation of the reverse mechanism, and it lacks a forward-only control. It shows that alternating backward and forward steps outperforms generating one long reverse chain (83.8% vs 69.8% on GSM8K), but it does not show that the backward component adds value over a forward-only reasoner that accumulates states and uses the same state checker. The Single Reasoning condition does not include the accumulated-state R() loop, so the comparison conflates directionality with the presence of incremental forward information. A forward-only variant of RFF, using R() and C()/V() but no G(), or with G() replaced by a trivial continuation target, would isolate the reverse-reasoning contribution. This is load-bearing because the paper's stated essence is the reverse mechanism.","section":"Appendix B, §3.2"}],"minor_comments":[{"comment":"The baselines sentence says 'we choose COT, CR, Least-to-Most and CR as our experiment baselines'; this repeats CR and omits Give-me-Hint, even though Give-me-Hint appears in Table 3. Also, the benchmark is called both CommonQA and CommonsenseQA in the section and table.","section":"§4.3"},{"comment":"The pseudocode line 9, 'if j == i then break', is confusing because V() is described as returning the previous state j to revisit when a path is wrong; the condition j == i is not explained. Additionally, Algorithm 2 uses V() in the termination test, while Section 3.3(b) defines the stopping criterion as the state checker C(); the naming should be made consistent.","section":"Algorithm 1"},{"comment":"The introduction says 'We evaluate RFF in five datasets' and then lists Game of 24, GSM8K, ASDiv, SVAMP, and MATH-500, but Section 4.3 adds two commonsense benchmarks and Section 4.5 adds GSM-Symbolic; the dataset counts and lists should be reconciled.","section":"Abstract and Introduction"},{"comment":"Some entries are missing without explanation: ToT(n=1) has no visited-states value, AoT has no visited-states value for either model, and CoT and ToT rows are only given for GPT-4. Please add footnotes or em-dashes with a legend explaining why certain cells are absent.","section":"Table 1"},{"comment":"The left example computes '10 + 10 - 5 = 15' in response to 'How many fruits in the blanket?', but the question does not state that smaller bananas cease to be fruits. If this is meant to illustrate an erroneous forward chain, the figure should label it as incorrect; otherwise the example is misleading.","section":"Figure 1"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"RFF is a prompt-only reasoning strategy that alternates backward generation of the last step with forward reasoning, keeping an accumulated state and an avoid-attempt memory. The paper is worth reading: the empirical sweep across Game of 24, GSM8K, ASDiv, SVAMP, MATH-500, and two commonsense benchmarks is broad, and the gains on 7B-8B models are consistent and often large (e.g., Llama3-8B on GSM8K 83.8% vs 75.6% CoT; Game of 24 at width 5, 89% vs 19% for CR with far fewer visited states). The robustness checks on GSM-Symbolic and the 5-number Game of 24 strengthen the case. The method is clearly described with algorithms and prompts, and the authors include a candid Limitations section.\n\nThe main soft spot is not the absence of error bars or code, though both are missing and should be supplied. It is that the reverse-step generator G() is never independently measured. The paper claims the accuracy and search-space gains come from goal-oriented reverse reasoning constraining the forward steps, but G() might be doing the hard decomposition itself; the striking state-count reduction could reflect G() guessing the final decomposition rather than the reverse mechanism pruning the search. The Limitations section concedes that the method relies on the model's reverse-thinking ability, but end-to-end accuracy cannot validate that premise because success could come from the accumulated-state prompting and the LLM-based state check. Appendix B shows alternating direction matters, but it does not include a forward-only planner with the same state-accumulation and checker machinery, so the unique contribution of the reverse step is not isolated. That is a real gap, but it is a strengthening-required gap, not a fatal flaw.\n\nAlso, Table 1 mixes GPT-4 and Llama baselines in the same comparison, which reads as misleading until you check the rows, and the paper does not cite existing backward-reasoning and reverse-CoT work. Both are fixable.\n\nOverall: the central claim that alternating backward/forward reasoning helps small LLMs on math and search tasks is plausible and qualitatively supported. The mechanism claim needs more work. I'd send it to a serious referee, asking for code, significance testing, and a controlled comparison that isolates the reverse step.","headline":"A solid, broad empirical paper on alternating backward/forward prompting, but the core mechanism is not isolated because G() is never measured.","tokens_in":14628,"tokens_out":3461,"would_cite":true,"duration_ms":31845,"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":"Reason from Future claims that alternating backward target generation with forward steps reduces search space and improves LLM accuracy on math and search tasks.","keywords":["reason from future","bidirectional reasoning","reverse reasoning","chain-of-thought prompting","search-space reduction","math word problems","Game of 24","small language models"],"falsifier":"Take a fixed set of GSM8K and Game of 24 problems, record every intermediate target proposed by the Last Step Generator, and independently check whether that target is reachable from the current state in one forward transition; if RFF solves problems where a large fraction of proposed targets are invalid, then the reverse step is not doing the goal-steering the paper attributes to it.","tokens_in":13545,"feed_emoji":"🧠","tokens_out":7262,"duration_ms":67564,"temperature":0.7,"pith_summary":"The paper proposes Reason from Future (RFF), a prompting paradigm in which a language model repeatedly looks backward from the goal to propose a plausible previous state, then takes one forward reasoning step toward that state, alternating until the two meet. The authors' claim is that this bidirectional loop gives the model a global, goal-oriented perspective that forward-only chains like CoT lack, so it explores smaller search spaces and makes fewer cumulative errors. On 7B-8B models, they report higher accuracy on GSM8K, SVAMP, ASDiv, MATH-500, and commonsense benchmarks, and in Game of 24 they report high accuracy with a fraction of the visited states of Tree-of-Thought-style search. The load-bearing idea is that the reverse step acts as a planning constraint: the model states the last calculation explicitly, and forward reasoning is steered toward it rather than branching blindly.","feed_headline":"Backward reasoning lifts small-LLM accuracy and shrinks search space","feed_subtitle":"On GSM8K, Llama3-8B goes from 75.6% with CoT to 83.8% with RFF, with fewer states explored in Game of 24.","key_machinery":"The load-bearing mechanism is the alternating pair of generators: the Last Step Generator $G(p_\\theta, S_{i-1}, T_{i-1})$ proposes the state just before the current target and explicitly outputs the transition connecting them, and the Stepwise Forward Reasoner $R(p_\\theta, S_{i-1}, T_i)$ advances the current state toward that target. Two variants handle different problem geometries: RFF-T, for tree-search tasks like Game of 24, records failed attempts to avoid and backtracks through a verifier; RFF-G, for math and commonsense problems, accumulates all computed information into the state and stops when the State Checker decides the target is reachable. The State Checker $C(\\cdot)$ is what turns the loop from open-ended generation into a bounded, goal-constrained search.","core_discovery":"The central discovery is that reverse reasoning is not just a one-time planning pass; it is an iterative state-transition mechanism. RFF maintains a current solution state and a target state, and at each round the Last Step Generator derives a tighter pre-target state from the goal, the Stepwise Forward Reasoner advances one step toward that pre-target, and the State Checker stops when the states coincide; for tree-like problems a verifier backtracks from incorrect branches. Because the backward step must explicitly state the transition between pre-target and target, the model is forced to identify the core logical relation before computing, which the paper argues is why the search space collapses and error accumulation is reduced. The authors report that this pattern holds across search-tree tasks, directed-acyclic-graph math problems, and commonsense benchmarks, with the largest observed gains on smaller 7B-8B models.","pith_inferences":["If the Last Step Generator can be made reliable through fine-tuning or reinforcement learning, RFF-style alternating reasoning could become a decoding-time strategy for long-horizon planning tasks beyond math and the 24 game.","The paper does not report standalone accuracy for the Last Step Generator; logging every proposed backward target and checking reachability would reveal whether the gains come from reverse planning itself or merely from the extra computation the alternating loop performs.","RFF's framing of reasoning as alternating state transitions suggests a testable extension to tasks where each reverse step must name a resource or precondition, such as program synthesis or tool-use planning.","The robustness on semantically transformed GSM8K variants hints that goal-anchored reasoning may generalize better under distribution shift than forward-only token-by-token calculation, a claim worth testing on other shifted benchmarks."],"forward_implications":["On GSM8K, RFF raises Llama3-8B accuracy from 75.6% with CoT to 83.8%, and Qwen2.5-7B from 87.2% to 89.5%.","In Game of 24, RFF at width 5 reaches 89% accuracy on Llama3-8B while visiting 9.9 states, versus Cumulative Reasoning at 19% with 89.8 states.","In the redundant-number Game of 24 experiment, RFF still solves 85% of five-number puzzles with 28.62 visited states, while Cumulative Reasoning falls to 26% with 96.56 states.","On GSM-Symbolic variants, RFF keeps a higher and more concentrated accuracy distribution than CoT across 50 transformed versions of GSM8K questions.","Because RFF's state checker stops early when the forward state meets the backward target, it avoids the overthinking that hurts progressive-hint baselines on easy questions."],"supporting_citations":[{"why":"Introduces Chain-of-Thought prompting, the primary forward-only baseline RFF compares against and builds from.","marker":"Wei et al. (2022)"},{"why":"Supplies Tree-of-Thought and the Game of 24 benchmark and protocol used in RFF's search experiments.","marker":"Yao et al. (2024)"},{"why":"Cumulative Reasoning is a key progressive-hint baseline for both math and Game of 24 comparisons.","marker":"Zhang et al. (2023)"},{"why":"Provides the GSM8K dataset, the main math word problem benchmark in the accuracy tables.","marker":"Cobbe et al. (2021)"},{"why":"Provides MATH-500, included in the math benchmark accuracy comparisons.","marker":"Lightman et al. (2023)"},{"why":"Provides the GSM-Symbolic transformed benchmark used to test RFF's robustness on question variants.","marker":"Mirzadeh et al. (2024)"},{"why":"Least-to-Most is a baseline whose one-time plan-then-solve structure RFF contrasts with its iterative backward planning.","marker":"Zhou et al. (2022)"},{"why":"Give-me-Hint is a hint-based baseline in the math and commonsense evaluations.","marker":"Agrawal et al. (2024)"}],"fun_headline_variants":["Reverse reasoning reduces search space and boosts LLM scores","Backward chains help small LLMs outthink forward CoT","Thinking backward makes LLMs accurate with fewer steps","Future-driven reasoning solves tasks with less exploring","Reverse thought chain: better accuracy, smaller search"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything depends on the Last Step Generator reliably naming a valid pre-target state and an explicit transition each round; the paper itself states in its Limitations section that the model was not trained for reverse thinking and that rare backward-step errors can cause failure.","fun_headline_variants_meta":{"raw":{"variants":["Reverse reasoning reduces search space and boosts LLM scores","Backward chains help small LLMs outthink forward CoT","Thinking backward makes LLMs accurate with fewer steps","Future-driven reasoning solves tasks with less exploring","Reverse thought chain: better accuracy, smaller search"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000312,"raw_usage":{"total_tokens":1747,"prompt_tokens":892,"completion_tokens":855,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":508,"completion_tokens_details":{"reasoning_tokens":781}},"tokens_in":508,"tokens_out":855,"duration_ms":9532,"temperature":1.0,"reasoning_tokens":781,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:57:17.583972+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a fixed set of GSM8K and Game of 24 problems, record every intermediate target proposed by the Last Step Generator, and independently check whether that target is reachable from the current state in one forward transition; if RFF solves problems where a large fraction of proposed targets are invalid, then the reverse step is not doing the goal-steering the paper attributes to it.","supporting_citations":[],"review_version":1}