Reasoning Beyond Limits: Advances and Open Problems for LLMs

In plain words

Newer language models can be trained to think through a problem in steps before answering, instead of replying straight away. This survey looks at the models and training methods behind that ability over 2023 to 2025. It covers 27 recent models, from small ones to very large open ones, and it groups the methods for teaching step-by-step reasoning. Those methods include learning from rewards, learning from preference pairs, mixing expert sub-networks, looking up documents while reasoning, and spending more compute at answer time.

The survey also reviews two side topics. One is models that work well in languages other than English. The other is a newer kind of network, the state space model, which handles very long inputs more cheaply than standard attention. The last part lists open problems, such as reasoning without human-labelled steps and keeping long chains of steps from breaking down.

The paper runs one experiment of its own: it asks 12 models a set of questions that need tools. Everything else is a summary of other people's work.

TL;DR

A review, not a method. It tabulates 27 LLMs (2023 to 2025), surveys multilingual LLMs and state-space models, and organises training methods for reasoning into groups with short descriptions. Its one original result is a count of correct, incorrect and skipped answers on the authors' DIA benchmark §3.25. Use it as an entry point and a list of sources. Do not take its quoted numbers as results of this paper.

Problem

Reasoning models produce long chains of intermediate steps. The survey says these chains can overthink, and that an error in one step, caused by a gap in knowledge, can carry into later steps §1. It names inference-time scaling, pure reinforcement learning, supervised fine-tuning followed by reinforcement learning, and distillation as the main ways to build such models §1 §8. It asks how to get multi-step reasoning without human supervision, how to make chained tasks more robust, how to balance structured output with flexible reasoning, and how to combine long-context retrieval with external tools §1 §7.

Method

The paper has no algorithm of its own. Its structure is:

• Introduction and contributions: a list of 27 models, multilingual and SSM overviews, a grouped survey of training methods, and a challenges section §1 fig. 2.
• Related surveys, compared in a table on coverage (training methods, models, challenges) §2 tab. 1.
• Top 27 LLMs, each with a short description; two summary tables give the parameters, headline metrics, innovations and a note for each §3 tab. 2 tab. 3. The DeepSeek-R1 training pipeline is shown as a figure §3.4 fig. 3.
• Multilingual LLMs: one table of works on reasoning alignment, translation, instruction tuning and architecture §4 tab. 6.
• State-space models: Mamba and nine derived or hybrid models §5 tab. 7.
• Training methods, in two grouped tables. Groups 1 to 6 cover general training, MoE and architecture, retrieval, reasoning-trace methods, test-time compute and distillation, and miscellaneous tools. Group 7 covers reinforcement learning §6 tab. 4 tab. 5.
• Challenges and open problems, one subsection per question, with a summary table §7 tab. 8.
• Conclusion §8.

Key formulas, as the survey prints them. Check each against its original paper before implementing (see Pitfalls):

• LoRA update: the weight change is a scaled product of two low-rank factors, with scale α/r §6.2 eq. 1.
• Sparse MoE output: a gate-weighted sum over experts, where only the top-k gates are non-zero §6.6 eq. 2.
• Agent Q: the log-probability of a composite action splits into plan, environment and explanation terms §6.1.
• Reward model (Bradley-Terry) loss and KL-regularised RLHF objective §6.10.3.
• PPO clipped objective §6.10.14.
• Group-relative advantage, normalised over sampled completions §6.10.21 eq. 9.
• DPO loss, as printed §6.10.16.
• APO-zero and APO-down losses §6.10.1.
• Chain-of-retrieval losses for sub-queries, sub-answers and final answer §6.11.1.
• Scaled dot-product attention, and a block-wise softmax sketch of FlashAttention §6.17.

# Group-relative advantage, as printed in DAPO eq. 9  [§6.10.21] [eq. 9]
# Input:  prompts (B,), group size G (not stated), reward function
# Output: advantages (B, G)

def group_advantages(prompts, policy, reward_fn):
    # 1. Sample G completions per prompt from the current policy  [§6.10.15]
    completions = policy.sample(prompts, num=G)
    # 2. Score each completion with a reward model or verifier  [§6.10.15]
    rewards = reward_fn(prompts, completions)        # (B, G)
    # 3. Normalise within the group. The survey says "over the batch",
    #    so the group reading here is an assumption. See Pitfalls.  [§6.10.21]
    mean = rewards.mean(axis=1, keepdims=True)
    std = rewards.std(axis=1, keepdims=True)
    advantages = (rewards - mean) / std               # (B, G)
    return advantages

Hyperparameters

The survey trains and evaluates no model of its own, so this table lists only values it quotes from cited work. Values not given in the survey are marked "not stated".

Results

Author-reported. This is a review, so every row except the DIA benchmark is quoted from the cited work under that work's own setup. The "Baseline" column gives the comparison the survey names, or "not stated".

DIA benchmark (the survey's own run; 12 models). Counts are as the text reports them. Scoring rules are not stated §3.25 fig. 4.

Paper vs code

No official code. The paper has no code link in its body, and the abstract gives none. A GitHub repository search on the title words returned only unrelated repositories. The survey implements nothing, and the methods it cites have their own papers and code, which this card does not cover.

Pitfalls

• Quoted numbers are not this paper's results. Every row of the Results table except the DIA counts comes from another paper's setup. The survey does not re-run them or check them §1.
• No selection method. The paper does not state how the "top 27" models were chosen, nor how the training methods were searched or included §1 tab. 2 tab. 3. The coverage table scores the survey against others, but gives no search protocol §2 tab. 1.
• Self-citation. The DIA benchmark is by Tihanyi and others, and the survey has Tihanyi as a co-author §3.25 fig. 4. The paper's only original data comes from that benchmark. The survey also cites a cybersecurity survey by its first author §2. Check the DIA design yourself before relying on its ranking.
• DIA counts. The text gives the counts but not the scoring rule or the prompt or tool setup. The CS and security row for Gemini 2.5 Pro sums to 503, not 505 as the other rows do. The DeepSeek-R1 CS correct count is a range in the text, not a single number. Codegemma and Mistral-NeMo CS counts are given as a range §3.25.
• Figure and model details can be mixed up. The Qwen2.5-VL entry describes Qwen2-VL's features (Naive Dynamic Resolution, M-RoPE) and gives Qwen2-VL sizes of 2B, 8B and 72B, under the Qwen2.5-VL heading. The table gives Qwen2.5-VL sizes as 3B, 7B and 72B §3.5 tab. 2. Take Qwen2.5-VL facts from its own paper.
• Attribution of efficiency claims. FP8 quantisation with a 75% memory cut, and MTP with 2 to 3 times faster generation, are listed under DeepSeek-R1 §3.4. FP8 training is listed under DeepSeek-V3 §3.13. The survey does not say which report each number comes from. The MTP architecture details in §6.9 (cross-depth residuals, depth-aware loss weighting, depth-conditioned routing, and the 22%, 1.5 times and 18% figures) carry no more specific citation. Treat them as unverified here.
• Prices and dates. Model prices (for example Amazon Nova, $0.035 to $3.20 per million tokens) are quoted without a date §3.19 tab. 3. Check them before use.
• Reasoning about the equations. Each item below is a fault in the printed formula, not a claim about the original method. Check the original paper before implementing:
  • DPO §6.10.16. The printed loss has no β and no sigmoid. As printed, minimising it can be driven without bound by raising the winning log-ratio, so it cannot be the intended loss. Use the original DPO form.
  • APO-down §6.10.1. As printed, it is −σ(r_w) − σ(r_l). Minimising it raises σ(r_l), which is the opposite of the text, where the losing output should be pushed down.
  • GRPO KL §6.10.15. The estimator E[π_θ/π_ref − 1] under π_ref has expectation 0 when the supports match, so it cannot estimate the KL divergence. The survey also contradicts itself: §3.14 says GRPO puts a KL term in the loss, while §6.10.15 says it does not add an explicit KL penalty.
  • DAPO §6.10.21, eq. 9. The clip bounds are written as an interval inside the min, and the printed condition 0 < |o_i| < G is a length check, not the dynamic-sampling filter the text describes. The text says the advantage statistics are computed "over the batch", but the pseudocode above uses the group.
  • iLR-DPO §6.10.17. The equation is a gradient expression, not a loss. The sign of α and the length-margin definition in the penalty term are not fully stated. The values of β and α are not stated.
  • LoRA initialisation §6.2. The text says "common practice initializes A and B to zero". With both factors zero, both gradients are zero at the first step, so the sentence cannot be literal. Check the LoRA paper.
  • Block-wise softmax §6.17. The FlashAttention sketch normalises each block on its own and omits the running-maximum rescaling needed to combine blocks. It is not the full online softmax. Use the original algorithm.
  • Attention scale §6.17. The text says √d, where d is the model's hidden dimension. The MLA formula in §6.7 uses the per-head dimension d_h for the same scale, which suggests per-head, but the survey does not state it.
• Thin descriptions. Several entries describe a method in one or two sentences, for example the Learn-by-interact and Mind Evolution summaries. Some subsections of the training methods (for example CoALA §6.3) name the framework without giving its equations. Read the original paper for any method you intend to implement.
• Open problems are opinions. The challenges section states open questions and proposed directions. These are the authors' views, not findings §7.

Lineage

• Builds on: the transformer and self-attention §6.17; chain-of-thought prompting §6.15; RLHF and PPO as cited in §6.10.3 and §6.10.14; DPO §6.10.16; GRPO, from DeepSeekMath §6.10.15.
• Compared against: nine related surveys on post-training, reasoning, RL, cybersecurity and agent evaluation §2 tab. 1.
• Superseded by: not stated.