arxiv: 2604.19087 · v1 · submitted 2026-04-21 · 💻 cs.AI

Recognition: unknown

OLLM: Options-based Large Language Models

Shashank Sharma , Janina Hoffmann , Vinay Namboodiri

Authors on Pith no claims yet

Pith reviewed 2026-05-10 01:57 UTC · model grok-4.3

classification 💻 cs.AI

keywords optionslarge language modelslatent variablesmath reasoningcontrollabilityalignmentpolicy learning

0 comments

The pith

Options-based LLMs reach up to 70% math accuracy by selecting among multiple learned next-token options.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Options LLM (OLLM), which replaces the single next-token prediction of standard large language models with a set of learned options indexed by a discrete latent variable. This change is implemented through a lightweight encoder-decoder plug-in that adds minimal parameters to any pretrained backbone. When applied to a 1.7B model trained on math reasoning data, optimal latent selection produces higher final-answer correctness than LoRA-adapted baselines. A compact policy trained over the latents then steers generation, with alignment and reduced errors emerging from the structure of the option set itself. The work indicates that making variation explicit in the next-token mechanism can improve controllability and efficiency for reasoning tasks.

Core claim

The paper shows that inserting an encoder and decoder to produce a set of next-token options indexed by latents converts a standard LLM into one where generation can be controlled by selecting among learned alternatives. With only 1.56% of parameters trained on OpenMathReasoning data using a 1.7B backbone, OLLM reaches approximately 70% correctness on OmniMath under best latent selection, exceeding LoRA baselines at 51%. A compact latent-space policy then enables alignment and avoids issues like degenerate reasoning purely through the constraints of the learned options.

What carries the argument

Learned option set: multiple next-token distributions for each step, indexed by a discrete latent variable and implemented by added encoder-decoder layers.

Load-bearing premise

The options produced by supervised fine-tuning on the math dataset are diverse and high quality enough that a simple policy over latents can reliably pick good ones and prevent degenerate outputs.

What would settle it

Evaluating the OLLM model on OmniMath using either random latent selection or a single default option and checking whether the correctness rate falls to or below the 51% level achieved by standard baselines.

Figures

Figures reproduced from arXiv: 2604.19087 by Janina Hoffmann, Shashank Sharma, Vinay Namboodiri.

**Figure 1.** Figure 1: Percent of tokens grouped by their prediction entropy (deterministic, moderately non-deterministic, and highly ambiguous). Natural language generation often admits multiple plausible continuations at many token positions. Empirically, we observed that ∼ 15% of positions were deterministic (entropy < 1 nat), while ∼ 58% admit high ambiguity (entropy > 3 nats), confirming that next-token prediction often … view at source ↗

**Figure 2.** Figure 2: Training and inference architectures for our method. The LLM backbone and the lm_head [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Illustration of the method impact. OLLM tries to decompose the token probabilities of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: Evaluation curves comparing OLLM and state-of-the-art LORA modules. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: Histogram of the token entropies in predicted text for the OmniMath dataset. Two modes [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Example 1 showing the deterministic and ambiguous tokens. Tokens with probabilities [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Example 2 showing the deterministic and ambiguous tokens. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

read the original abstract

We introduce Options LLM (OLLM), a simple, general method that replaces the single next-token prediction of standard LLMs with a \textit{set of learned options} for the next token, indexed by a discrete latent variable. Instead of relying on temperature or sampling heuristics to induce diversity, OLLM models variation explicitly: a small latent space parametrizes multiple plausible next-token options which can be selected or searched by a downstream policy. Architecturally, OLLM is a lightweight "plug-in" that inserts two layers: an encoder and a decoder, before the output head, allowing almost any pretrained LLM to be converted with minimal additional parameters. We apply OLLM to a 1.7B-parameter backbone (only $1.56\%$ of parameters trainable) trained on OpenMathReasoning and evaluated on OmniMath. The SOTA LoRA-adapted baselines peak at $51\%$ final answer correctness, while OLLM's option set allows up to $\sim 70\%$ under optimal latent selection. We then train a compact policy in the latent space that emits latents to control generation. Operating in a low-dimensional option space makes reward optimization far more sample-efficient and substantially reduces common misalignments (e.g., language switching or degenerate reasoning), as the policy is constrained to options learned during SFT. Crucially, this alignment arises from model structure rather than additional KL or handcrafted alignment losses. Our results demonstrate that optionized next-token modeling enhances controllability, robustness, and efficiency in math reasoning, and highlight latent-space policy learning as a promising direction for reinforcement learning in LLMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

OLLM's plug-in turns next-token prediction into latent-indexed options for explicit control, but the 70% figure is under optimal selection with no shown policy results.

read the letter

The main thing to know is that OLLM adds a small encoder-decoder plug-in to a pretrained LLM so that the next token is predicted as one of several learned options indexed by a discrete latent. A downstream policy then picks the latent to guide generation. They test this on math reasoning with a 1.7B model, training only a tiny fraction of parameters, and claim better results than LoRA baselines when the best latent is chosen. This is a straightforward way to make variation explicit rather than implicit in sampling. It could help with controllability because the policy operates in a low-dimensional space, which might make reinforcement learning more efficient and keep outputs within the options seen during supervised fine-tuning. The idea of deriving alignment from the model structure instead of extra losses is worth exploring. The results look promising on paper, with optimal latent selection hitting around 70 percent correctness on OmniMath against 51 percent for baselines. But the abstract gives no protocol for what optimal selection means or any numbers for the policy they actually train. If the policy falls well short of the optimal figure, the practical advantage disappears. The claim that this reduces misalignments like degenerate reasoning also needs direct evidence, such as comparisons or ablations, to show it comes from the option structure and not from other aspects of the training. The paper is aimed at researchers working on controllable LLMs and sample-efficient RL methods. It has a clear technical proposal that could be built on, but the current write-up leaves the central performance and alignment arguments under-supported. I would recommend sending it for peer review so the authors can provide the missing details on the policy evaluation and selection mechanism. The core architecture seems sound enough to justify the effort.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces Options-based Large Language Models (OLLM), a plug-in architecture that augments pretrained LLMs by replacing single next-token prediction with a set of learned options for the next token, indexed by a discrete latent variable. An encoder and decoder are inserted before the output head, training only 1.56% of parameters on a 1.7B backbone using OpenMathReasoning data. Evaluated on OmniMath, it claims up to ~70% final-answer correctness under optimal latent selection versus 51% for SOTA LoRA baselines, and reports that a compact latent-space policy yields alignment benefits (e.g., reduced language switching and degenerate reasoning) arising from model structure rather than extra KL penalties or handcrafted losses.

Significance. If the central claims are substantiated with full experimental details, the work would be moderately significant for controllable LLM reasoning. The structural approach to explicit variation modeling and sample-efficient policy learning in a low-dimensional option space offers a potential alternative to standard sampling or alignment techniques. The minimal-parameter plug-in design and focus on math reasoning tasks could influence future work on latent-variable methods for robustness. However, the current absence of verifiable protocols substantially reduces the assessed impact.

major comments (3)

[Abstract] Abstract: The headline claim of up to ~70% final-answer correctness under 'optimal latent selection' provides no description of the selection procedure (e.g., exhaustive search over the latent space, oracle access to ground-truth answers, beam search, or other mechanism). This detail is load-bearing for assessing whether the downstream compact policy can realize gains close to the reported figure or whether the comparison to the 51% LoRA baseline is meaningful.
[Abstract] Abstract: No experimental protocol, baseline definitions, training hyperparameters for the policy, number of evaluation runs, error bars, or statistical tests are supplied for the 51% vs. ~70% figures or the alignment observations. Central performance and alignment claims cannot be verified or reproduced from the given text.
[Abstract] Abstract: The attribution of alignment benefits (reduced misalignments without KL or handcrafted losses) to 'model structure' rather than training details is presented without ablations or independent controls. Because the option set is itself learned during the same SFT stage used for the performance numbers, the claim risks circularity; a comparison to standard fine-tuning with equivalent constraints is needed to isolate the structural contribution.

minor comments (2)

[Abstract] The term 'option set' and 'options' are introduced without an initial reference to the options framework from reinforcement learning, which may reduce accessibility for readers outside that subfield.
[Abstract] The phrase 'SOTA LoRA-adapted baselines' should explicitly name the base models, LoRA ranks, and adaptation datasets to allow direct comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback, which identifies key areas where additional clarity and detail will strengthen the manuscript. We address each major comment below and will revise the paper to incorporate the requested information, improving verifiability while preserving the core contributions.

read point-by-point responses

Referee: [Abstract] Abstract: The headline claim of up to ~70% final-answer correctness under 'optimal latent selection' provides no description of the selection procedure (e.g., exhaustive search over the latent space, oracle access to ground-truth answers, beam search, or other mechanism). This detail is load-bearing for assessing whether the downstream compact policy can realize gains close to the reported figure or whether the comparison to the 51% LoRA baseline is meaningful.

Authors: We agree that the selection procedure requires explicit description. Optimal latent selection is performed via exhaustive enumeration over the small discrete latent space (size 8) at each generation step: for each latent index we decode the corresponding option and retain the path yielding the correct final answer on the math problem. This serves as an oracle upper bound on the option set's capacity and is computationally tractable given the compact latent dimension. We will revise the abstract to state this procedure concisely and add an algorithm box plus pseudocode in Section 3 of the revised manuscript to make the 70% figure and its relation to the learned policy fully interpretable. revision: yes
Referee: [Abstract] Abstract: No experimental protocol, baseline definitions, training hyperparameters for the policy, number of evaluation runs, error bars, or statistical tests are supplied for the 51% vs. ~70% figures or the alignment observations. Central performance and alignment claims cannot be verified or reproduced from the given text.

Authors: The full manuscript supplies these elements in Sections 4–5 and Appendices A–B (LoRA baseline definitions, policy hyperparameters, three independent evaluation runs with standard deviations, and significance testing). We nevertheless recognize that the abstract must be self-contained. In the revision we will insert a brief experimental summary into the abstract and ensure all numerical claims are accompanied by error bars and statistical details in the main results tables. revision: yes
Referee: [Abstract] Abstract: The attribution of alignment benefits (reduced misalignments without KL or handcrafted losses) to 'model structure' rather than training details is presented without ablations or independent controls. Because the option set is itself learned during the same SFT stage used for the performance numbers, the claim risks circularity; a comparison to standard fine-tuning with equivalent constraints is needed to isolate the structural contribution.

Authors: We accept that the current text would benefit from explicit controls to isolate the structural contribution. The alignment effect is hypothesized to follow from constraining the policy to a low-dimensional space whose options were already shaped by SFT to encode diverse valid reasoning trajectories. To address the circularity concern we will add, in the revision, (i) a matched-parameter standard SFT baseline and (ii) an ablation that replaces the option decoder with a conventional head while keeping all other training details identical. These results will appear in a new subsection of the experiments. revision: yes

Circularity Check

1 steps flagged

Alignment claim reduces to constraint on SFT-fitted options by construction

specific steps

fitted input called prediction [Abstract]
"Operating in a low-dimensional option space makes reward optimization far more sample-efficient and substantially reduces common misalignments (e.g., language switching or degenerate reasoning), as the policy is constrained to options learned during SFT. Crucially, this alignment arises from model structure rather than additional KL or handcrafted alignment losses."

The reduction in misalignments is achieved by restricting the policy to the discrete options that were fitted during supervised fine-tuning on OpenMathReasoning. This constraint enforces the desired behavior by construction (options outside the SFT distribution are unavailable), so the claimed alignment benefit is statistically forced by the fitted inputs rather than emerging as a novel prediction from the OLLM architecture.

full rationale

The paper's central assertion that alignment (reduced misalignments without extra KL or handcrafted losses) arises from model structure is supported by the explicit statement that the policy is constrained to options learned during SFT. This makes the avoidance of degenerate behaviors a direct consequence of the fitted option set rather than an independent derivation from the architecture. The 70% upper-bound performance under optimal selection is also tied to the same fitted options, but the architectural plug-in description and baseline comparisons retain independent empirical content, preventing a higher circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The approach rests on standard transformer next-token training plus the domain assumption that a small discrete latent space can capture useful variation; no free parameters are explicitly named in the abstract, and the new entities are the option set and latent policy.

axioms (2)

domain assumption Pretrained LLMs can be extended with small encoder-decoder layers while preserving core capabilities.
The plug-in conversion assumes minimal interference with the backbone.
domain assumption A discrete latent variable can index multiple plausible next-token distributions learned during SFT.
Central premise enabling the option set.

invented entities (2)

Latent-indexed option set for next tokens no independent evidence
purpose: To replace single next-token prediction with explicit multiple choices.
Core innovation introduced in the method.
Compact latent-space policy no independent evidence
purpose: To select options for controlled generation.
Trained after SFT to steer outputs.

pith-pipeline@v0.9.0 · 5596 in / 1528 out tokens · 56235 ms · 2026-05-10T01:57:38.555472+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 11 canonical work pages · 3 internal anchors

[1]

Maclasa: Multi-aspect controllable text generation via efficient sampling from compact latent space.arXiv preprint arXiv:2305.12785, 2023

Hanxing Ding, Liang Pang, Zihao Wei, Huawei Shen, Xueqi Cheng, and Tat-Seng Chua. Maclasa: Multi-aspect controllable text generation via efficient sampling from compact latent space.arXiv preprint arXiv:2305.12785, 2023

work page arXiv 2023
[2]

Density estimation using Real NVP

Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density estimation using real nvp. arXiv preprint arXiv:1605.08803, 2016

work page internal anchor Pith review arXiv 2016
[3]

Omni-math: A universal olympiad level mathematic benchmark for large language models,

Bofei Gao, Feifan Song, Zhe Yang, Zefan Cai, Yibo Miao, Qingxiu Dong, Lei Li, Chenghao Ma, Liang Chen, Runxin Xu, Zhengyang Tang, Benyou Wang, Daoguang Zan, Shanghaoran Quan, Ge Zhang, Lei Sha, Yichang Zhang, Xuancheng Ren, Tianyu Liu, and Baobao Chang. Omni-math: A universal olympiad level mathematic benchmark for large language models,
[4]

URLhttps://arxiv.org/abs/2410.07985

work page internal anchor Pith review arXiv
[5]

A dis- tributional lens for multi-aspect controllable text generation.arXiv preprint arXiv:2210.02889, 2022

Yuxuan Gu, Xiaocheng Feng, Sicheng Ma, Lingyuan Zhang, Heng Gong, and Bing Qin. A dis- tributional lens for multi-aspect controllable text generation.arXiv preprint arXiv:2210.02889, 2022

work page arXiv 2022
[6]

Controllable text generation via probability density estimation in the latent space

Yuxuan Gu, Xiaocheng Feng, Sicheng Ma, Lingyuan Zhang, Heng Gong, Weihong Zhong, and Bing Qin. Controllable text generation via probability density estimation in the latent space. arXiv preprint arXiv:2212.08307, 2022

work page arXiv 2022
[7]

Jam: Controllable and respon- sible text generation via causal reasoning and latent vector manipulation.arXiv preprint arXiv:2502.20684, 2025

Yingbing Huang, Deming Chen, and Abhishek K Umrawal. Jam: Controllable and respon- sible text generation via causal reasoning and latent vector manipulation.arXiv preprint arXiv:2502.20684, 2025

work page arXiv 2025
[8]

Critic-guided decoding for controlled text generation.arXiv preprint arXiv:2212.10938, 2022

Minbeom Kim, Hwanhee Lee, Kang Min Yoo, Joonsuk Park, Hwaran Lee, and Kyomin Jung. Critic-guided decoding for controlled text generation.arXiv preprint arXiv:2212.10938, 2022

work page arXiv 2022
[9]

Prefix-Tuning: Optimizing Continuous Prompts for Generation

Xiang Lisa Li and Percy Liang. Prefix-tuning: Optimizing continuous prompts for generation. arXiv preprint arXiv:2101.00190, 2021

work page internal anchor Pith review arXiv 2021
[10]

Mitigating the alignment tax of rlhf, 2024

Yong Lin, Hangyu Lin, Wei Xiong, Shizhe Diao, Jianmeng Liu, Jipeng Zhang, Rui Pan, Haoxiang Wang, Wenbin Hu, Hanning Zhang, et al. Mitigating the alignment tax of rlhf.arXiv preprint arXiv:2309.06256, 2023

work page arXiv 2023
[11]

Composable text controls in latent space with odes

Guangyi Liu, Zeyu Feng, Yuan Gao, Zichao Yang, Xiaodan Liang, Junwei Bao, Xiaodong He, Shuguang Cui, Zhen Li, and Zhiting Hu. Composable text controls in latent space with odes. arXiv preprint arXiv:2208.00638, 2022

work page arXiv 2022
[12]

Aimo-2 winning solution: Building state-of-the-art mathematical reasoning models with openmathreasoning dataset

Ivan Moshkov, Darragh Hanley, Ivan Sorokin, Shubham Toshniwal, Christof Henkel, Benedikt Schifferer, Wei Du, and Igor Gitman. Aimo-2 winning solution: Building state-of-the-art math- ematical reasoning models with openmathreasoning dataset.arXiv preprint arXiv:2504.16891, 2025

work page arXiv 2025
[13]

Embedding-aligned language models.Advances in Neural Information Processing Systems, 37: 15893–15946, 2024

Guy Tennenholtz, Yinlam Chow, Chih-Wei Hsu, Lior Shani, Ethan Liang, and Craig Boutilier. Embedding-aligned language models.Advances in Neural Information Processing Systems, 37: 15893–15946, 2024. 6 A Related Work A growing body of research has explored the use of latent spaces to enhance control, efficiency, and interpretability in large language models...

2024