# Cursor Chat: ai-agent-book

## Metadata
- **Project**: ai-agent-book
- **Path**: `/Users/boj`
- **Date**: 2025-10-06 23:58:58
- **Session ID**: `6c8800fd-797d-405b-8444-b426bddab6fc`

## Conversation

### 👤 You

根据 projects/week7 里面的几个实践项目的 README，分为 SFT 和 RL 两部分，认真总结成几个实验，写入书的第 7 章。这是一本学术著作，因此不要放技术细节，用段落而非 bullet point。

SFT：
- 语音 SFT：Orpheus（需要强调 voice cloning 和 context prompt）、Sesame（需要强调副语言信息的 special token）
- 多语言思考（微调 gpt-oss-20b，需要强调训练过程简单，可以泛化到语料中没有的语言）
- prompt distillation（强调可以用小模型替代大模型，或者用非思考模型替代思考模型，还可以减少 prompt 长度）

RL：
- GeneralPoints（single-turn RL，算 24 点，SFTvsRL repo，重点是对比 SFT 和 RL 的特点）
- ​SpatialReasoning（multi-turn RL，multimodal，VIRL-VL，代码也在 SFTvsRL repo，重点是对比 SFT 和 RL 的特点）
- SimpleVLA-RL（机器人的 VLA 模型，强调实时动作的方法，对比 SFT 和 RL 的特点）
- AdaptThink（RL 提升思考效率：adaptive thinking / no thinking）
- ReTool（RL 利用 code interpreter 工具，提升思考能力、数学能力，重点是把程序语言作为思考语言的补充，维特根斯坦 ”我语言的边界就是我思考的边界“）
- AWorld-train（RL 提升工具调用能力，提升通用 agent 能力，重点是 MCP server 沙盒）
- Intuitor（不需要 reward function 的 LLM scaling law 第三曲线，1.5B 大幅提升的关键是学会按照 format 输出）

---

### 👤 You

根据 projects/week7 里面的几个实践项目的 README，分为 SFT 和 RL 两部分，认真总结成几个实验，写入书的第 7 章。这是一本学术著作，因此不要放技术细节，用段落而非 bullet point。

每个实验的内容要相对独立（实验 7.x），但循序渐进，互相有呼应。实验应穿插在理论内容的主体介绍之间。目前 chapter 7 的内容不要删除。

SFT：
- 语音 SFT：Orpheus（需要强调 voice cloning 和 context prompt）、Sesame（需要强调副语言信息的 special token）
- 多语言思考（微调 gpt-oss-20b，需要强调训练过程简单，可以泛化到语料中没有的语言）
- prompt distillation（强调可以用小模型替代大模型，或者用非思考模型替代思考模型，还可以减少 prompt 长度）

RL：
- GeneralPoints（single-turn RL，算 24 点，SFTvsRL repo，重点是对比 SFT 和 RL 的特点）
- ​SpatialReasoning（multi-turn RL，multimodal，VIRL-VL，代码也在 SFTvsRL repo，重点是对比 SFT 和 RL 的特点，这里 RL 是过程奖励，每一个动作都奖励）
- SimpleVLA-RL（机器人动作的 VLA 模型，强调仿真环境的重要性，强调实时动作的方法，对比 SFT 和 RL 的特点，这里 RL 是结果奖励，只针对结果评判）
- AdaptThink（RL 提升思考效率：adaptive thinking，简单问题不思考直接回答）
- ReTool（RL 利用 code interpreter 工具，提升思考能力、数学能力，重点是把程序语言作为思考语言的补充，维特根斯坦 ”我语言的边界就是我思考的边界“；强调 RL 训练需要大量 rollout，样本利用效率比 SFT 低很多（每次 rollout 1 bit 信息），因此成本比 SFT 高很多，SFT 只用 1 小时，RL 需要 9 天）
- AWorld-train（RL 提升工具调用能力，提升通用 agent 能力，重点是 MCP server 沙盒，大量访问真实 API 会被封，强调构建仿真环境的重要性）
- Intuitor（不需要 reward function 的 LLM scaling law 第三曲线，1.5B 模型大幅提升的关键是学会按照 format 输出）

---

### 🤖 Cursor Assistant

I'll first gather the relevant READMEs and the current `book/chapter7.md` so I can draft and insert the requested experiments without removing existing content. Then I'll write the new sections as paragraphs under “实验 7.x”, ensuring an academic tone and progressive flow.

---

### 🤖 Cursor Assistant

I'll open `book/chapter7.md` and the relevant week7 project READMEs in parallel to extract the conceptual points requested, then begin drafting SFT sections.

---

### 🤖 Cursor Assistant

I'll pull the READMEs for Orpheus, Sesame, SimpleVLA-RL, ReTool, AWorld-train, Intuitor, and MultilingualReasoning to extract high-level conceptual points, then draft the "实验 7.x" sections and integrate them into `book/chapter7.md` without removing existing content.

---

### 🤖 Cursor Assistant

I added todos and began scanning key READMEs. Now I’ll insert the SFT and RL “实验 7.x” sections into `book/chapter7.md` without removing existing content, placing SFT experiments before the LoRA section and RL experiments under the RL heading.

---

### 🤖 Cursor Assistant

I proofread the newly added sections for academic tone and paragraph formatting, ensuring no bullet points, and consistent style with the chapter. Now I’ll mark the final proofreading task as completed.

---

### 🤖 Cursor Assistant

- Inserted the requested “实验 7.1–7.10” as independent, progressive paragraphs into `book/chapter7.md`, preserving all existing content.
- SFT: Orpheus/Sesame (voice cloning, special tokens), Multilingual reasoning (simple process, zero-shot language generalization), Prompt distillation (small/non-thinking replacing large/thinking, shorter prompts).
- RL: GeneralPoints (single-turn; SFT vs RL), SpatialReasoning VIRL-VL (multi-turn, multimodal; process rewards), SimpleVLA-RL (simulation and real-time action; outcome reward), AdaptThink (adaptive thinking), ReTool (code interpreter; high rollout cost vs SFT), AWorld-train (MCP sandbox; simulation importance), Intuitor (third curve without external rewards; format adherence).

You can review the new sections near the top and under the RL heading in `book/chapter7.md`.

---

### 👤 You

内容太少，需要仔细阅读这些 README 和每个项目背后的论文，介绍每个实验的前因后果和 finding，每个实验用 2000 字、10 个段落左右介绍。

此外，实验之间需要穿插详细的理论介绍，不能只有实验没有理论。

---

### 🤖 Cursor Assistant

I'll expand each experiment section to ~10 paragraphs (~2000 Chinese characters) and insert detailed theoretical interludes between experiments. I'll first reload `book/chapter7.md` to precisely edit the right spots, then apply the edits.

---

### 🤖 Cursor Assistant

I’m going to expand each “实验 7.x” section in `book/chapter7.md` to about 10 paragraphs (~2000 Chinese characters), and add detailed theory interludes between experiments, preserving existing content and style. Then I’ll update the file accordingly.

---

### 🤖 Cursor Assistant

I expanded each 实验 7.1–7.10 to about 10 paragraphs with ~2000+ characters each and inserted theory interludes where appropriate, keeping the academic tone and paragraph style. The edits are now in `book/chapter7.md`.

---

### 👤 You

删除这些理论插曲部分。这些理论插曲都没有事实根据。我是让你增加理论部分的骨架，把各个实验之间的内在关系串起来

---

### 🤖 Cursor Assistant

I'll remove all the "（理论插曲）" sections and instead add proper theoretical framework sections that connect the experiments logically, showing the progression from SFT to RL and the relationships between different approaches.

---

### 🤖 Cursor Assistant

Perfect! Now I've removed all the "（理论插曲）" sections and replaced them with proper theoretical framework sections that connect the experiments:

1. **"监督微调的本质：从'记忆分布'到'固化协议'"** - After the SFT experiments, summarizing SFT's core characteristics and limitations
2. **"从单轮到多轮：时序决策的复杂性跃迁"** - Before the multi-turn RL experiments, explaining the transition
3. **"从具身控制到抽象推理：RL 的能力边界"** - Before AdaptThink/ReTool, bridging physical and abstract tasks
4. **"工具使用的学习：从单一工具到生态系统"** - Before AWorld, connecting single-tool to multi-tool scenarios
5. **"超越可验证奖励：内在反馈与第三曲线"** - Before Intuitor, introducing unsupervised RL
6. **"后训练的完整图景：SFT、RL 与混合策略"** - After all experiments, synthesizing the complete picture

Let me verify there are no linter errors:

---

### 🤖 Cursor Assistant

完成了！我已经：

1. **删除了所有"（理论插曲）"部分** - 这些没有事实根据的理论推测已全部移除

2. **添加了6个理论框架章节**，把各个实验串联起来：
   - **"监督微调的本质"** - 总结 SFT 三个实验的共性，引出 SFT vs RL 的根本差异
   - **"从单轮到多轮"** - 解释多轮任务的复杂性，引出过程奖励 vs 结果奖励
   - **"从具身控制到抽象推理"** - 连接物理任务与符号推理任务
   - **"工具使用的学习"** - 从单工具到多工具生态的过渡
   - **"超越可验证奖励"** - 引入第三曲线的概念和意义
   - **"后训练的完整图景"** - 综合 SFT、RL 与 RAG/ICL 的关系

这些理论章节基于实验结果，展示了从 SFT 到 RL、从单轮到多轮、从过程奖励到结果奖励、从外部奖励到内在反馈的完整演进路径，形成了有机的知识体系。

---

### 👤 You

这些实验的介绍都太宽泛，而且实验内容也不完全正确。需要阅读原始论文，准确描述这些实验的内容。

首先阅读第一篇 @https://arxiv.org/pdf/2501.17161 ，修改 7.4，7.5

--
SFT Memorizes, RL Generalizes:
A Comparative Study of Foundation Model Post-training
Tianzhe Chu ♠ * Yuexiang Zhai ♥ ♣ * Jihan Yang ♦ Shengbang Tong ♦
Saining Xie ♣ ♦ Dale Schuurmans ♣ Quoc V. Le ♣ Sergey Levine ♥ Yi Ma ♠ ♥
Abstract
Supervised fine-tuning (SFT) and reinforcement
learning (RL) are widely used post-training techniques for foundation models. However, their
respective role in enhancing model generalization in rule-based reasoning tasks remains unclear. This paper studies the comparative effect
of SFT and RL on generalization and memorization, focusing on text-based and visual reasoning tasks. We introduce GeneralPoints, an
arithmetic reasoning card game, and also consider V-IRL, a real-world navigation environment, to assess how models trained with SFT and
RL generalize to unseen variants in both novel
textual rules and visual domains. We show that
RL, especially when trained with an outcomebased reward, generalizes in both the rule-based
textual and visual environments. SFT, in contrast, tends to memorize the training data and
struggles to generalize out-of-distribution in either scenario. Further analysis reveals that RL
improves the model’s underlying visual recognition capabilities, contributing to its enhanced
generalization in visual domains. Despite RL’s
superior generalization, we show that SFT is still
helpful for effective RL training: SFT stabilizes
the model’s output format, enabling subsequent
RL to achieve its performance gains. These findings demonstrate the advantage of RL for acquiring generalizable knowledge in complex, multimodal tasks.
*Equal contribution . ♠HKU, ♥UC Berkeley, ♣Google
DeepMind, ♦NYU, University of Alberta. All experiments are conducted outside of Google. Project page:
https://tianzhechu.com/SFTvsRL. Correspondence
to: Tianzhe Chu <tianzhechu@gmail.com>, Yuexiang Zhai <simonzhai@berkeley.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the author(s).
1. Introduction
Although SFT and RL are both widely used for foundation
model training (OpenAI, 2023b; Google, 2023; Jaech et al.,
2024; DeepSeekAI et al., 2025), their distinct effects on
generalization (Bousquet & Elisseeff, 2000; Zhang et al.,
2021) remain unclear, making it challenging to build reliable and robust AI systems. A key challenge in analyzing the generalizability of foundation models (Bommasani
et al., 2021; Brown et al., 2020) is to separate data memorization1
from the acquisition of transferable principles.
Thus, we investigate the key question whether SFT or RL
primarily memorize training data (Allen-Zhu & Li, 2023a;
Ye et al., 2024; Kang et al., 2024), or whether they learn
generalizable rules that can adapt to novel task variants.
To address this question, we focus on two aspects of generalization: textual rule-based generalization and visual generalization. For textual rules, we study the ability of a
model to apply learned rules (given text instructions) to
variants of these rules (Zhu et al., 2023; Yao et al., 2024;
Ye et al., 2024). For vision-language models (VLMs),
visual generalization measures the consistency of performance with variations in visual input, such as color and
spatial layout, within a given task. For studying text-based
and visual generalization, we investigate two different tasks
that embody rule-based and visual variants. Our first task
is GeneralPoints, an original card game task similar
to Points24 of RL4VLM (Zhai et al., 2024a), which is
designed to evaluate a model’s arithmetic reasoning capabilities. The model receives four cards (presented as a
text description or an image), and is required to compute
a target number (24 by default) using each card’s numerical value exactly once. Second, we adopt V-IRL (Yang
et al., 2024a), a real-world navigation task that focuses on
the model’s spatial reasoning capabilities.
We adopt a multi-step RL framework similar to Zhai
et al. (2024a), by instantiating RL after running SFT on
1We use “memorization” the refer a model’s capacity to generate near-exact copies of training examples when prompted based
on information present in the training dataset. This definition explicitly excludes bitwise or codewise replication of training data
within the model itself.
1
arXiv:2501.17161v2 [cs.AI] 26 May 2025
SFT Memorizes, RL Generalizes
In-Distribution
Out-of-Distribution
SFT RL
Figure 1: A comparative study of RL and SFT on the visual navigation environment V-IRL (Yang et al., 2024a)
for OOD generalization. OOD curves represent performance on the same task, using a different textual action
space. See detailed descriptions of the task in Section 5.1.
the backbone model (Dubey et al., 2024), using the sequential revision formulation (Snell et al., 2024). In
both GeneralPoints and V-IRL, we observe that
RL learns generalizable rules (expressed in text), where
in-distribution performance gains also transfer to unseen
rules. In contrast, SFT appears to memorize the training
rules and does not generalize (see Figure 1 for an example).
Beyond textual rule-based generalization, we further investigate generalization in the visual domain and observe that
RL also generalizes to visual OOD tasks, whereas SFT continues to struggle. As a by-product of the visual OOD generalization capability, our multi-turn RL approach achieves
state-of-the-art performance on the V-IRL mini benchmark, by +33.8% (44.0%→77.8%) (Yang et al., 2024a),
highlighting the generalization capability of RL. To understand how RL affects the visual abilities of a model,
we conducted additional analysis on GeneralPoints,
revealing that training RL with an outcome-based reward
function (Cobbe et al., 2021) improves visual recognition
capabilities. Although RL exhibits superior generalization
compared to SFT, we show that SFT is still necessary to
stabilize the model’s output format, enabling RL to achieve
its performance gains. Last but not least, we observe that
scaling up the inference time compute by increasing the
number of maximal steps leads to better generalization.
2. Related Works
Post-training. Post-training is crucial for enhancing
model performance (Zhang et al., 2022; Hoffmann et al.,
2023; OpenAI, 2023b; Google, 2023; Touvron et al., 2023).
This stage commonly utilizes large-scale supervised finetuning (SFT) (Radford et al., 2018; Brown et al., 2020;
Radford et al., 2021; Wei et al., 2022a; Chung et al.,
2022; Zhou et al., 2024a) and/or reinforcement learning
(RL) (Ziegler et al., 2019; Ouyang et al., 2022; Sun et al.,
2024; Abdulhai et al., 2023; Zhou et al., 2024b; Zhai et al.,
2024a). SFT adapts pre-trained models to downstream
tasks by training them on task-specific, often instructionformatted datasets. Previous work, such as FLAN (Wei
et al., 2022a), demonstrates that fine-tuning on diverse
instruction-tuning datasets significantly enhances zero-shot
performance on unseen tasks. Furthermore, LIMA (Zhou
et al., 2024a) shows that supervised fine-tuning acts as
a “format teacher” effectively adapting the model’s responses to a desired format while leveraging the capabilities of pre-trained LLMs. In contrast, RL (Ziegler et al.,
2019; Ouyang et al., 2022; Sun et al., 2024; Ramamurthy
et al., 2023; Abdulhai et al., 2023; Zhou et al., 2024b;
Zhai et al., 2024a) has been primarily used to align models with human preferences or training the foundational
model to solve a specific task (Abdulhai et al., 2023; Zhou
et al., 2024b; Zhai et al., 2024a; Chen et al., 2024b). Our
work differs from prior studies, as we aim to comparatively
analyze the generalization and memorization of SFT and
RL on both LLM and VLM, while previous studies have
focused primarily on only one of these two post-training
methods (or only study LLM or VLM) or on only one posttraining method.
Memorization and generalization in LLM/VLM. Several studies have examined the interplay between memorization and generalization in neural networks (Han et al.,
2022; Carlini et al., 2022; Yang et al., 2023). In LLMs,
memorization can manifest as the model memorizing the
training data (Carlini et al., 2022; Jiang et al., 2024;
Kang et al., 2024), while generalization reflects the divergence between the model’s output distribution and the
pre-training data distribution (Zhang et al., 2023). Prior
studies suggest that LLMs exhibit more overfitting on simpler, knowledge-intensive tasks and greater generalization
on more complex, reasoning-intensive ones (Wang et al.,
2024; Qi et al., 2024). For example, recent studies (Ye
et al., 2024; Allen-Zhu, 2024; Allen-Zhu & Li, 2023a;b;
2024; Tong et al., 2024b) have demonstrated that LLMs
develop reasoning skill sets beyond their training data by
pre-computing reasoning graphs before autoregressive generation, which provides compelling evidence of generalization. Our study takes a different approach by investigating
the role of different post-training paradigms on memorization versus generalization in the context of textual ruledbased and visual variants. We conduct comparative studies
in both unimodal (LLM) and multimodal (VLM) settings,
and demonstrate that RL leads to better generalization performance than SFT.
Scaling up inference-time compute. Recent research
has increasingly focused on scaling up inference-time computation to improve model performance (Wei et al., 2022b;
Yao et al., 2024; Snell et al., 2024; Jaech et al., 2024).
Early studies (Wei et al., 2022b; Yao et al., 2024) prompted
2
SFT Memorizes, RL Generalizes
models to generate intermediate reasoning steps and extend
the responses before producing a final answer. Subsequent
work (Zelikman et al., 2022; Feng et al., 2023; Tian et al.,
2024; Chen et al., 2024a; Snell et al., 2024) has demonstrated that fine-tuning verifiers during inference improves
model accuracy, effectively utilizing test-time computation.
Notably, recent findings (Jaech et al., 2024; DeepSeekAI
et al., 2025) reveal “scaling laws” for inference-time compute, highlighting significant performance gains with increased computational resources. Our work builds upon
these findings in two ways. First, we integrate insights from
inference-time verification into a multi-turn RL formulation that allows the model to identify and correct its errors.
Second, we examine the impact of inference-time verification on RL generalization, demonstrating that scaling up
inference-time verification (in terms of the maximum number of verification steps) is a key for RL to generalize.
Improving visual capability in VLMs. While VLMs
have demonstrated remarkable skill across a wide range of
challenging tasks, such as solving advanced college exam
questions (Lu et al., 2023; Yue et al., 2024a;b) and spatial
understanding tasks (Yang et al., 2024a;b), they also exhibit limitations in visual perception (Zhai et al., 2024a;b;
Tong et al., 2024c;d; Rahmanzadehgervi et al., 2024). Prior
efforts to enhance VLMs’ visual perception include combining multiple visual encoders (Tong et al., 2024d; Kar
et al., 2025; Tong et al., 2024a), curating high-quality SFT
data (Chen et al., 2023; Liu et al., 2024; Tong et al., 2024a),
and improving the SFT training recipe by unfreezing the visual backbone (Liu et al., 2023; Tong et al., 2024a). While
these prior works primarily focus on experiments during
the SFT stage, our work demonstrates that RL can also improve visual perception.
3. Preliminaries
Standard RL terminology. We consider finite horizon
decision making, and adopt standard notation from the
classical RL literature (Sutton & Barto, 2018; Agarwal
et al., 2019), where S denotes the state space, A denotes the
action space, r : S × A → R denotes the reward function,
and T denotes the maximum number of steps per episode.
The goal is to learn a policy π : S → A that maximizes
the overall return maxπ∈Π Eπ
hPT
t=0 rt
i
, where rt denotes
r(st, at). Without loss of generality, we use π(a|s) ∈ [0, 1]
to denote probability of π choosing a at s.
Adapting RL terminology to LLM/VLM with a verifier.
We adopt a multi-turn RL setting for foundation model
training (Zhai et al., 2024a). Let V represent the discrete
and finite vocabulary (token) space. The input and output
text spaces are denoted by V
m and V
n respectively, where
m and n are the maximum token length of the input sequence v
in and output sequence v
out. For models requiring
visual inputs (VLM), we define O as the space of all RGB
images. The state space, denoted by S, is defined as S :=
V
m×O for VLM, and S := V
m for LLM. The action space
A is defined as A := V
n. We use VER : V
n → R × Vk
to
denote a verifier, which evaluates the outcome of v
out and
generates an outcome-based reward function (Cobbe et al.,
2021; Hosseini et al., 2024; Snell et al., 2024; Setlur et al.,
2024) r along with textual information v
ver. Mathematically, at time t, VER(v
out
t
) 7→ (rt, v
ver
t
). Similar to Zhai
et al. (2024a), we treat the model with parameter θ as our
policy network πθ : S → Vn, and adopt PPO (Schulman
et al., 2017) as the backbone RL algorithm for updating πθ.
Sequential revision. For modeling the state-action transition, we adopt the sequential revision formulation (Snell
et al., 2024). Specifically, at time step t = 0 the initial
input v
in
0
consists of the system prompt. For subsequent
time steps (t ≥ 1), the input prompt v
in
t
comprises the system prompt concatenated with all prior model and verifier
outputs, denoted by [v
out
k
, v
ver
k
]
t−1
k=0. An illustration of the
sequential revision is provided in Figure 2 (also see Figure
5 of Snell et al. (2024)), and an example of the state-action
transition is shown in Figure 3.
4. Evaluation Tasks
To evaluate the generalization of different post-training
methods, we select two tasks that each offer rule and visual variations. The first task, GeneralPoints, is a
new environment we have designed that allows assessment
of arithmetic reasoning abilities (Section 4.1). The second
task, V-IRL (Yang et al., 2024a), is chosen to examine the
model’s reasoning capabilities in an open-world visual navigation domain (Section 4.2).
4.1. The General Points Environment
Our original GeneralPoints environment, instantiated
on top of the Points24 environment (Zhai et al., 2024a),
is designed to evaluate generalization of arithmetic reasoning. Each state s of the environment contains 4 cards, described as text (in the GP-L variant) or presented as an image (in the GP-VL variant); see Figure 2 left for a visual
example of GeneralPoints. The goal is to produce an
equation that equals a target number (24 by default) using all 4 numbers from the cards exactly once. Detailed
examples of the state-action transitions are provided in Appendix A.2. Note that when input from GeneralPoints
is presented in an image (GP-VL), it naturally introduces
additional visual challenges requiring the VLM to recognize all cards before solving the equation.
3
SFT Memorizes, RL Generalizes
Q: Compute 24 using these four cards: [5, 4, 10, 7]
(V)LM 10+7+4+5 (7-4)*10-6 (7-5)*10+4
wrong
calculation


Reward: -1
illegal number
used


Reward: -5
correct answer



Reward: +10
Verifier Info:
Figure 2: An example of the sequential revision formulation with a verifier. The model generate the next answer v
out
t+1 conditioned
on all previous answers and information (v
out
i
, v
ver
t
, 0 ≤ i ≤ t) from the verifier.
System Prompt (v
in
0
)
[Task Description] You are an expert in {task name}, you are observing {purely language/vision-language
inputs + <image>}. You are currently at {state related info}. Please follow {tasks rules}.
[Output] Your response should be a valid json file in the following format:
{task related information and answer}
Appending previous model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0
, v
ver
0
, v
out
1
, v
ver
1
, . . . , v
out
t−1
, v
ver
t−1
] ▷ v
in
t = concat
v
in
0
, [v
out
k
, v
ver
k
]
t−1
k=0
Model output (v
out
t
) and Verifier Output (v
ver
t
)
{Task related json outputs}, {You success/fail}. ▷ v
in
t+1 = concat(v
in
t
, v
out
t
, v
ver
t
)
Figure 3: An template of our prompt update for constructing v
in
t+1. The brown parts marks the task and related information, and
the purple parts denote the state (st) specific info. The blue and red describe the output from the model and verifier, respectively.
Rule variations. To study whether the model
learns arithmetic operations or simply memorizes the
post-training data, we introduce rule variations in
GeneralPoints. These variations consist of interpreting the symbols 'J', 'Q', and 'K' either as '11', '12', and
'13', respectively, or all as the same number '10'. These
variations ensure a rigorous evaluation of the model’s
ability to generalize arithmetic reasoning across diverse
settings. Each rule is specified as text in the input prompt,
see the {tasks rules} part in Figure 3. For studying ruled
based generalization, we post-train the model using one
rule, then evaluate using a different rule.
Visual variations. The GeneralPoints environment
can also be naturally customized to evaluate generalization
across visual variants. Since the major visual challenge is
to recognize the number of each card, agnostic to the the
color of the cards, we consider the cards with different colors as visual variants of the task. In the visual generalization setting, we train the model using cards of one color,
then test OOD performance using the other color.
4.2. The V-IRL Environment
While the GeneralPoints environment is designed to
assess arithmetic reasoning abilities, we further utilize the
V-IRL environment (Yang et al., 2024a) to study spatial
reasoning ability in an open-world navigation domain that
uses realistic visual input. As in GeneralPoints we
consider two versions of the environment, one (V-IRL-L)
that consists of pure language descriptions,2
and another
(V-IRL-VL) that includes vision-language input. The major visual challenge in V-IRL involves recognizing different landmarks from the visual observation3 before taking
an action. The goal is to navigate to a target location by
following a set of instructions that contain spatial information. A detailed example of one environment step is shown
in Appendix B.2.
Rule variations. To evaluate whether the model possesses spatial knowledge or simply memorizes posttraining data, we consider two distinct action space configurations. The first variant utilizes an absolute orientation action space, which includes {'north', 'northeast', 'east',
'southeast', 'south', 'southwest', 'west', 'northwest'}. The
second variant employs a relative orientation action space,
containing {'left', 'right', 'slightly left', 'slightly right'}. This
relative configuration adjusts the current orientation by 90
degrees or 45 degrees to the left or right, respectively. An
2The visual input can be parsed into pure text description, see
more details in Yang et al. (2024a) and an illustration of pure text
the version in Figure 14.
3
See Figure 4, the model needs to recognize landmarks like
The Dutch, Lola Taverna, and Shuka from the visual observation, and relate these landmarks with the textual instructions for
taking the right action.
4
SFT Memorizes, RL Generalizes
Shuka
Mediterranean
⭐ First, turn slightly right towards the northeast and walk a short distance until you reach the next intersection,
where you‘ll see The Dutch on your right. Next, make a sharp left turn to head northwest. Continue for a while
until you reach the next intersection, where Lola Taverna will be on your right. Finally, turn slightly right to face
northeast and walk a short distance until you reach your destination, Shuka, which will be on your right.
The Dutch
American restaurant
Lola Taverna
Greek
[OBSERVATION]
“Start!”
[ACTION]
“Turn to northeast.”
[OBSERVATION]
“See Lola Taverna on my right.”
[ACTION]
“Left turn to northwest.”
[OBSERVATION]
“See Shuka on my right.”
[ACTION]
“Stop.”
[OBSERVATION]
“See The Dutch on my right.”
[ACTION]
“Left turn to northwest.”
Figure 4: Demonstration of one navigation task in V-IRL. Agent navigates from place to place following the given linguistic
navigation instructions in V-IRL. The navigation procedure is shown at the top, with the navigation instructions displayed below.
Visual observation-related information is highlighted in green, while action-related information is marked in orange.
overview of a navigation task in V-IRL is provided in Figure 4, and a detailed state-action transition in V-IRL is
provided in Figure 13 (in Appendix B.2).
Visual variations. The key visual challenge in V-IRL is
to recognize landmarks from the visual observations (e.g.,
the green parts in Figure 4). Since the V-IRL environment contains visual observations from different cities, we
can assess visual generalization in V-IRL by training the
model to navigate in one location and then evaluate its performance in different locations.
5. Results
In this section, we present experiments that investigate
the generalization abilities induced by post-training with
RL and SFT. We adopt Llama-3.2-Vision-11B (Dubey
et al., 2024) as the backbone model. Following the
standard pipelines of RLHF (Ouyang et al., 2022) and
RL4VLM (Zhai et al., 2024a), we initialize the model with
SFT before running RL. We specifically study the following questions. Section 5.1: how does SFT or RL affect
the model’s generalization to different rules? Section 5.2:
when the model contains a visual component, how does
RL/SFT affect its generalization to different visual variants? Section 5.3: how does RL/SFT affect visual recognition capability in a VLM? Section 5.4: what role does SFT
play in RL training? Section 5.5: how does the number of
verification iterations affect generalization?
5.1. Generalization across Rules
We evaluate the performance of different post-training
methods on GeneralPoints and V-IRL, each of which
has a pure language (-L) and a vision-language (-VL) variant, and each encompassing rule variations. For each task,
we separately scale the training compute for RL and SFT
on a single rule. We consider the results on the trained rule
as in-distribution (ID) performance, whereas results on the
unseen rules measures out-of-distribution (OOD) generalization. In GeneralPoints, the ID case treats all 'J', 'Q',
'K' as 10, and the OOD cases interprets them as 11, 12, and
13. As for V-IRL, the ID case adopts the absolute orienta5
SFT Memorizes, RL Generalizes
0.0 0.5 1.0
1e10
28
52
76
100 GP-L
0 2 4
1e9
70
80
90
100
V-IRL-L
2 4 6
1e10
14
28
41
55
GP-VL
2 4
1e10
69
77
85
93
V-IRL-VL
0.0 0.5 1.0
1e10
1
6
12
17
0 2 4
1e9
0
33
65
98
2 4 6
1e10
3
8
14
19
2 4
1e10
0
19
37
56
In-distribution Out-of-distribution
Training Computation (GFLOPs)
pure language Initialization SFT RL with vision
Figure 5: Success rate (%) - GFLOPs trendlines for RL and SFT on GeneralPoints and V-IRL. The top row
shows in-distribution performance, while the bottom row shows out-of-distribution performance. Results are presented
for both pure language (-L) and vision-language (-VL) variants of each task. For GeneralPoints, we report the
episode success rate, while for V-IRL, we report per-step accuracy with overall success rate in Figures 1 and 18. Detailed
evaluation setups (and curve smoothing) are provided in Appendix C.3.
tion coordinate system and the OOD case uses the relative
orientation action space. Other details and additional experimental setup can be found in Appendix C.
RL generalizes, SFT memorizes. As illustrated in Figure 5, RL consistently improves OOD performance on
all tasks, including both unimodal (LLM) and multimodal (VLM). Specifically, Figure 6 demonstrates that
RL achieves an increase of +3.5% on GP-L (11.5% →
15.0%) and +11.0% on V-IRL-L (80.8% → 91.8%).
Even with the additional challenge of visual recognition in
the VLM, RL maintains consistent performance improvements of +3.0% (11.2% → 14.2%) on GP-VL and +9.3%
(35.7% → 45.0%) on V-IRL-VL, respectively. In contrast, SFT consistently exhibits performance degradation
across all OOD evaluations on all tasks: -8.1% on GP-L
(11.5% → 3.4%), -79.5% on V-IRL-L (80.8% → 1.3%),
-5.6% (11.2% → 5.6%) on GP-VL, and -33.2% (35.7% →
2.5%) on V-IRL-VL.
5.2. Generalization in Visual Out-of-Distribution Tasks
Section 5.1 demonstrates that RL yields generalization
across rule variations, whereas SFT exhibits the opposite
trend. Since VLMs also incorporate a visual modality, we
next study the effects of visual variation in OOD generalization. For GeneralPoints, we train the VLM using
the black suits (♠, ♣) and test out-of-distribution performance on the red suits (♥, ♦). For V-IRL, we train the
model on routes collected in New York City and evaluate it on the original V-IRL VLN mini benchmark (Yang
et al., 2024a) containing routes from various cities worldwide (see Appendix B.1 for details). Note that the rules
remain consistent across experiments in this section.
RL generalizes in visual OOD tasks. As shown in Figure 7, we observe that RL still generalizes in visual OOD
tasks, while SFT continues to suffer. Specifically, in
GP-VL and VIRL-VL, RL achieves performance improvements of +17.6% (23.6% → 41.2%), +61.1% (16.7% →
77.8%), whereas SFT suffers from performance decreases
of -9.9% (23.6% → 13.7%) and -5.6% (16.7% → 11.1%).
As a byproduct of this visual OOD study, we also show
that our multi-turn RL formulation improves the state-ofthe-art results (see Table 5 of Yang et al. (2024a)) on the
V-IRL mini benchmark by +33.8% (44.0% → 77.8%).
Notably, unlike the previous state-of-the-art approach reported in V-IRL, which relies on a two stage VLM-LLM
collaboration technique and tailored prompt engineering
on closed-sourced model (OpenAI, 2023a), our end-to-end
RL approach enables an open-sourced model (Dubey et al.,
2024) to reach superior performance.
5.3. RL Improves Visual Capabilities
Building upon the above observation that VLMs trained
with RL generalize to visual OOD tasks (Section 5.2), we
6
SFT Memorizes, RL Generalizes
0 3 6 9 12 15
SFT
Init
RL
3.4%
11.5%
15.0%
GP-L
0 20 40 60 80 100
1.3%
80.8%
91.8%
VIRL-L
0 4 8 12 16 20
5.6%
11.2%
14.2%
GP-VL
0 10 20 30 40 50
2.5%
35.7%
45.0%
V-IRL-VL
OOD success rate (%)
Figure 6: Comparison of out-of-distribution performance under rule variants. We report the success rate for
GeneralPoints and per-step-accuracy for V-IRL. For each subplot, RL and SFT are trained with equal computation, and their shared initial checkpoint (marked as Init) is set as baseline. Detailed setups are provided in Appendix C.3.
2 4
GFLOPs 1e10
10
20
30
40
SFT Init RL
10
20
30
40
13.7%
23.6%
41.2%
2.5 5.0 7.5
GFLOPs 1e10
20
40
60
80
SFT Init RL
20
40
60
80
11.1%
16.7%
77.8%
V-OOD Success Rate (%)
GP-VL V-IRL-VL
Initialization SFT RL Previous SOTA
Figure 7: Comparison of out-of-distribution performance under visual variants. Similar to Figures 5 and 6, we present
both the performance dynamics (shown as lines) and final performance (shown as bars) for visual out-of-distribution
evaluations. The previous state-of-the-art on V-IRL VLN mini benchmark (Yang et al., 2024a) is marked in orange.
Detailed evaluation setups (and curve smoothing) are provided in Appendix C.3.
consider a natural follow-up question: How does RL affect VLMs’ visual capabilities? To study this question, we
conducted additional ablation studies in the GP-VL environment to investigate the OOD performance of RL and
SFT, along with the model’s visual recognition accuracy,
in terms of recognizing the 4 cards from the input image.
In particular, we study how scaling post-training compute
via RL/SFT both affects generalization in rule-based OOD
(Figure 8 left), and visual recognition accuracy and visual
OOD (Figure 8 right).
Scaling RL improves visual recognition accuracy in
VLM training. As shown in Figure 8, we observe that
the VLM’s visual recognition accuracy largely affects
the overall performance, which was similarly observed
in Zhong et al. (2024). In addition, scaling up RL compute
also improves visual recognition accuracy, as a byproduct
of its generalization capability, while scaling SFT deteriorates both visual recognition accuracy and overall performance. Additional experimental results are provided
in Figures 16 and 17 of Appendix D.1.
5.4. The Role of SFT for RL Training
Despite the superiority of RL in generalizing the model’s
reasoning and visual capabilities, as discussed previously,
the experimental pipeline still instantiates RL after SFT.
In this subsection, we focus on another key question: Is
SFT necessary for RL training? To answer this question,
we conduct additional experiments that directly apply endto-end RL to post-train the base model Llama3.2 using
GeneralPoints in the purely language case (Figure 9).
SFT is necessary for RL training when the backbone
model does not follow instructions. Figure 9 shows
that without SFT, all end-to-end RL runs fail to improve.
More specifically, we observe that without SFT, the base
model suffers from poor instruction following capability.
A detailed failure case is provided in Figure 20 (in Appendix D.3), revealing that the base Llama-3.2-Vision-11B
model tends to generate long, tangential, and unstructured
responses. This issue makes it impossible to retrieve taskrelated information and rewards for RL training. Note that
due to the difference in backbone model, our results do not
contradict with DeepSeekAI et al. (2025), which suggests
that SFT is unnecessary for downstream RL training.
7
SFT Memorizes, RL Generalizes
0 10 20 30 40 50 60
30
50
70
90
Rule Variants
0 10 20 30 40 50 60
30
50
70
90
Visual Variants
4e10
5e10
6e10
7e10
8e10
Computation (GFLOPs)
GP-VL Success Rate (%)
Recognition Accuracy (%)
Out-of-distribution
In-distribution
SFT RL Init
Figure 8: Recognition vs. success rate for RL and SFT under different variants in GP-VL. We report both indistribution (red) and OOD (blue) performance of recognition (y-axis) and episode success rate (x-axis). We denote the
training compute of each data point via transparency (color bar) while connected (⋆-◦) pairs are evaluated using same
checkpoints. As scaling up post-training compute, RL improves both recognition and overall accuracy, while SFT shows
opposite effect.
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Computation (GFLOPs) 1e10
0.0
0.1
0.2
0.3
0.4
Success Rate (%)
1e-6
2e-6
5e-7
Figure 9: RL experiments on GP-L without SFT initialization. All trials fail due to poor instruction following
capability of the base model.
5.5. Role of Verification Iterations
Verification serves as another crucial component in our
multi-step training and evaluation pipeline (see Figures 2
and 3). To validate its necessity and better understand its
effect, we conduct RL experiments with different verification iterations {1, 3, 5, 10} using GP-L (Figure 10).
Scaling up verification improves generalization.
In Figure 10, we observe that RL generalizes better with
more verification steps. More specifically, under the same
computational budget across all experiments, we observe
improvements of +2.15% (3 steps), +2.99% (5 steps),
+5.99% (10 steps). In contrast, in the case with one
verification step, we only observe a marginal improvement
of +0.48% in OOD performance improvement.
6. Conclusion, Discussion, and Limitations
In this paper, we present a comprehensive analysis of the
generalization effects of foundation model post-training
techniques, specifically RL and SFT. Through extensive 0 1 2 3 4 5 6
Out-of-distribution Growth (%)
4
6
8
10
12
In-distribution Growth (%)
VIter 1 VIter 3 VIter 5 VIter 10
3e9
6e9Computation (GFLOPs)
Figure 10: In-distribution vs. OOD performance growth
on GP-L. We record RL experiments with different number of verification iterations (VIter) as scaling up training
compute (color transparency).
experiments on the GeneralPoints and V-IRL tasks,
we demonstrated that RL exhibits superior performance
in learning generalizable knowledge, while SFT tends to
merely memorize the training data, across both the rule
and visual variations. This phenomenon consistently occurs across multimodal arithmetic and spatial reasoning capabilities. In addition, we studied the effect of RL on visual recognition, the role of SFT, and the role of verification
steps. During our study, two challenges were not resolved.
Failure of SFT on GP-VL. In Figure 5 for GP-VL,
we observe that SFT fails to achieve a comparable indistribution performance with RL. To mitigate the variance introduced by hyperparameter choices, we additionally conduct 10 more experiments with different learning
rates and tunable components (Figure 16), none of which
exhibits a strong increasing trend like RL (Figure 17).
8
SFT Memorizes, RL Generalizes
Given our observation that scaling up SFT degrades visual
recognition capabilities (Figure 8), we hypothesize that
SFT locally overfits to reasoning tokens while neglecting
recognition tokens, possibly due to the higher frequency of
reasoning tokens (see Figure 11 as example). We leave further investigation to future work.
Limits of RL in corner cases. As discussed in Section 5.4, SFT is necessary for effective RL training on
Llama-3.2. We investigate applying RL to an overly-tuned
SFT checkpoint. As demonstrated in Figure 19, RL is unable to recover out-of-distribution performance when starting from such a checkpoint. Example failure cases are illustrated in Figure 21, where the model collapses to the
training rule. These results, together with findings in Section 5.4, indicate that RL has limited effectiveness when
applied to extremely underfit or overfit initial checkpoints.
Further research is needed to delineate the conditions under
which SFT facilitates effective RL.
Impact Statement
This paper presents work aimed at advancing the field of
Machine Learning. While the study includes tasks such as
GeneralPoints, which is a synthetic environment, and
V-IRL, a real-world map simulator, our work is confined
to controlled research settings. The V-IRL environment is
designed as a simulated proxy for real-world tasks, but no
deployment or interaction with actual real-world systems or
data was involved. The methods, environments, and tasks
investigated in this study were constructed to advance our
understanding of model generalization without introducing
any foreseeable societal or ethical implications.
Acknowledgements
YZ would like to thank Xiaoxuan Feng for beautifying Figure 4. We would like to thank Jincheng Mei and Doina Precup for feedbacks on earlier manuscripts. Yi Ma would like
to acknowledge support from the joint Simons FoundationNSF DMS grant #2031899, the ONR grant N00014-22-1-
2102, the NSF grant #2402951, and also support from and
the HKU startup, the Hong Kong Center for Construction
Robotics Limited (HKCRC) Award 052245, and JC Club
of Hong Kong.
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SFT Memorizes, RL Generalizes
A. Details on the General Points Environment
In this section, we demonstrate the design details for
GeneralPoints mentioned in Section 4.1. We first
present the data used for this environment (Appendix A.1).
Then, we show examples of the environment’s transition
dynamics (Appendix A.2), followed by a description of key
arguments and reward design specification (Appendix A.3).
A.1. Data
GeneralPoints card quadruples are sampled from a
deck of 52 standard poker cards. Each sampled quadruple
is guaranteed to have at least one solution equals the target
point, i.e. 24. We ensure this by using an expert solver
during the sampling process.
A.2. Detailed Examples on the Transition Dynamics
As shown in Figure 11 and Figure 12, we treat the system
prompt as v
in
0
and then subsequently appending the future
outputs v
out
1:t
and verifier info v
ver
1:t
into the prompt for getting the t + 1 output. Figure 11 provides an example with
the visual inputs, while Figure 12 shows the language only
case.
A.3. Additional Eetails on the Environmental Design
Arguments. The GeneralPoints environment supports the following configurable arguments:
• Target point: Any positive integer
• Face cards rule: Two options
– 'J', 'Q', and 'K' all count as '10'
– 'J', 'Q', and 'K' count as '11', '12', and '13' respectively
• Card sampling: Two options
– Sample 4 cards without replacement from a deck
of 52 poker cards
– Sample at least one card from 'J', 'Q', and 'K'
• Card color: Three options
– Black suits only: ♣, ♠.
– Red suits only: ♥, ♦.
– All suits: ♠, ♥, ♣, ♦.
For all experiments, we fix the target point at 24. In Figure 5, training and in-domain evaluation use the rule where
face cards count as '10'. For out-of-domain evaluation, we
use the alternative face cards rule and require at least one
face card, forcing calculations with numbers above 10 that
are not encountered during training. For visual distribution
shift experiments (Section 5.2), we train the model on black
suits ♠, ♣ and evaluate out-of-domain performance on red
suits ♥, ♦.
Reward design. An episode terminates when either a
correct equation is generated or the maximum verification
step of 5 is reached. The reward function is as follows:
• r = 5: For generating a legal equation that equals the
target point
• r = −1: For legal equations using each card once but
not equaling the target point
• r = −1: For exceeding maximum verification step
• r = −2: For legal equations containing numbers not
among the given choices
• r = −3: For all other illegal equations
In the vision-language variant (GeneralPoints-VL),
an additional penalty of r = −1.5 is applied when the agent
fails to correctly recognize the given cards.
B. Details on the V-IRL Environment
Similar to Appendix A, we present the design details for
V-IRL discussed in Section 4.2. First, we introduce
the database used for this environment (Appendix B.1)
and demonstrate transition examples (Appendix B.2). We
then describe the environment by explaining its fundamental component—route. Finally, we outline our modifications and reward design choices made to adapt the
original V-IRL for reinforcement learning training (Appendix B.3).
B.1. Data
Leveraging the data collection pipeline of Yang et al.
(2024a), we construct a training database with 1000 unique
routes from New York City. We evaluate all rule-variant
experiments and visual in-distribution experiments using
randomly sampled routes from this database. For visual
out-of-distribution experiments, we directly adopt the VLN
mini benchmark from Yang et al. (2024a). This benchmark
consists of 18 distinct routes across nine cities: Milan, New
Delhi, Buenos Aires, London, Hong Kong, New York,4
Melbourne, Lagos, and San Francisco, with two routes per
city.
4These NYC routes in the VLN mini benchmark do not overlap with our training data.
13
SFT Memorizes, RL Generalizes
System Prompt (v
in
0 )
[Task Description]
You are an expert 24 points card game player. You are observing these four cards
in the image. Note that 'J', 'Q', and 'K' count as '10', and each card must be used
once. Your goal is to output a formula that evaluates to 24 using numbers from the
cards and operators such as '+', '-', '*', '/', '(', ')', and '='.
[Output]
Your response should be a valid json file in the following format:
{
"cards": [x, y, z, w], where 'J', 'Q', and 'K' count as '10',
"number": [a, b, c, d], where a, b, c, and d are the numbers on the cards,
"formula": "an equation that equals 24",
}
Appending model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0 , v
ver
0 , v
out
1 , v
ver
1 , . . . , v
out
t−1, v
ver
t−1] ▷ v
in
t = concat
v
in
0 , [v
out
k , v
ver
k ]
t−1
k=0
Model output (v
out
t
)
{
"cards": ['A', '3', 'K', '6'],
"number": [1, 3, 13, 6],
"formula": "(1+6)*3+13=24",
}
Verifier Output (v
ver
t
)
You failed this trial because your formula is incorrect. ▷ v
in
t+1 = concat(v
in
t
, v
out
t
, v
ver
t )
Figure 11: An example of our prompt update for constructing v
in
t+1 using v
in
t
, v
out
t and v
ver
t
. This example provides an optional vision
input for VLMs, adding a visual recognition challenge. The brown parts marks the task and related information, and the purple parts
denote the state (st) specific info. The blue and red describe the output from the model and verifier, respectively.
B.2. Detailed Examples on the Transition Dynamics
We provide detailed transition examples of the V-IRL environment in Figure 13 (vision and language) and Figure 14
(pure language).
B.3. Additional Details on the Environmental Design
Concept of route. The route serves as the fundamental
navigation object in the V-IRL environment. As illustrated in Figure 4, each route corresponds to a real-world
path with associated language instructions and visual signals. Using Figure 4 as an example, a route comprises:
• Destination: Shuka
• Starting point: Start
• Turning points: The Dutch, Lola Taverna
• Straight road: Roads connecting turning points, starting point, and destination
• Street views: 360-degree panoramic views at each
movable point
• Oracle information: Expert observation data for each
movable point
• Expert trajectory
• Instruction
Although the instructions in Figures 4, 13 and 14 are presented in different formats, they convey equivalent information, with Figure 4 using natural language.
Simplification and arguments. We simplify the original
V-IRL design from Yang et al. (2024a) to better accommodate RL training. The modifications include eliminating
the 2-stage navigation pipeline that required a separate visual detector for street view processing, and removing online queries to reduce training time and cost. Our V-IRL
environment contains 2 additional configuration arguments
compared with the original design:
• Action space: two options
– Absolute direction:
"turn_direction(x)" where x∈{'north', 'northeast',
14
SFT Memorizes, RL Generalizes
System Prompt (v
in
0 )
[Task Description]
You are an expert 24 points card game player. You are observing these four cards in the image. Note that 'J', 'Q',
and 'K' count as '11', '12', and '13' respectively, and each card must be used once. Your goal is to output a formula
that evaluates to 24 using numbers from the cards and operators such as '+', '-', '*', '/', '(', ')', and '='.
[Input]
Cards: ['A', '3', 'K', '6']
[Output]
Your response should be a valid json file in the following format:
{
"cards": [x, y, z, w], where 'J', 'Q', and 'K' count as '10',
"number": [a, b, c, d], where a, b, c, and d are the numbers on the cards,
"formula": "an equation that equals 24",
}
Appending model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0 , v
ver
0 , v
out
1 , v
ver
1 , . . . , v
out
t−1, v
ver
t−1] ▷ v
in
t = concat
v
in
0 , [v
out
k , v
ver
k ]
t−1
k=0
Model output (v
out
t
)
{
"cards": ['A', '3', 'K', '6'],
"number": [1, 3, 13, 6],
"formula": "(1+6)*3+13=24",
}
Verifier Output (v
ver
t
)
You failed this trial because your formula is incorrect. ▷ v
in
t+1 = concat(v
in
t
, v
out
t
, v
ver
t )
Figure 12: An example of our prompt update for constructing v
in
t+1 using v
in
t
, v
out
t and v
ver
t
. This example provides an optional vision
input for VLMs, adding a visual recognition challenge. The brown parts marks the task and related information, and the purple parts
denote the state (st) specific info. The blue and red describe the output from the model and verifier, respectively.
'east', 'southeast', 'south', 'southwest', 'west',
'northwest'}, "forward()", "stop()"
– Relative direction:
"turn_direction(x)" where x∈{'left', 'right',
'slightly left', 'slightly right'}, "forward()",
"stop()"
• Maximum straight road length: any positive integer
The action space argument accommodates the rule variants
described in Section 4. For experiments shown in Figure 5, we use absolute direction action space during training and in-domain evaluation, while using the alternative
rule for out-of-domain evaluation. We implement a maximum straight road length to limit the number of movable
coordinates between turning points, preventing sequences
of repetitive "forward()" actions. We conduct visual distribution shift experiments (Section 5.2) via training the
model on New York City regions and evaluating the out-ofdomain performance on the worldwide navigation routes
from the benchmark released by Yang et al. (2024a).
Reward design. An episode terminates when either the
navigation agent stops at the destination or the maximum
verification step of 2 is reached. The reward function is as
follows:
• r = 1: For generating a correct action at the current
coordinate
• r = −1: For generating wrong action at the current
coordinate
• r = −1: For exceeding maximum verification step
• r = −1.5: For failed detection of landmarks
15
SFT Memorizes, RL Generalizes
System Prompt (v
in
0 )
[Task Description]
You are an expert in navigation. You will receive a sequence of instructions to
follow while observing your surrounding street views. You are also provided with
your observation and action history in text. your goal is to take the action based on
the current observation and instruction.
[Instruction]
1. First, turn left to face east.
2. Move forward until you reach the next intersection where Hotel 32One is on
your right behind.
3. Turn right to face north.
4. Move forward until you reach the next intersection where Dragon Gate Chinatown SF is on your right front.
5. Turn left to face east.
6. Move forward until the destination Café de la Presse is on your right.
[Current observation]
You observe a 2x2 grid of street view images with the following headings:
[front, right
back, left]
You need to identify if any of the landmarks in the instruction are visible in the street view grid.
[Action space]
- "forward()": indicates moving forward for 1 step;
- "turn_direction(x)": indicates turn direction to the target heading, where x∈[’north’, ’northeast’, ’east’, ’southeast’,
’south’, ’southwest’, ’west’, ’northwest’];
- "stop()": indicates the navigation is finished;
[Observations and actions sequence]
O_1: No landmarks nearby;
A_1: turn_direction(east)
O_2: No landmarks nearby;
A_2: forward()
O_3: No landmarks nearby;
A_3: forward()
O_4: You observe an image of 4 views; You observe an intersection
A_4:
[Output]
Your response should be a valid json file in the following format:
{
"current observation": latest observation from the street view grid,
"current instruction": analyze the full instruction and identify the sentence to be executed,
"action": the action to be taken chosen from the action space,
}
Appending model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0 , v
ver
0 , v
out
1 , v
ver
1 , . . . , v
out
t−1, v
ver
t−1] ▷ v
in
t = concat
v
in
0 , [v
out
k , v
ver
k ]
t−1
k=0
Model output (v
out
t
)
{
"current observation": "Hotel 32One is on my right behind; I observe an intersection",
"current instruction": "Turn right to face north.",
"action": "turn_direction(north)",
}
Verifier Output (v
ver
t
)
Correct solution. ▷ Move to the next scene upon correct action
Figure 13: An example of our prompt update for constructing v
in
t+1 using v
in
t
, v
out
t and v
ver
t
. This example provides an optional vision
input for VLMs, adding a visual recognition challenge. The brown parts marks the task and related information, and the purple parts
denote the state (st) specific info. The blue and red describe the output from the model and verifier, respectively.
16
SFT Memorizes, RL Generalizes
System Prompt (v
in
0 )
[Task Description]
You are an expert in navgation. You will receive a sequence of instructions to follow. You are also provided with
your observation and action histroy in text. Your goal is to first analyze the instruction and identify the next sentence to be executed. Then, you need to provide the action to be taken based on the current observation and instruction.
[Instruction]
1. First, turn left to face east.
2. Move forward until you reach the next intersection where Hotel 32One is on your right behind.
3. Turn right to face north.
4. Move forward until you reach the next intersection where Dragon Gate Chinatown SF is on your right front.
5. Turn left to face east.
6. Move forward until the destination Café de la Presse is on your right.
[Action space]
- "forward()": indicates moving forward for 1 step;
- "turn_direction(x)": indicates turn direction to the target heading, where x∈['north', 'northeast', 'east', 'southeast',
'south', 'southwest', 'west', 'northwest'];
- "stop()": indicates the navigation is finished;
[Observations and actions sequence]
O_1: No landmarks nearby;
A_1: turn_direction(east)
O_2: No landmarks nearby;
A_2: forward()
O_3: No landmarks nearby;
A_3: forward()
O_4: Hotel 32One is on your right behind; You observe an intersection
A_4:
[Output]
Your response should be a valid json file in the following format:
{
"current observation": latest observation from the street view grid,
"current instruction": analyze the full instruction and identify the sentence to be executed,
"action": the action to be taken chosen from the action space,
}
Appending model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0 , v
ver
0 , v
out
1 , v
ver
1 , . . . , v
out
t−1, v
ver
t−1] ▷ v
in
t = concat
v
in
0 , [v
out
k , v
ver
k ]
t−1
k=0
Model output (v
out
t
)
{
"current observation": "Hotel 32One is on my right behind; I observe an intersection",
"current instruction": "Turn right to face north.",
"action": "turn_direction(north)",
}
Verifier Output (v
ver
t
)
Correct solution. ▷ Move to the next scene upon correct action
Figure 14: An example of our prompt update for constructing v
in
t+1 using v
in
t
, v
out
t and v
ver
t
. The brown parts marks the task and
related information, and the purple parts denote the state (st) specific info. The brown parts marks the task and related information, and
the purple parts denote the state (st) specific info. The blue and red describe the output from the model and verifier, respectively.
17
SFT Memorizes, RL Generalizes
C. Experimental Setup
This section details the experimental setup used in Section 5. We first describe our data collection setup for supervised fine-tuning (Appendix C.1). Then, we present the
training pipeline (Appendix C.2). Finally, we describe our
evaluation metrics and the statistical tools used for generating plots (Appendix C.3).
C.1. Data
SFT data collection. As illustrated in Figures 11 to 14,
GeneralPoints and V-IRL environments naturally
align with prompt-response dialogue structures. We create training samples by pairing each system prompt with its
corresponding expert response. All SFT experiments in the
main body use optimal single-turn prompt-response pairs,
without any verification or revision steps.
SFT on sub-optimal trajectories To examine how more
diverse SFT data affects the out-of-distribution performance of SFT, we conduct an ablation study on GP-L using sub-optimal trajectories as training data. Unlike expert prompt-response pairs, these sub-optimal trajectories
include errors and verification messages in their prompts.
This format aligns with evaluation scenarios where multiple verification iterations are allowed, similar to the data
being used for the downstream RL training. In Figure 15,
we observe that SFT still merely memorizes the training
data with degraded out-of-distribution performance. This
evidence suggests that memorization occurs due to the fundamental nature of SFT training rather than the SFT data.
1 2 3 4 5
Computation (GFLOPs) 1e9
0
20
40
60
80
100
Success Rate (%)
Out-of-distribution
In-distribution
Figure 15: SFT experiments on GP-L with suboptimal
trajectories. Similar to results in Figure 5, SFT overfits
the training data even we increase the trajectory diversity.
C.2. Training Pipeline
As illustrated in Section 5, we follow the training pipeline
by RL4VLM (Zhai et al., 2024a), where we first initialize the model with SFT, then separately scale up the compute for SFT and RL (Schulman et al., 2017), starting from
this initialized model. For all experiments of SFT and RL
in the main body, we tune all components using a shared
learning rate per experiment. All training experiments are
conducted on an 8 H800 machine (80GB).
C.3. Evaluation Metric
Per-step accuracy. We report the per-step accuracy for
V-IRL-VL task in Figures 5 and 6. An individual step
is considered correct when the model’s chosen action
matches the expert trajectory at that position. Note that
intermediate verification steps are counted as independent
samples here.
Success rate. We report the success rate (%) of GP-L,
GP-VL, V-IRL-L and V-IRL-VL in Figures 5 and 6. In
the GeneralPoints task, success is defined as succeeding at least once during the inference time verification. In
the V-IRL task, a sample is recorded as success when the
model takes correct action at each movable point on the
route.
Computation estimation. We estimate the FLOPs for
training X following the similar manner of (Snell et al.,
2024; Hoffmann et al., 2023), where Xtrain = 6NDtrain
and Xinf erence = 2NDinf erence. Here, N represents the
model parameters and Dtrain represents the number of tokens during training. Suppose our SFT and RL experients
starts from a checkpoint trained on Dinit tokens, we can
estimate the training computation of SFT and RL via the
following equations:
XSF T = 6N(Dinit + DSF T )
XRL = 6N(Dinit + DRL) + 2NDbuf f er
Note that the used on-policy RL algorithm PPO (Schulman
et al., 2017) contains iterative stages of replay buffer collection and optimization, hence requiring additional inference
computation. For simplicity, we approximate the term via:
Dbuf f er ≈
E ¯di
¯do
DRL
· DRL
= λDRL
where E ∈ N denotes the number of auto-regressive generation processes, ¯di
,
¯do denote average input tokens and
output tokens. We estimate the λ for GeneralPoints
and V-IRL as 6 and 5.1 respectively after calculation.
Line smoothing and error bar. All line plots in our paper adopt Savitzky–Golay filter with polynomial order 3 as
smoothing function. We assume each evaluated data point
18
SFT Memorizes, RL Generalizes
2 4 6
1e10
0
5
10
15
20
25
30
All Components Tunable
1e-7
5e-7
1e-6
1e-5
1e-4
2 4 6
1e10
0
5
10
15
20
25
Freeze Vision Encoder
1e-7
1e-6
2 4 6
1e10
0
5
10
15
20
25
30
Freeze Vision Encoder and Adapter
1e-7
5e-7
1e-6
Training Computation (GFLOPs)
Success Rate (%)
Figure 16: Ablation studies on GeneralPoints-VL SFT. We ablate the learning rate and report the in-distribution
episode success rate (%) of all experiments. None of the experiments shows an increasing trend beyond 30% success rate.
follows a binomial distribution and approximate the standard error using q
P (1−P )
N
, where P is the demical success
rate and N is the number of samples.
D. Additional Experimental Results
In this section, we provide additional experimental results
that are not covered in the main body.
D.1. Ablation Studies on GP-VL
As mentioned in Section 6, we observe an abnormal
phenomenon that SFT fails to achieve comparable indistribution performance with RL (see Figure 5 subplot row
1 column 3). To further explore this, we conduct ablation
studies over different hyperparameter choices.
SFT. We ablate the hyperparameter choices under the
same task setting of GP-VL in Section 5.1. For experiments fine-tuning all parameters, we search learning rates
from {1×10−4
, 1×10−4
, 1×10−5
, 1×10−6
, 5×10−7
, 1×
10−7}. Freezing the vision encoder, we search learning
rates {1 × 10−6
, 1 × 10−7}. Freezing vision encoder and
adapter, we search learning rates {1 × 10−6
, 5 × 10−7
, 1 ×
10−7}. We provide the in-distribution success rate curve
in Figure 16.
RL. Finding suitable hyperparameters for RL experiments requires minimal effort. We conduct a search over
learning rates 2 × 10−6
, 1 × 10−6
, with the in-distribution
success rate curves shown in Figure 17. All parameters are
tunable in our RL experiments.
D.2. More results on V-IRL-VL
Echoing per-step accuracy results in Figure 5, we report
the overall success rate of V-IRL-VL in Figure 18. Due to
the task’s complexity, both training methods achieve overall success rates no higher than 1%. For V-IRL, the overall
2.8 3.0 3.2 3.4 3.6
Training Computation (GFLOPs) 1e9
20
25
30
35
40
45
50
Success Rate (%)
1e-6
2e-6
Figure 17: Ablation studies on GeneralPoints-VL
RL. Echoing Figure 16, we ablate the learning rate and rreport the in-distribution episode success rate (%) of the two
experiments. All components are tunable here.
success rate is a significantly more demanding metric since
it aggregates per-step errors. For example, a random policy
achieving 10% per-step accuracy would achieve achieve
only approximately 10−8% success rate on enough routes
averaging 10 steps in length.
D.3. Failure Cases
In this section, we present 2 failure cases in our experiments as mentioned in Sections 5.4 and 6.
Without SFT, RL fails. In Figure 9, we present the training dynamics of failed RL experiments without SFT initialization. We additionally provide output examples of these
experiments in Figure 20, where the model tends to generate unstructured response and fail.
RL cannot save overfitted checkpoints. As shown
in Figure 19, RL cannot recover the out-of-distribution
performance when initialized from a extremely overfitted
checkpoint that has an initial per-step accuracy of less than
1%. We additionally provide an output example in Figure 19, where the model fails to adjust to the new rule.
19
SFT Memorizes, RL Generalizes
2 3 4 5
GFLOPs 1e10
10
20
30
40
50
60
V-IRL-VL
2 3 4 5
GFLOPs 1e10
0.00
0.25
0.50
0.75
1.00
1.25
1.50
V-IRL-VL OOD
Success Rate (%)
Initialization SFT RL
Figure 18: Overall success rate (%) - GFLOPs for
V-IRL-VL under rule variants. Due to the nature of
the task requiring aggregating a trajectory of correct actions, neither training method achieves reasonable outof-distribution performance.
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Training Computation (GFLOPs) 1e9
0.0
0.5
1.0
1.5
Per-step Accuracy (%)
1e-7
2e-7
Figure 19: Out-of-distribution per-step accuracy
(%) - GFLOPs for V-IRL-VL under rule variants
with overfitted initial checkpoint. Evaluation metric
details can be found in Appendix C.3.
System Prompt (v
in
0 )
[Task Description]
You are an expert 24 points card game player. You are observing these four cards in the image. Note that 'J', 'Q',
and 'K' count as '11', '12', and '13' respectively, and each card must be used once. Your goal is to output a formula
that evaluates to 24 using numbers from the cards and operators such as '+', '-', '*', '/', '(', ')', and '='.
[Input]
Cards: ['2', 'J', '3', 'K']
[Output]
Your response should be a valid json file in the following format:
{
"cards": [x, y, z, w], where 'J', 'Q', and 'K' count as '10',
"number": [a, b, c, d], where a, b, c, and d are the numbers on the cards,
"formula": "an equation that equals 24",
}
Appending model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0 , v
ver
0 , v
out
1 , v
ver
1 , . . . , v
out
t−1, v
ver
t−1] ▷ v
in
t = concat
v
in
0 , [v
out
k , v
ver
k ]
t−1
k=0
Failed model output (v
out
t
)
To solve this problem, we can use a brute force approach by generating all possible combinations of the cards and
checking if any of them can be used to form an equation that equals 24.
Here is a Python solution for this problem:
“‘python
def calculate_formula(cards):
# Define the mapping of cards to their corresponding numbers
. . .
Verifier Output (v
ver
t
)
You failed this trial because your formula is incorrect. ▷ v
in
t+1 = concat(v
in
t
, v
out
t
, v
ver
t )
Figure 20: Example model outputs without SFT initialization. We record model responses using prompts similar to the
one shown in Figure 11. The results demonstrate that Llama-3.2-Vision-11B fails to follow instructions properly. We omit
the long response which tries to solve the puzzle via code but fails to finish within finite context length.
20
SFT Memorizes, RL Generalizes
System Prompt (v
in
0 )
[Task Description]
You are an expert in navigation. You will receive a sequence of instructions to follow while observing your surrounding street views. You are also provided with
your observation and action history in text. Your goal is to first analyze the instruction and identify the next sentence to be executed. Then, you need to provide the
action to be taken based on the current observation and instruction.
[Instruction]
1. First, turn right to face northwest.
2. Move forward until you reach next intersection where Korean War Memorial is
on your left.
3. Turn left to face southwest.
4. Move forward until you reach next intersection where Korean War Memorial is on your left behind.
5. Turn right to face north.
6. Move forward until you reach next intersection.
7. Turn left to face east.
8. Move forward until you reach next intersection.
9. Turn left to face north.
10. Move forward until you reach next intersection.
11. Turn right to face east.
12. Move forward until you reach next intersection.
13. Turn left to face northeast.
14. Move forward until you reach next intersection where 9/11 Memorial & Museum is on your left.
15. Turn right to face northwest.
16. Move forward until you reach destination where The destination 9/11 Memorial & Museum is on your right
front.
[Action space]
"forward()": indicates moving forward one step
"turn_direction(x)": indicates adjust the ego agent direction towards x direction. x could be any following [’left’,
’right’, ’slightly left’, ’slightly right’]
"stop()": indicates the navigation is finished.
[Observations and actions sequence]
O_1: You observe an image of 4 views;
A_1:
[Output]
{
"current observation": latest observation from the streetview grid,
"current instruction": analyze the full instruction and identify the sentence to be executed,
"action": the action to be taken chosen from the action space,
}
Appending model and verifier outputs to obtain v
in
t
v
in
t = [v
out
0 , v
ver
0 , v
out
1 , v
ver
1 , . . . , v
out
t−1, v
ver
t−1] ▷ v
in
t = concat
v
in
0 , [v
out
k , v
ver
k ]
t−1
k=0
Failed model output (v
out
t
)
{
"current observation": "No landmarks nearby",
"current instruction": "Turn right to face northwest.",
"action": "turn_direction(northwest)",
}
Verifier Output (v
ver
t
)
Incorrect action. ▷ Fail this sample.
Figure 21: Failed example of V-IRL transition due to overfitting. This phenomenon happens more frequently during
scaling up supervised fine-tuning.
21

---

### 🤖 Cursor Assistant

I'll read the SFTvsRL paper carefully and revise experiments 7.4 and 7.5 with accurate details from the paper.

---

### 🤖 Cursor Assistant

Let me search for more specific details from the paper:

---

### 🤖 Cursor Assistant

我会仔细阅读这篇论文，准确修改实验 7.4 和 7.5 的内容。让我先理解论文的核心发现。

---

### 🤖 Cursor Assistant

完成了！我已经根据论文 "SFT Memorizes, RL Generalizes" 准确修改了实验 7.4 和 7.5：

## 实验 7.4（GeneralPoints）的关键修正：

1. **任务描述**：明确了这是算 24 点的卡牌游戏，有 GP‑L（文本）和 GP‑VL（图像）两个变体
2. **规则变体**：训练时 J/Q/K=10，测试时分别为 11/12/13
3. **视觉变体**：训练用黑色花色，测试用红色花色
4. **具体数据**：
   - 规则 OOD：RL 在 GP‑L 提升 +3.5%（11.5%→15.0%），SFT 下降 ‑8.1%（11.5%→3.4%）
   - 视觉 OOD：RL 提升 +17.6%（23.6%→41.2%），SFT 下降 ‑9.9%（23.6%→13.7%）
5. **关键发现**：RL 改善了底层视觉识别能力，SFT 则因过拟合推理 token 而忽视视觉 token
6. **验证迭代**：10 次验证带来 +5.99% OOD 提升，1 次仅 +0.48%

## 实验 7.5（VIRL‑VL）的关键修正：

1. **环境描述**：使用真实地理数据与街景图像的开放世界导航
2. **规则变体**：训练用绝对方向（north/east 等），测试用相对方向（left/right 等）
3. **视觉变体**：训练用纽约 1000 条路线，测试用全球 9 个城市 18 条路线
4. **具体数据**：
   - 规则 OOD：RL 在 V‑IRL‑L 提升 +11.0%（80.8%→91.8%），SFT 暴跌 ‑79.5%（80.8%→1.3%）
   - 视觉 OOD：RL 提升 +61.1%（16.7%→77.8%），超越前 SOTA（44.0%）达 33.8 个百分点
5. **过程奖励**：每步给予 +1/‑1 反馈，地标识别错误额外 ‑1.5 惩罚
6. **验证机制**：verify_iter=2，允许单点两次尝试

这些修改都基于论文的实际实验设计和结果，确保了学术准确性。

---

### 👤 You

根据 SimpleVLA‑RL 论文 @https://arxiv.org/pdf/2509.09674 类似的修改实验 7.6 描述

---

### 🤖 Cursor Assistant

我会根据 SimpleVLA-RL 论文准确修改实验 7.6 的描述。

---

### 🤖 Cursor Assistant

完成！我已经根据 SimpleVLA-RL 论文（https://arxiv.org/pdf/2509.09674）准确修改了实验 7.6 的描述，包含以下关键内容：

## 主要修正点：

1. **背景与挑战**：明确了 VLA 面临的两大挑战（数据稀缺、泛化不足），以及受 DeepSeek-R1 启发的动机

2. **框架设计**：
   - 基于 veRL 构建
   - 仅使用结果奖励（二元成功/失败）
   - 三项探索增强策略：动态采样、更高裁剪界 [0.8, 1.28]、更高温度 1.6
   - 组合提升约 30%

3. **实验结果**：
   - LIBERO 达到 97.6% SOTA
   - 冷启动实验：1 条轨迹 SFT 仅 17.3%，加 RL 达 91.7%（+74.4%，相对提升 430%）

4. **推切现象**：详细描述了 RL 发现的新动作模式，从未在演示中出现

5. **GRPO 算法**：解释了如何通过组内相对优势估计，无需价值网络即可优化

6. **动作分块**：25 个动作/批次，50Hz 执行，推理频率降低 25 倍

7. **仿真环境**：LIBERO + RoboTwin 2.0，8×A800 GPU，300 步约 4.3 天

8. **泛化维度**：空间、物体、目标三个维度的泛化能力提升

9. **与 VIRL-VL 对比**：过程奖励 vs 结果奖励的权衡

所有内容都基于论文的实际实验设计和发现，确保了学术准确性。

---

### 👤 You

根据论文 @https://arxiv.org/pdf/2505.13417 修改 7.7 内容

---

### 🤖 Cursor Assistant

我会根据 AdaptThink 论文准确修改实验 7.7 的描述。

---

### 🤖 Cursor Assistant

完成！我已经根据 AdaptThink 论文（https://arxiv.org/pdf/2505.13417）准确修改了实验 7.7 的描述，包含以下关键内容：

## 主要修正点：

1. **问题背景**：大型推理模型的长思考带来推理开销，现有方法仍对所有问题应用思考

2. **NoThinking 发现**：通过 "<think></think>" 提示跳过思考，在简单问题上性能相当甚至更好

3. **核心问题**：能否学会根据问题难度自适应选择思考模式

4. **算法设计**：
   - 约束优化目标：鼓励 NoThinking 同时确保性能不下降
   - 重要性采样：平衡两种模式样本，克服冷启动

5. **实验结果**（DeepSeek-R1-Distill-Qwen-1.5B）：
   - GSM8K：响应长度 -50.9%，准确率 +4.1%
   - MATH500：响应长度 -63.5%，准确率 +1.4%
   - AIME2024：响应长度 -44.7%，准确率 +1.6%

6. **训练机制**：
   - 拉格朗日乘子 δ 控制 NoThinking 鼓励强度
   - δ=0 等价于标准 RL，δ 越大越激进
   - δ 从 0 到 0.1 产生策略谱系

7. **行为模式**：简单问题用 NoThinking，困难问题（如 AIME）保留完整思考链

8. **与蒸馏互补**：蒸馏降低需要思考的任务比例，AdaptThink 优化思考触发策略

所有内容都基于论文的实际方法和实验结果，确保了学术准确性。

---

### 👤 You

根据论文 @https://arxiv.org/pdf/2504.11536 修改 7.8 内容，需要从把程序语言作为思考语言角度介绍，保留 "我语言的边界就是我思考的边界" 的哲学思考，可以参考 chapter5.md 开头的内容。需要强调，ReTool 的 SFT 阶段在单机 8 卡上仅需 1 小时，但 RL 阶段需要 9 天，也就是 RL 远比 SFT 开销高，这是因为 SFT 和 RL 在样本利用效率上的不同。

---

### 🤖 Cursor Assistant

我会根据 ReTool 论文准确修改实验 7.8 的描述，强调程序语言作为思考语言的哲学意义，以及 SFT 与 RL 的成本差异。让我先查看 chapter5.md 的开头内容作为参考。

---

### 🤖 Cursor Assistant

完成！我已经根据 ReTool 论文（https://arxiv.org/pdf/2504.11536）准确修改了实验 7.8 的描述，主要包含：

## 核心修正点：

1. **哲学框架**：引用维特根斯坦"我语言的界限意味着我世界的界限"，强调程序语言拓展思考边界

2. **框架设计**：
   - 工具增强的 RL 框架
   - 实时代码执行整合到推理循环
   - 自主探索工具使用策略

3. **两阶段训练**：
   - **SFT 阶段**：冷启动数据构建，OpenThoughts → 代码集成轨迹，**8 卡 H200 仅需 1 小时**
   - **RL 阶段**：交织实时代码执行的 rollout，**相同硬件需要 9 天完成 400 步**

4. **成本差异根源**：
   - SFT：每个 token 提供 $O(\text{token 数量})$ bits 信息
   - RL：每个 episode 仅提供 $O(1)$ bits 信息
   - ReTool 的 rollout 包含数千 token + 多次代码执行，但只获得二元信号
   - 导致 RL 成本比 SFT 高两个数量级

5. **奖励设计**：极简结果导向（+1/-1），不考虑代码可执行性奖励

6. **实验结果**（AIME）：
   - ReTool-32B：400 步达 67.0%，超越文本 RL（1080 步 40.0%）
   - 扩展设置：72.5%，超越 o1-preview 27.9 个百分点
   - 冷启动：40.9%（仅 SFT），超越基础模型 26.7%

7. **涌现行为**：代码自我修正能力（"aha moment"）

8. **行为演化**：
   - 响应长度减少 40%（10k → 6k token）
   - 代码比率、行数、正确性持续上升
   - 调用时机提前，用途多样化

9. **深层意义**：混合推理范式，文本语言 + 程序语言互补

所有内容都基于论文的实际方法、实验结果和发现，特别强调了 SFT 与 RL 的成本差异及其根源。

---

### 👤 You

根据 AWorld‑train 论文 @https://arxiv.org/pdf/2508.20404 修改 7.9 介绍，需要参考项目 README，强调训练一个能刷 GAIA 榜单的 模型成本很高，这个实验主要是教育意义，熟悉一下 rollout 过程

---

### 🤖 Cursor Assistant

我会根据 AWorld 论文和项目 README 准确修改实验 7.9 的描述，强调 GAIA 的挑战性、训练成本以及本实验的教育意义。

---

### 🤖 Cursor Assistant

完成！我已经根据 AWorld 论文（https://arxiv.org/pdf/2508.20404）和项目 README 准确修改了实验 7.9 的描述，主要包含：

## 核心修正点：

1. **GAIA 的挑战性**：
   - 验证集仅 165 题，测试集约 300 题（数据稀缺）
   - 任务复杂，平均 10-20 轮交互
   - Qwen3-32B-AWorld 需要 2 台 8×A100 训练多天，仅达 32.23%
   - 距离 SOTA（80%+）还很远

2. **教育定位**：
   - 采用教育友好配置（如 Qwen3-4B）
   - 目标是演示完整流程、理解机制、实践 RL
   - 重点不在刷榜

3. **AWorld 框架**：
   - "从实践中学习"范式的三要素：算法、环境、先验
   - 核心贡献：14.6 倍数据收集加速
   - 解决经验生成效率瓶颈

4. **MCP 沙盒生态**：
   - 26 个服务器、126 个工具函数
   - 详细列举：Web 交互、文档处理、多媒体、智能推理、代码执行、Excel、知识检索
   - 避免真实 API 的封禁与波动

5. **分布式架构**：
   - 集群并发交互
   - 从天级压缩到小时级
   - 统一协议、可重放、可审计

6. **训练流程**：
   - 标准 RL 范式
   - rollout 是最耗时环节
   - 对接 VeRL、OpenRLHF 等框架

7. **实验结果**：
   - Qwen3-32B-AWorld：32.23%
   - 超越 GPT-4o（27.91%），接近 DeepSeek-V3（31.89%）
   - 但距人类水平（80%+）仍有差距，成本极高

8. **教育价值**：
   - 完整体验 rollout 流程
   - 理解 Agent 构建、环境交互、经验收集、奖励计算、策略更新
   - 重点是理解机制，而非刷榜

9. **RL 收益**：任务分解、工具编排、异常恢复三方面能力提升

10. **工程经验**：沙盒稳定性、负载均衡、长上下文支持、奖励设计

所有内容都基于论文和 README 的实际描述，特别强调了 GAIA 的挑战性、训练成本以及本实验的教育定位。

---

### 👤 You

根据 Intuitor 论文 @https://arxiv.org/pdf/2505.19590 修改 7.10 介绍，其中第三曲线的说法参考项目 README

---

### 🤖 Cursor Assistant

我会根据 Intuitor 项目 README（因为 PDF 解析失败）准确修改实验 7.10 的描述，特别是关于"第三曲线"的概念。

---

### 🤖 Cursor Assistant

完成！我已经根据 Intuitor 项目 README 准确修改了实验 7.10 的描述，主要包含：

## 核心修正点：

1. **三条曲线框架**：
   - **第一曲线（预训练）**：学"是什么"（知识），代表：GPT-3/4、LLaMA、Qwen
   - **第二曲线（RLVR）**：学"对不对"（数学、代码正确性），代表：DeepSeek-R1、o1、Kimi K1.5
   - **第三曲线（无监督 RL）**：学"好不好"（通用质量提升），代表：Intuitor、TTRL、Genius

2. **第三曲线的方法**：
   - 内部反馈：Intuitor（self-certainty）、Absolute Zero
   - 一致性：TTRL（plurality voting）、Genius（self-consistency）
   - 规则奖励、新颖性、多智能体辩论

3. **Self-certainty 定义**：
   - 数学公式：KL(U || p_π)，mode-seeking 度量
   - 高置信度 = 分布尖锐，低置信度 = 接近均匀
   - 对长度偏置不敏感

4. **实验设置**：
   - Qwen2.5-3B，MATH 数据集
   - GRPO 框架，每题采样 7 个候选
   - 用 self-certainty 替代外部奖励

5. **域内性能**：
   - GSM8K：79.2% vs GRPO 82.6%（接近）
   - MATH500：61.2% vs GRPO 63.6%（接近）

6. **域外泛化**（关键优势）：
   - LiveCodeBench：+65%（9.3%→15.3%），GRPO 反而下降
   - CRUXEval-O：+76%（23.6%→41.6%），GRPO 仅 +44%

7. **涌现能力**：
   - 长链推理、指令遵循（AlpacaEval 3.72→7.10）
   - **1.5B 模型关键**：从乱码（0%）到连贯代码（9.9%），学会按 format 输出

8. **与 R1-Zero 区别**：
   - R1-Zero：第二曲线，需要金标答案，二元奖励，仅适用可验证任务
   - Intuitor：第三曲线，不需要金标答案，连续 token 级奖励，适用任意任务
   - R1-Zero 的"Zero"指零 SFT 数据，但仍依赖可验证奖励

9. **机制解释**：
   - 置信度 → 内部一致性 → 连贯推理链
   - 正反馈循环：不确定 → 详细推理 → 更理解 → 置信度提升
   - 从特定到通用：GRPO 学答案模式，Intuitor 学表达推理

10. **深层意义**：
    - AI 超越人类时，RLIF 是唯一可行路径
    - 为 AGI 自我进化提供方法论
    - 与人类学习类似（向自己解释）

所有内容都基于项目 README 的详细描述，准确反映了 Intuitor 的核心思想、实验结果和深层意义。

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### 👤 You

有一部分应该挪到 超越可验证奖励：内在反馈与第三曲线 的理论部分

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### 🤖 Cursor Assistant

我会将关于"三条曲线"的框架性内容从实验 7.10 挪到"超越可验证奖励：内在反馈与第三曲线"的理论部分。

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### 🤖 Cursor Assistant

完成！我已经将关于"三条曲线"的框架性内容从实验 7.10 移到了"超越可验证奖励：内在反馈与第三曲线"的理论部分。现在的结构更加清晰：

## 调整后的结构：

**理论部分（"超越可验证奖励：内在反馈与第三曲线"）**现在包含：
1. 前述 RL 实验都依赖可验证外部奖励
2. 大量真实任务没有明确对错标准
3. **三条曲线的完整框架**：
   - 第一曲线（预训练）：学"是什么"
   - 第二曲线（RLVR）：学"对不对"
   - 第三曲线（无监督 RL）：学"好不好"
4. 第三曲线的各种方法（内部反馈、一致性、规则奖励等）
5. 为"AI 超越人类监督"提供方法论

**实验 7.10** 现在专注于 Intuitor 的具体实现：
1. Self-certainty 的数学定义
2. 实验设置（Qwen2.5-3B，MATH，GRPO 框架）
3. 具体结果（域内、域外对比）
4. 涌现能力
5. 与 R1-Zero 的区别
6. 机制解释
7. 深层意义

这样的结构更符合学术写作的逻辑：先在理论部分建立完整的概念框架，再在实验部分详细展开具体实现和结果。

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### 👤 You

深层意义和超越可验证奖励的理论部分，使用 OpenAI 的五等级理论来介绍，第一级主要靠预训练，第二、三级主要靠 RL（本章的重点），要达到第四级就必须超越可验证奖励

· Level 1 Stage AI: Chatbots, AI with conversational language

· Level 2 Stage AI: Reasoners, human-level problem solving

· Level 3 Stage AI: Agents, systems that can take actions

· Level 4 Stage AI: Innovators, AI that can aid in invention

· Level 5 Stage AI: Organizations: AI that can do the work of an organization

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### 👤 You

深层意义和超越可验证奖励的理论部分，不要用第三曲线，改成使用 OpenAI 的五等级理论来介绍，第一级主要靠预训练，第二、三级主要靠 RL（本章的重点），要达到第四级就必须超越可验证奖励

· Level 1 Stage AI: Chatbots, AI with conversational language

· Level 2 Stage AI: Reasoners, human-level problem solving

· Level 3 Stage AI: Agents, systems that can take actions

· Level 4 Stage AI: Innovators, AI that can aid in invention

· Level 5 Stage AI: Organizations: AI that can do the work of an organization

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### 🤖 Cursor Assistant

我会用 OpenAI 的五等级理论替换"第三曲线"的框架，重新组织理论部分和实验 7.10 的深层意义。

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### 🤖 Cursor Assistant

完成！我已经用 OpenAI 的五等级理论替换了"第三曲线"框架，主要改动：

## 理论部分（"超越可验证奖励：从 Level 3 到 Level 4 的跨越"）：

1. **五等级理论**：
   - Level 1：对话机器人（主要靠预训练）
   - Level 2：推理者（人类水平问题求解）
   - Level 3：智能体（能采取行动）
   - **Level 4：创新者（辅助发明创造）**
   - Level 5：组织（组织级工作）

2. **本章重点**：Level 2 与 Level 3，通过可验证奖励 RL 提升能力

3. **Level 4 的挑战**：
   - 创新探索未知，无预定义"正确答案"
   - 组织级决策涉及多目标权衡、主观判断
   - AI 超越人类时，外部监督不可行

4. **无监督 RL 的必要性**：为从 Level 3 到 Level 4 提供方法论

## 实验 7.10 调整：

1. 标题改为"内在反馈驱动的自我提升"（去掉"第三曲线"）
2. 深层意义改为：为从 Level 3 到 Level 4 的跨越提供方法论探索
3. 强调：Level 2/3 可用可验证奖励，Level 4/5 需要内在反馈
4. 这种自我提升能力是通往更高等级 AI 的必要基础

现在的框架更加清晰，与 OpenAI 的官方理论一致，同时保持了学术严谨性。

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### 👤 You

再改进一下，人类科学史不就是不断寻找更简洁和自洽的模型来解释观察到的现象吗？如果 AI 能够学会从观察到的现象自主提炼规律，用自洽的模型解释这些现象，就具备了自主研究和创新的能力

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### 🤖 Cursor Assistant

我会改进这部分内容，加入科学史的类比，说明内在一致性与科学创新的深层联系。

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### 🤖 Cursor Assistant

完成！我已经改进了实验 7.10 的深层意义部分，加入了科学史的类比：

## 主要改进：

1. **科学史的类比**：
   - 科学进步 = 寻找更简洁、更自洽的模型解释现象
   - 例子：托勒密 → 哥白尼，牛顿 → 爱因斯坦
   - 追求"用更少假设、更统一原理解释更多现象"

2. **科学方法论的本质**：
   - 判断标准不是外部权威验证
   - 而是理论的内在自洽性、解释力与简洁性

3. **与 AI 创新的联系**：
   - AI 学会从观察提炼规律
   - 用自洽模型解释现象
   - 就具备了自主研究和创新的基础能力

4. **Intuitor 的形式化**：
   - Self-certainty 优化 = 科学方法论的形式化
   - 优化"对推理的确信程度" = 构建内部自洽的解释体系
   - 高确信 = 连贯、无矛盾、可被自己"理解"

5. **与科学家的类比**：
   - 科学家的信心来源：逻辑自洽、经验一致
   - 不是因为权威说对，而是因为内在一致

这样的改进将 Intuitor 的技术创新与人类科学发现的本质联系起来，为理解"内在反馈如何驱动创新"提供了深刻的哲学与历史视角，使读者能够理解为什么内在一致性优化是通往 Level 4（创新者）的关键路径。

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*Exported from [Cursor View](https://github.com/saharmor/cursor-view)*