[Project Notes] Push Any Letter: 52 Shapes, Planner Demonstrations, and Eight Imitation Policies

17 minute read

Published: October 26, 2026

With ten demonstrations per letter and target orientation, our state-based ACT policy solved 319 of 520 unseen-angle tasks (61.35%). The image comparison was much closer: ACT solved 227 and Flow Matching solved 226. That one-episode difference is too small to support a reliable ranking from one training seed.

I built Push Any Letter to extend planar pushing beyond a single T and make the geometry of contact part of the experiment. This report records the completed V1 comparison: 52 letters, 6,240 successful planner demonstrations, and four algorithms trained with each of two observation types. My starting recommendation for this state benchmark is ACT. For images, I would keep both ACT and Flow in the next comparison.

Lixin Xu (许立昕) · Interactive project and replays · Code and planning method · Dataset

The final result, with the evaluation unit attached

All eight policies use the final EMA checkpoint at 100,000 optimizer updates. Each receives the same 520 tasks: ten target orientations absent from the demonstration grid, shared across 52 letters, with a fresh start for every letter–orientation pair. A rollout has at most 2,400 control steps and succeeds when geometric coverage reaches 95%. Coverage in the table is the mean at the end of each rollout, including failures.

Algorithm	State successes / 520	State coverage	Image successes / 520	Image coverage
BC	0/520 (0.00%)	18.28%	5/520 (0.96%)	35.79%
Diffusion Policy	33/520 (6.35%)	47.00%	191/520 (36.73%)	69.12%
Flow Matching	25/520 (4.81%)	47.55%	226/520 (43.46%)	72.05%
ACT	319/520 (61.35%)	83.33%	227/520 (43.65%)	79.93%

Final success rates for state and image policies

The stronger image results for Diffusion and Flow do not establish that pixels are generally preferable to object state. The visual encoder changes the representation and parameter count; the pose-only state input describes the shape through a letter identity rather than an explicit outline. We did not isolate those effects. ACT’s higher mean image coverage also deserves attention: it reaches 79.93%, versus Flow’s 72.05%, despite their nearly equal thresholded success rates.

These are results of our compact implementations and one seed, not a reproduction of the original papers’ benchmark rankings. Download exact counts and configurations or the final-results CSV.

A letter is a rigid body with a particular outline

The environment uses Pymunk for physics and Pygame for display. Font outlines become polygonal geometry, then triangles attached to one rigid body. Holes remain empty. Disconnected pieces, such as the dot on a lowercase i, move with the rest of the letter. A circular pusher follows a force-limited position servo in a 640 × 640 arena. The simulator runs on CPU and supports macOS.

The V1 distribution contains A–Z and a–z in Arial Bold, with every target centered at (320, 320). Target orientations are 0°, 30°, …, 330°. Starts vary in position and angle; the complete rotated glyph starts at least 48 pixels inside the inner wall. Initially solved states are rejected. The pusher starts clear of the object.

The benchmark uses object contact friction 1.4, pusher friction 0.6, and Pymunk space damping 0.12. The generic environment constructor defaults to object friction 0.7, so reproduction must set 1.4 explicitly. Damping and contact friction are different parameters. Control runs at 20 Hz with ten physics substeps per action, or 200 Hz physics. This report contains no controlled friction ablation.

Coverage is intersection area divided by goal area. This definition accepts geometric symmetries: an orientation label can differ while the visible shape is aligned. It also gives the same success meaning to wide, narrow, concave and hollow glyphs.

Where the 6,240 demonstrations came from

The demonstrations were generated by our contact-sampling model-predictive controller. It has privileged access to object state, collision geometry and a simulator. At each planning iteration it samples approach/contact candidates, simulates different push directions and lengths in copied environments, and keeps a useful action prefix. The cost combines squared translation error with a rotation term scaled by the body’s moment-to-mass ratio; detected rotational symmetries are considered. An approach-length penalty discourages unnecessarily long detours. The real episode advances only through the selected pusher actions.

The released generation run used 20 contact samples, at most 40 planning iterations and 2,400 control steps per attempt, with generation seed 20261026 and 128 CPU workers. Different initial states and planner seeds provide multiple solutions per condition. It accepted 6,240 of 6,269 attempts, filling 52 × 12 × 10 slots. That acceptance fraction describes this data-generation procedure, including retries; it is not a held-out learned-policy score or evidence that paths are optimal.

Every accepted episode was replayed independently from its reset state, using only the saved actions. The validator checks finite arrays, action bounds, matching rewards and termination flags, no steps after termination, arena bounds, state error below 0.001 and pusher penetration below 3 pixels. Replay must finish successfully. Recorded maximum state error across the release was zero under the matching setup. Replay consistency certifies agreement with this simulator, not physical realism outside it.

V1 contains 4,736,343 transitions, with 23–2,385 steps per episode and a mean of 759.0. Its 52 TAR shards occupy about 3.19 GB; each episode is an internally compressed NPZ. All 52 published shard hashes and sizes were rechecked against the V1 release source for this report.

The public dataset’s default branch can advance. These results use center12-friction14-v1, pinned to Hugging Face revision 8c02168906f991bc07ee3648bee6290babf13e47. The matching font hash is d72db21f9242aedd6b917d8549ad5921766b24d5f8d0becfda2ff4c620b3c2e0. Font binaries are excluded from the release; changing the font changes the task geometry.

What the policies observe and predict

Stored state observations have eight values: pusher XY, object XY, object angle, goal XY and goal angle. Stored actions are absolute pusher XY targets, clipped to [28, 612]². RGB observations are 96 × 96 × 3 uint8 frames captured before the corresponding action. The records also contain next states, rewards, termination flags and metadata.

For state training, each frame becomes 62 features: six normalized position coordinates, sine and cosine of object and goal angles, and a 52-way letter one-hot vector. Every policy receives a two-frame history. Velocities and planner internals are not inputs to these imitation policies.

For image training, each frame contains RGB plus 58 auxiliary values: pusher XY, goal XY, sine/cosine of the goal angle, and the letter one-hot vector. Current object pose and velocity are excluded. A trainable residual CNN with GroupNorm, 32 spatial-softmax keypoints and a 256-dimensional embedding encodes each frame. This is image plus proprioception and task information. The goal outline is visible in the image. Each algorithm has its own independently trained encoder.

History repeats the initial frame at reset. Sample windows never cross episode boundaries, and padded end-of-episode actions are masked from the loss. All ten demonstrations per condition are used for training; there is no held-out demonstration split. Online evaluation supplies new starts instead.

Four objectives under a fixed update budget

Algorithm	Implementation in this project	Predict / execute
Vanilla BC	Three 256-wide MLP layers, action MSE	1 / 1
Diffusion Policy	Conditional 1D U-Net with FiLM; noise prediction over 100 cosine diffusion steps; 10-step DDIM sampling	16 / 4
Flow Matching	Same U-Net; independent Gaussian-to-action linear paths; velocity regression; 10 Euler integration steps	16 / 4
ACT	Transformer CVAE, latent 32, width 128, two encoder/decoder layers; L1 + 10 × KL; zero latent at inference	16 / 4

The method sources are Diffusion Policy, Chi et al., Flow Matching, Lipman et al., and ACT / ALOHA, Zhao et al.. Push-T also motivates the environment. Our implementation keeps the stated objectives but changes architecture size, observations and task. ACT executes four actions before replanning and does not use temporal aggregation. Flow uses independently paired noise and data, without an optimal-transport coupling. BC has a shorter horizon than the other methods, which limits causal interpretations of the comparison.

Every run uses seed 42, 100,000 updates, effective batch size 256, AdamW with learning rate 1e−4, warmup and cosine decay, weight decay 1e−4, gradient clipping at 1, and EMA decay 0.995. Image training accumulates four microbatches of 64. Episodes and within-episode times are sampled uniformly, so longer episodes do not automatically dominate. Runs used four shared RTX 5090 GPUs with PyTorch 2.8.0 and CUDA 12.8. Equal updates do not imply equal compute.

Parameter counts range from 0.164M to 1.793M for state policies and 3.114M to 4.743M for image policies. The public source reference is revision 73289a1. We compared deployed source hashes with that revision: the core model, training, evaluation and environment files match; public data-loading, font-resolution and launch adapters include portability changes. The downloadable results record preserves the exact training-source hashes and names the differences, rather than claiming a historical training Git revision that was not recorded.

Loss falls much more easily than rollout failure disappears

Loss was logged every 100 updates. Faint lines below are raw observations; bold lines are trailing means over 20 logged points. Each algorithm has its own logarithmic axis because action MSE, noise MSE, velocity MSE and L1-plus-KL are different objectives. Comparing their vertical values would be misleading.

Four state-policy loss histories

Four image-policy loss histories

BC reaches low supervised error but solves zero state tasks and only five image tasks. A plausible explanation is the difficulty of choosing among contact strategies with a single-step deterministic regressor, followed by compounding errors during execution. The current comparison does not isolate that mechanism from architecture, horizon or optimization. The failed rollouts are a reason to keep closed-loop evaluation alongside loss.

Seen starts and unseen angles use smaller curves

The success curves use 52 fixed training starts and 52 fixed unseen-angle starts, one per letter. The training starts come from demonstrations; the test starts are a subset of the 520-task manifest. These are simulator rollouts from those states, not accuracy on recorded expert actions. A single success changes a curve point by 1.92 percentage points.

The test manifest was sampled with seed 20261027 before training. Curve-subset selection uses seed 20261028; policy sampling during evaluation resets the PyTorch RNG to 20261026. Its ten angles are at least 3° from the twelve demonstration angles and from one another. Test starts were not filtered for planner success. All algorithms and both observation types share the tasks. The curves monitor progress; the final EMA at the predetermined update budget remains the reported model.

Training-start and unseen-angle success curves for both observation types

State success snapshots were added after training had begun. The first available checkpoints are BC 38k, Diffusion 12k, Flow 10k and ACT 6k; missing earlier success rates are left absent. The image curves include initialization and every 10k updates. Loss history exists earlier than the state success history.

At the final checkpoint, the 52-case curve counts are:

Observation	Algorithm	Training starts / 52	Unseen-angle starts / 52
state	BC	0/52	0/52
state	Diffusion Policy	0/52	1/52
state	Flow Matching	4/52	4/52
state	ACT	27/52	36/52
image	BC	0/52	3/52
image	Diffusion Policy	17/52	17/52
image	Flow Matching	22/52	22/52
image	ACT	28/52	23/52

For example, state ACT’s 36/52 test curve point is 69.23%, while its full final score is 319/520, or 61.35%. Both are correct for their respective sets. The 52-case number should not replace the final score. Raw loss CSV · Success-curve CSV · All final episode outcomes.

Failures that the aggregate still hides

The following state-ACT examples come from the same final evaluation. All six were independently replayed locally with zero recorded state discrepancy. They were selected to show success and failure for T, S and a; their balanced selection is not a success-rate estimate.

Three successful state-ACT episodes with pusher history

Successful T, S and a examples take 568, 618 and 280 steps respectively. Their final coverages are 95.45%, 95.02% and 95.19%.

Three failed state-ACT episodes with pusher history

Each failure reaches the 2,400-step limit. T briefly reaches 87.89% coverage but ends at 47.24%; S reaches 90.55% and ends at 88.03%; a ends at 50.74%. The pale lines trace pusher history. Proximity and repeated contact can coexist with a persistent alignment error. The interactive project replays expose the motion and its history; the selection record gives exact task identities and replay checks.

The next data comparison

This report fixes the training condition at 10 demonstrations per letter–orientation pair. The published V2 dataset raises that to 100, or 62,400 episodes. The next policy comparison should retain a clearly identified data revision and the same evaluation tasks. Its purpose is to measure how much the ranking changes with data coverage. Results from that larger condition are not part of the tables above.

I would repeat the seeds and match action horizons before turning these numbers into a broad algorithm recommendation. The present tasks use known letters, one font and center targets. They do not measure transfer to new characters, fonts or arbitrary target locations. Successful-only demonstrations also leave failed recovery behavior underrepresented, and geometry symmetries complicate a literal interpretation of “unseen angle.”

Online reinforcement learning is a separate experiment: it generates interaction data during training, so demonstration release labels V1/V2/V3 do not define its training input. Reward, reset distribution, code and seed still need versions. The two PPO attempts so far did not establish a successful policy; they are not included in this imitation-learning ranking.

每个字母、每个目标朝向使用十条示范时，状态版 ACT 在 520 个未见角度任务中完成了 319 个，成功率为 61.35%。图像版的结果接近得多：ACT 完成 227 个，Flow Matching 完成 226 个。只有一个案例的差距，加上每种方法只训练了一个 seed，尚不足以给出可靠的先后排名。

我开发 Push Any Letter，是想把平面推动从单个 T 扩展到多种字母，让接触几何成为实验中的一个变量。这篇报告记录已经完成的 V1 比较：52 种字母、6,240 条成功规划示范，以及状态与图像两种观测下的四种模仿学习算法。对于当前状态任务，我会优先选 ACT 作为后续基线；图像任务则值得同时保留 ACT 和 Flow。

Lixin Xu（许立昕） · 交互项目与回放 · 代码与规划方法 · 数据集

最终结果：先分清统计对象

八个策略都使用第 100,000 次优化更新的最终 EMA 权重。测试包含相同的 520 个任务：十个不在示范网格中的目标朝向，每个朝向覆盖全部 52 个字母，并为每个字母与朝向组合采样一个新起点。每次 rollout 最多执行 2,400 步，几何覆盖率达到 95% 算成功。表中的覆盖率是全部 rollout 结束时的平均值，包含失败案例。

算法	状态版成功数 / 520	状态版覆盖率	图像版成功数 / 520	图像版覆盖率
BC	0/520 (0.00%)	18.28%	5/520 (0.96%)	35.79%
Diffusion Policy	33/520 (6.35%)	47.00%	191/520 (36.73%)	69.12%
Flow Matching	25/520 (4.81%)	47.55%	226/520 (43.46%)	72.05%
ACT	319/520 (61.35%)	83.33%	227/520 (43.65%)	79.93%

状态与图像策略的最终成功率

Diffusion 和 Flow 的图像版分数高于状态版，但这还不能说明像素输入普遍优于物体状态。视觉编码器改变了表示方式和参数量；状态输入通过字母类别标识形状，没有直接输入轮廓。本实验没有单独控制这些因素。另一个值得保留的差别是最终覆盖率：图像 ACT 达到 79.93%，Flow 为 72.05%，虽然二者按 95% 阈值统计的成功率几乎相同。

这些数字对应本项目的紧凑实现和单个训练 seed，不能替代原论文的基准结果。完整计数与配置 · 最终结果 CSV。

字母轮廓决定接触方式

环境采用 Pymunk 处理物理、Pygame 显示画面。字体轮廓转换成多边形后进行三角剖分，再把各部分绑定到同一个刚体。孔洞保持为空；小写 i 的点等分离部分随字母整体移动。圆形推杆在 640 × 640 场地内跟随有限力的位置伺服目标。仿真运行在 CPU 上，支持 macOS。

V1 包含 Arial Bold 字体的 A–Z 与 a–z。目标始终位于 (320, 320)，朝向为 0°、30°……330°。初始位置和朝向随机，完整旋转轮廓距内墙至少 48 像素；已成功的初态会被拒绝，推杆也从无碰撞的位置开始。

本基准将物体接触摩擦系数设为 1.4，推杆摩擦为 0.6，Pymunk 空间阻尼为 0.12。通用环境构造函数的物体摩擦默认值为 0.7，复现实验时必须显式设置为 1.4。阻尼与接触摩擦是不同参数。控制频率为 20 Hz，每个动作执行十次物理子步，对应 200 Hz 物理频率。这篇报告不包含受控的摩擦消融实验。

覆盖率定义为当前字母与目标的交集面积除以目标面积。因此，几何上对称的朝向可以被判为成功，不要求恢复一个不可见的朝向标签。这个判据也适用于细长、凹形和带孔洞的字母。

6,240 条示范如何生成

示范由我们实现的接触采样 MPC 生成。规划器可以访问物体状态、碰撞几何和仿真器。每轮规划采样接近路径与接触点，在复制的环境中尝试不同推动方向和长度，然后选择一段有用的动作前缀。代价由平移误差平方与旋转误差组成，旋转项按刚体转动惯量与质量之比缩放，并考虑检测到的旋转对称性；接近路径长度另有小幅惩罚。真实 episode 只执行选出的推杆动作。

发布数据的生成配置使用 20 个接触采样点，每次尝试最多规划 40 轮、执行 2,400 步，基础 seed 为 20261026，使用 128 个 CPU worker。不同初始状态和规划随机种子为同一条件提供不同解法。总共 6,269 次尝试接受了 6,240 条轨迹，填满 52 × 12 × 10 个位置。这个接受比例描述包含重试的数据生成过程，不能当成学习策略的泛化成功率，也不意味着轨迹最优。

每条接受的轨迹都从 reset 状态重新开始，仅使用已保存的动作独立回放。验证器检查数组有限性、动作边界、reward 与终止标志一致性、终止后没有继续执行、场地边界、低于 0.001 的状态误差，以及小于 3 像素的推杆穿透量；回放最终必须成功。在匹配的运行配置下，发布数据记录到的最大状态误差为零。这个检查保证了与当前仿真的一致性，并不证明现实世界中的物理精度。

V1 共含 4,736,343 个 transition。单条轨迹长 23–2,385 步，平均 759.0 步。52 个 TAR 分包约占 3.19 GB，各 episode 内部采用压缩 NPZ。本报告再次核对了公开 V1 的全部 52 个分包哈希与大小。

数据集默认分支可能继续更新。本次训练固定使用 center12-friction14-v1，对应 Hugging Face 提交 8c02168906f991bc07ee3648bee6290babf13e47。匹配字体的 SHA-256 是 d72db21f9242aedd6b917d8549ad5921766b24d5f8d0becfda2ff4c620b3c2e0。发布内容不含字体二进制文件；更换字体会改变任务几何。

观测、动作和训练窗口

数据记录中的状态是八维：推杆 XY、物体 XY、物体角度、目标 XY、目标角度。动作是 推杆的绝对 XY 目标，范围为 [28, 612]²。RGB 为动作执行前的 96 × 96 × 3 uint8 图像。记录还包括下一状态、reward、终止标志和元数据。

状态版把每帧转换为 62 维：六个归一化位置坐标、物体与目标角度的正弦和余弦，以及 52 维字母 one-hot。所有模型都接收连续两帧历史。速度和规划器内部信息不属于这些模仿学习策略的输入。

图像版每帧输入 RGB 与 58 维辅助信息：推杆 XY、目标 XY、目标角度正弦/余弦和字母 one-hot。当前物体位姿、速度均被排除。每种算法各自训练一个带 GroupNorm 的残差 CNN，经 32 个 spatial-softmax 关键点得到 256 维视觉特征。因此，这组实验使用的是 图像、本体信息与任务信息的组合；图像本身也显示目标轮廓。

reset 时重复首帧填充历史；采样窗口不会跨 episode，末尾补齐的动作不计入 loss。每个条件的十条示范全部用于训练，没有预留示范轨迹作为验证集。新的起点由在线仿真测试提供。

四种实现与固定更新预算

算法	本项目实现	预测 / 执行步数
Vanilla BC	三层、每层 256 宽的 MLP，动作 MSE	1 / 1
Diffusion Policy	FiLM 条件 1D U-Net；100 步余弦扩散、噪声预测；10 步 DDIM 采样	16 / 4
Flow Matching	相同 U-Net；独立高斯噪声到动作的线性路径、速度回归；10 步 Euler 积分	16 / 4
ACT	Transformer CVAE，latent 32、宽度 128、两层 encoder/decoder；L1 + 10 × KL；推理使用零 latent	16 / 4

方法来源分别为 Chi 等人的 Diffusion Policy、Lipman 等人的 Flow Matching 和 Zhao 等人的 ACT / ALOHA。推动任务也受到 Push-T 启发。我们的实现保留表中的训练目标，但改变了网络规模、观测和任务：ACT 每执行四步重新规划，不使用 temporal aggregation；Flow 独立配对噪声与数据，没有最优传输耦合。BC 的动作 horizon 也短于其余方法，不能把全部差异归因于某一种 loss。

每次训练使用 seed 42、100,000 次优化更新、有效 batch size 256。优化器为 AdamW，初始学习率 1e−4，采用 warmup 与余弦衰减，weight decay 1e−4，梯度裁剪阈值为 1，EMA 衰减为 0.995。图像版累积四个大小为 64 的 microbatch。episode 和 episode 内的时间位置分别均匀采样，长轨迹不会自动得到更多权重。训练使用四张共享 RTX 5090，PyTorch 2.8.0、CUDA 12.8；相同更新次数不等于相同计算量。

状态模型参数量为 0.164M–1.793M，图像模型为 3.114M–4.743M。公开代码参考版本是提交 73289a1。部署源码与该提交的哈希对照显示，核心模型、训练、评估及环境文件一致；公开版的数据载入、字体解析和启动适配层有可移植性修改。可下载结果保留了实际源码哈希与差异文件列表，不把参考提交冒充成当时未记录的训练 Git 提交。

Loss 降低之后，闭环任务仍可能失败

Loss 每 100 次更新记录一次。下图浅线为原始值，深线为最近 20 个记录点的滑动均值。动作 MSE、噪声 MSE、速度 MSE 与 L1 加 KL 的含义不同，所以各方法使用独立的对数纵轴，不能直接比较曲线的绝对高低。

四种状态策略的 loss 曲线

四种图像策略的 loss 曲线

BC 的监督误差已经较低，但状态版一个任务也没完成，图像版只完成五个。单步确定性回归可能难以选择不同接触策略，执行误差又会在 rollout 中累积；这是一种解释，还没有通过单独控制网络、horizon 和优化设置来验证。失败结果说明，训练 loss 必须和闭环成功率一起看。

训练起点与未见角度的过程曲线

成功率曲线采用 52 个固定训练起点和 52 个固定未见角度起点，各自每个字母一个。训练起点来自示范；测试起点是 520 个最终测试任务的子集。这些分数都来自策略在仿真中的自主执行，不是对专家动作的预测准确率。每多成功一个案例，曲线就变化约 1.92 个百分点。

最终测试清单在训练前用 seed 20261027 生成。曲线子集的选择使用 seed 20261028；每次评估中的策略采样把 PyTorch RNG 重置为 20261026。十个测试角度距示范网格及彼此至少 3°，起点不经过规划器成功筛选。所有算法、两种观测使用相同任务。曲线用于监控训练，报告模型始终是预定预算结束时的最终 EMA，没有按测试结果挑选 checkpoint。

两种观测下的训练起点与未见角度成功率曲线

状态版在训练开始后才加入不可变 checkpoint。最早可用的成功率检查点分别是 BC 38k、Diffusion 12k、Flow 10k、ACT 6k，更早的分数保持缺失。图像版包含初始化和此后每 10k 更新的评估。Loss 记录比状态版成功率记录更早。

最终 checkpoint 对应的 52 例曲线计数如下：

观测	算法	训练起点成功数 / 52	未见角度起点成功数 / 52
state	BC	0/52	0/52
state	Diffusion Policy	0/52	1/52
state	Flow Matching	4/52	4/52
state	ACT	27/52	36/52
image	BC	0/52	3/52
image	Diffusion Policy	17/52	17/52
image	Flow Matching	22/52	22/52
image	ACT	28/52	23/52

例如，状态 ACT 在曲线测试子集上为 36/52，即 69.23%；完整最终测试则为 319/520，即 61.35%。二者统计对象不同，不能用前者替代后者。原始 loss CSV · 成功率曲线 CSV · 全部最终测试结果。

看见失败过程

下面六个状态 ACT 案例来自同一次最终评估，均已在本地独立回放，记录到的状态偏差为零。它们特意选取 T、S、a 各一条成功和失败轨迹，因此这组展示的成功比例不代表整体性能。

三条成功的状态 ACT 轨迹及推杆历史

成功的 T、S、a 分别执行了 568、618、280 步，最终覆盖率分别为 95.45%、95.02%、95.19%。

三条失败的状态 ACT 轨迹及推杆历史

失败案例都运行到 2,400 步上限。T 曾达到 87.89% 覆盖率，最终降到 47.24%；S 最高为 90.55%，最终为 88.03%；a 最终为 50.74%。浅色线条显示推杆的历史路径。靠近目标并反复接触，仍可能始终无法消除对齐误差。交互回放可以查看运动过程与轨迹线，案例记录提供精确任务信息和回放检查结果。

下一轮比较要回答的问题

本报告固定在 每个字母、每个朝向十条示范 的条件。已发布的 V2 数据集把它增加到 100 条，总计 62,400 条。下一轮策略比较应固定数据修订和测试任务，观察数据覆盖增加后算法排名如何变化。上述表格不包含更大数据条件的结果。

在给出更广泛的算法建议之前，我会增加训练 seed，并匹配动作 horizon。当前任务只覆盖已知字母、单一字体和中心目标，不能据此判断新字符、新字体或任意目标位置上的表现。训练数据只包含成功轨迹，也限制了失败状态下恢复行为的覆盖。字母的几何对称性还会影响“未见角度”的实际含义。

在线强化学习是另一组实验：训练时自己与环境交互，因此示范数据集的 V1/V2/V3 不定义它的训练输入。但 reward、重置分布、代码和 seed 仍然需要版本记录。目前两次 PPO 尝试尚未得到成功策略，不计入本篇模仿学习排名。

Citation / 引用

Environment, contact-sampling planning implementation and dataset by Lixin Xu (许立昕). Code: MIT. Demonstrations: CC BY 4.0. Third-party font rights are separate. Please cite both the software/method and dataset entries below, taken from the project’s CITATION.bib.

@software{xu2026pushanyletter,
  author = {Xu, Lixin},
  title = {Push Any Letter: A 2D Letter-Pushing Environment and Planning Baselines},
  year = {2026},
  version = {0.1.0},
  url = {https://github.com/DavidLXu/Push-Any-Letter}
}

@misc{xu2026pushanyletterdata,
  author = {Xu, Lixin},
  title = {Push Any Letter: Center-12 High-Friction Demonstrations},
  year = {2026},
  howpublished = {Hugging Face},
  note = {Version center12-friction14-v1, CC BY 4.0},
  url = {https://huggingface.co/datasets/DavidLXu/Push-Any-Letter}
}

Reproducibility assets / 复现材料：configuration, source hashes and results · final episode records · asset checksums · loss PDF: state / image · success-curve PDF.

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Lixin Xu