Latent Projection for Latent Planning

Computer Science > Machine Learning arXiv:2610.26979 (cs) [Submitted on 19 Oct 2026] Title: Latent Projection for Latent Planning Authors: Yoo Sung Jang, Michael Ryoo.

计算机科学 > 机器学习 arXiv:2610.26979 (cs) [提交于 2026 年 10 月 19 日] 标题：用于潜在规划的潜在投影 作者：Yoo Sung Jang, Michael Ryoo。

Abstract: Latent world models let an agent plan in latent space. The planner searches for an action sequence that minimizes a cost, and that cost is often the $\ell_2$ distance between the predicted terminal latent and the goal latent. The latent, however, is partly noise: the regularizer that prevents collapse during world model training promotes variance in the directions carrying no signal.

摘要：潜在世界模型允许智能体在潜在空间中进行规划。规划器搜索一个能使代价最小化的动作序列，而该代价通常是预测的终端潜在状态与目标潜在状态之间的 $\ell_2$ 距离。然而，潜在状态部分包含噪声：在世界模型训练期间防止崩溃的正则化器会促进在不携带信号的方向上的方差。

We show that the same regularizer also supplies the structure to prune that noise in the latent. SIGReg drives the latent marginal to a standard Gaussian at every step, and assuming further that the latent sequence is a Gauss-Markov process, the transition is linear with its covariance pinned by the map itself, $z’ \mid z \sim \mathcal{N}(Az,, I - AA^\top)$.

我们证明了相同的正则化器也提供了剔除潜在状态中噪声的结构。SIGReg 在每一步将潜在边缘分布驱动为标准高斯分布，并且进一步假设潜在序列是一个高斯-马尔可夫过程，其转换是线性的，且其协方差由映射本身确定，即 $z’ \mid z \sim \mathcal{N}(Az,, I - AA^\top)$。

Fitting the state dynamics $A$ therefore yields the covariance at no additional cost, and in its eigenbasis each latent direction carries its own uncertainty. Furthermore, constraining $A$ to be a normal matrix fixes that basis across timesteps, so one eigenbasis measures the uncertainty over an arbitrary number of steps and serves as a stable basis to compute the planning cost on.

因此，拟合状态动力学 $A$ 可以无需额外成本地得出协方差，并且在其特征基中，每个潜在方向都带有其自身的不确定性。此外，将 $A$ 约束为正规矩阵可以固定跨时间步的基，因此一个特征基可以衡量任意步数上的不确定性，并作为计算规划代价的稳定基。

We then restrict the $\ell_2$ cost to the $k$-dimensional subspace the state dynamics carry forward with the least uncertainty. The correction is post hoc: the encoder, the predictor, the rollout, and the planner are all left untouched, and only a single constrained matrix, $A$, is fit.

然后，我们将 $\ell_2$ 代价限制在状态动力学以最小不确定性向前推进的 $k$ 维子空间内。这种修正属于事后处理：编码器、预测器、展开过程和规划器均保持不变，仅拟合了一个单一的约束矩阵 $A$。

We evaluate across six environments and show large gains on the 2D navigation tasks, TwoRoom and PointMaze, raising success rate over the plain $\ell_2$ cost by up to $+54.7$ points under a harder planning setting. Code is available at this https URL.

我们在六个环境中进行了评估，并在二维导航任务 TwoRoom 和 PointMaze 上展示了巨大的收益，在更困难的规划设置下，成功率比单纯的 $\ell_2$ 代价提高了多达 $+54.7$ 个百分点。代码可在该 https URL 获取。