Sparsity Regularization in Latent Action Learning

• Sparsity regularization is a constraint mechanism that ensures latent variables encode only the minimal, agent-relevant information required for predicting future dynamics.
• It is operationalized via loss design and representational bottlenecks, such as slot-entropy regularization and sparse slot selection, to filter out distractor influences.
• Empirical evidence shows that integrating sparsity regularization improves sample efficiency and downstream policy performance by reducing action probe error and enhancing normalized returns.

A sparsity regularization principle directly relevant to latent action learning and world modeling is to constrain the latent variables—here, proxy actions or latent action codes—so that they encode only the minimal, task-relevant information required for predicting future agent-centric dynamics. In object-centric latent action learning, as developed in "Object-Centric Latent Action Learning" (Klepach et al., 13 Feb 2025), such regularization is operationalized both via loss design and representational bottlenecks aimed at filtering out irrelevant distractor dynamics, thereby improving robustness to high-dimensional, temporally correlated background noise.

1. Theoretical Role of Sparsity Regularization in Latent Action Learning

Sparsity in this context refers not only to standard $\ell_1$ norm penalties but, more generally, to the design of constraints and learning objectives that concentrate the latent action representation $z_t$ on the minimal set of degrees of freedom needed to explain agent-induced transitions, while suppressing entanglement with nuisance or environment-driven changes. The underlying motivation is that, in the presence of visual distractors—including background motion, lighting changes, or camera jitter—unsupervised models that maximize only transition likelihood or reconstruction error tend to allocate latent capacity to both control-relevant and control-irrelevant variations. This dilutes the informativeness of $z_t$ for downstream imitation and RL.

2. Object-Centric Representations as Implicit Sparsity Regularization

The architecture proposed in "Object-Centric Latent Action Learning" utilizes a Slot Attention module, producing $K$ slot vectors $s_t^k \in \mathbb{R}^d$, each intended to capture an independently moving entity in a frame. Regularization arises from several mechanisms:

• Slot-Entropy Regularization: Implicit in Slot Attention, a low-entropy slot-assignment distribution is promoted so that each pixel is explained by a single slot. This penalty suppresses diffuse, non-discriminative explanations, enforcing that only the most salient object-centric representations (typically, the agent and occasionally the floor) persist for downstream use. High-entropy assignments would otherwise allow single-pixel variations or noise to influence all slots, reducing sparsity and interpretability of the active latent code.
• Sparse Slot Selection: After object-centric pretraining, only a small subset (often just 1–2) of the $K$ slots is selected—by inspecting the slot decoder's spatial masks—for further processing. This selection manually enforces sparsity at inference: only those slots corresponding to agent-relevant entities are propagated into the latent action inference pipeline, while all background and distractor slots are discarded. The latent action models (IDM/FDM) then operate purely on this compact, agent-centric subspace, which excludes distractor influence by construction.

3. Loss Formulations and Implicit Regularization

The total object-centric loss combines multiple terms:

• Pixel Reconstruction Loss ($L_\text{recon}$): Promotes correct reconstruction of the original image via a sparse superposition of object slot reconstructions, weighted by spatial masks.
• Temporal Contrastive Loss ($L_\text{cs}$): Encourages features at corresponding spatial locations in consecutive frames to be similar only if the associated entity moves, discouraging encoding of static background or temporally uncorrelated distractor features.
• Slot-Entropy Regularization: Penalizes diffuse slot-attribution, enforcing sharp partitioning of the input among slots (low-entropy assignments).

The aggregation of these losses, each with carefully tuned weights, acts to regularize both feature and assignment sparsity. Operationally, this ensures that transitions in the agent slots dominate the change explained by $z_t$, relegating distractor variance to unselected slots with no downstream influence.

4. Empirical Impact of Sparsity Regularization

Direct empirical evaluation highlights the efficacy of these implicit sparsity mechanisms. In the Distracting Control Suite (DCS), standard LAPO models absorb spurious correlations from distractors, resulting in an average action-probe MSE degradation of $\times 5.3$ compared to distractor-free baselines; object-centric bottlenecks employing sparse slot selection reduce this gap by an average factor of $2.5$ to $2.7$, while also improving normalized downstream return by $2$ to $2.6 \times$ across domains. Sample efficiency is also greatly increased: on cheetah-run, the object-centric LAPO matches its no-distractor limit using only 32 finetuning trajectories, compared to the baseline requiring orders of magnitude more (Klepach et al., 13 Feb 2025).

Method	Action-Probe MSE Δ	Downstream Return Δ	Comments
LAPO	Baseline	Baseline	Distractor-sensitive; high variance
LAPO-slots	×2.5–2.7 better	×2–2.6 better	Object-centric, sparsity via slot mask
LAPO-no-distr	×5.3 better	×3.9 better	Idealized; no distractors present

The ablation evidence indicates that slot-based object-centric decomposition, serving as an implicit structural regularizer, is more effective under high-distractor conditions than pixel-level sparsity or naïve codebook quantization.

5. Relationship to Other Forms of Regularization

While explicit $\ell_1$ sparsity penalties on latent codes are not directly applied in this framework, the imposed architectural and training constraints functionally induce an analogous effect at the semantic level. Only agent-centric dynamics are entangled with $z_t$, while the high-dimensional observation space and all non-agent object motion (including distractors) are projected out by slot selection and entropy control.

Contrast this with prior approaches relying on VQ-VAE codebook sparsity or continuous latent penalization, which demonstrably collapse in the presence of correlated distractors due to the models' tendency to fill latent capacity with whatever maximizes reconstruction fidelity—even if those features are causally irrelevant for control (Nikulin et al., 1 Feb 2025). As such, the object-centric sparsification mechanism offers a data-bias-robust alternative to classic sparsity constraints.

6. Open Directions for Sparsity Regularization

The current pipeline requires manual selection of agent-relevant slots and fixed regularization hyperparameters, which may limit scalability to truly unconstrained internet video, where distractor statistics are unknown and slot semantics drift. A salient open problem is automatic, task-agnostic selection of relevant slots and adaptive regularization schedules—potentially driven by downstream probing performance or information-theoretic constraints applied dynamically to the latent code distributions.

Further, integrating object-centric sparse decomposition with multi-step temporal aggregation or jointly training slot-extraction and dynamics end-to-end may yield even richer, more invariant sparse action representations, retaining only those features causally tied to agent-initiated change.

7. Conclusion

Sparsity regularization in object-centric latent action learning emerges via an architectural and loss-driven bottleneck, which restricts latent action codes to agent-relevant information by construction. This reduces sensitivity to temporally correlated distractors, enhances sample efficiency, and permits robust semantics transfer from observational data to downstream policy learning, as evidenced by substantial empirical gains in both action-probe and behavior cloning metrics (Klepach et al., 13 Feb 2025). Object-centric sparsification thus constitutes a core methodological advance for scalable, distraction-robust latent action models in embodied AI.