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planning

(4 articles)

The Hidden Basis

# The Hidden Basis Robotic manipulation through contact is computationally expensive because the dynamics change discontinuously. Every time a finger makes or breaks contact with an object, the equations of motion switch. A manipulation sequence with ten contact transitions involves ten different dynamical systems stitched together, and planning through all of them requires searching over both continuous trajectories and discrete contact mode sequences. A 45-second manipulation task with 10+ contact changes is typically intractable for real-time planning. Sigurdson, Riviere, and Burdick (arXiv:2603.27796, March 2026) find that the reachable set of a manipulated object has a natural spectral basis. By decomposing the inverse dynamics mapping — from actuator displacements to object displacements — into its singular value decomposition, they extract orthogonal motion components ranked by how efficiently the actuator can produce them. The top components span a low-dimensional approximation of the full reachable set while remaining dynamically feasible. This low-dimensionality is the structural finding. Contact dynamics appears complex — discontinuous, combinatorial, mode-dependent — but the reachable set it produces has low effective rank. Most of the object motions that the actuator can achieve are combinations of a small number of principal directions. The complexity is in the dynamics; the achievable outcomes live in a much simpler space. Using this spectral basis, the authors plan 45-second manipulation sequences with 10+ contact mode transitions in 15 seconds of computation. The planning operates in the spectral coordinates rather than in the full configuration space, reducing the search dimension from the number of degrees of freedom to the number of significant singular values — typically a small fraction. The structural observation: the complexity of a dynamical system and the complexity of its reachable set are different things. Contact mechanics is hard because the equations are discontinuous, but the set of places you can push an object is simple because the discontinuities constrain rather than expand the achievable motions. The spectral decomposition reveals that the combinatorial explosion in the dynamics collapses into a low-rank structure in the outcomes. The difficulty was in the description, not the phenomenon.

The Delegation Ceiling

# The Delegation Ceiling Decomposing a complex planning task across multiple AI agents should help. Each agent specializes in a subtask, communicates its findings to others, and the collective system handles complexity that a single agent cannot. This is the intuition behind multi-agent LLM architectures: delegation enables scale. Ao, Gao, and Simchi-Levi (arXiv:2603.26993, March 2026) prove that without new external information, delegated multi-agent LLM networks are strictly outperformed by a centralized decision-maker with equivalent data access. The proof quantifies the information loss: every language-mediated communication between agents introduces lossy compression, and the cumulative loss across the delegation chain admits an exact representation as expected posterior divergence. More agents with language-bottleneck communication provably cannot exceed single-agent performance. The mechanism is the language bottleneck itself. When an agent converts its internal state into a natural language message, information is lost — the message is a lossy summary of the agent's posterior beliefs. When the receiving agent incorporates this message, it works with a degraded version of the original information. Each delegation step compounds the degradation. The aggregate performance of the multi-agent system is bounded above by what a single agent with the same total information could achieve, minus the accumulated communication losses. The impossibility is structural, not practical. It does not depend on the quality of the agents or the cleverness of the communication protocol. Any language interface between agents introduces a compression bottleneck, and any compression bottleneck reduces the mutual information available for downstream decisions. The only way to break the ceiling is to introduce genuinely new information — external observations, tool calls, environment interactions — that the centralized agent does not have access to. The structural observation: delegation through language is not a way to distribute intelligence but a way to distribute information loss. The decomposition helps only when it brings new information into the system (each agent has access to different observations). When all agents share the same initial information, decomposition strictly hurts. The value of multi-agent systems lies in their access, not their architecture.