More Tiers, Fewer Findings: When Agent Delegation Pays

TL;DR for operators

Adding subordinate agents does not necessarily preserve more information. Under the paper’s calibrated retention model, a two-tier architecture retains only 53.6% as many original findings as a flat architecture processing the same workload. Summarization and delegation introduce losses that compound across tiers.

Hierarchy can still be worthwhile for two different reasons. It reduces the number of potentially incorrect items entering the coordinator’s persistent context, and it can lower processing costs enough to accommodate more findings under a fixed budget. The calibrated model predicts an equal-budget crossover near 403 findings, but this is a structural calculation, not an experimentally validated deployment threshold.

For agent-system operators, the relevant decision is when delegation’s integrity or cost benefits outweigh its information losses. That requires measuring local retention, handoff reliability, persistent-context errors, and processing expenditure rather than assuming that more specialized agents produce better answers.

Smaller contexts do not guarantee more complete answers

Consider a research agent that has accumulated hundreds of search results. Its controller can continue examining them directly or delegate portions of the remaining work to subordinate agents. Each worker receives a smaller collection of material and returns a condensed report.

The second arrangement may reduce context pressure, but every report creates another opportunity to omit a finding. A relevant source can be discovered by a worker, excluded from its summary, and consequently never reach the coordinating agent.

Rong He examines this trade-off in Decomposition Buys Integrity, Not Yield.¹ The paper develops a probabilistic model of information passing through agent hierarchies and calibrates its parameters using public research-agent traces, annotated multi-agent trajectories, and production coding-agent sessions.

Its central contribution is to separate three outcomes that are often combined when evaluating agent architectures: information yield, persistent-root integrity, and computation cost. An architecture that performs poorly on the first can perform better on the other two.

Every additional tier creates another retention penalty

The paper defines information yield as the expected number of original atomic findings that survive all aggregation stages and reach the root agent. It is a measure of information preservation, not whether those findings are relevant, correct, or sufficient to complete the user’s task.

Suppose each aggregation node receives $b$ incoming items and retains any particular item with probability:

Here, $C$ is the baseline retention probability for one incoming item, and $\delta$ describes how retention declines as more items compete for attention.

For a uniform decomposition tree containing $N=b^k$ original findings and $k$ aggregation tiers, the paper derives:

The result separates the effect of task size from the effect of depth. Holding $N$ constant, adding a tier multiplies expected yield by $C$. Because $C$ cannot exceed one, additional tiers cannot improve expected yield under this particular retention model.

The paper establishes an even broader conservation result for the special case $r(b)=1/b$: every rooted decomposition tree, including irregular trees, delivers exactly one expected finding to the root. Numerical checks using 20,000 irregular trees verify the mathematical result, rather than independently establishing how production agents behave.

These theorems do not imply that every possible retention function favors flat architectures. The paper also derives a general fan-out rule based on the carrying number, $\rho(b)=br(b)$. Different retention curves, including those with near-lossless operating regions, can produce an interior optimum.

How much information disappears in observed traces?

The paper calibrates its power-law model using several distinct observational measurements.

The crowding analysis estimates eventual source usage while stratifying by remaining extraction opportunities. An alternative final-citation outcome produces a somewhat higher exponent of 0.398. Meanwhile, immediate next-turn representation remains relatively stable around one third for search batches of approximately five to 41 results.

This suggests that information loss is not confined to the moment a tool response is received. Findings can also become less likely to be used as additional context accumulates.

Delegation introduces another mechanism. A worker may receive a brief that does not accurately communicate the intended task. The model therefore extends expected yield to:

With the estimated parameters:

At fixed task size, moving from one tier to two reduces modeled information yield by approximately 46.4%.

That is a substantial structural penalty. However, the measurements have different meanings: $C$ captures next-turn representation of search results, whereas $\mu$ is inferred from annotated coordination failures. Neither directly measures the semantic completeness of arbitrary worker reports, and the handoff estimate comes from benchmark trajectories rather than the production coding-agent corpus.

Hierarchy can protect the coordinator’s persistent context

If hierarchy loses findings, why introduce it?

The paper identifies a separate benefit arising from the difference between persistent and temporary agent contexts. The coordinating agent retains information across the workflow, while subordinate agents can process intermediate material in isolated contexts that do not persist after their work is complete.

In a flat architecture, the root directly absorbs $N$ incoming items. A uniform depth-$k$ hierarchy reduces that exposure to $N^{1/k}$ aggregated inputs.

For example, processing 100 original findings through two aggregation tiers leaves the root directly receiving 10 summaries instead of 100 separate findings.

The paper represents the probability of keeping persistent root context entirely uncorrupted as:

Here, $\varepsilon$ is the probability that an incoming item contaminates persistent context. Reducing direct exposure increases the modeled probability that no contamination occurs.

Optimizing the product of information yield and root integrity produces an intermediate preferred depth. Under the paper’s calibration, the model selects two tiers for a median production session and three for a session at the 99th percentile.

Those predictions are sensitive to how integrity is defined. The specification effectively treats a single contaminated item as destroying full root integrity. The paper shows that substituting observed tool-error rates into this specification produces implausibly aggressive delegation recommendations.

An incorrect intermediate result does not necessarily invalidate an entire task. Consequently, the model establishes an error-containment mechanism, but its numerical optimal-depth predictions should not be treated as demonstrated reliability gains.

Equal-budget comparisons change the preferred architecture

Information preservation at fixed workload is only one operating objective.

Suppose a flat agent and a hierarchical agent receive the same processing budget. The hierarchical system loses more findings at each aggregation boundary, but smaller working contexts may reduce expenditure sufficiently to permit processing additional findings.

The paper estimates that production input-token consumption scales with session rounds at an exponent of 1.392 ± 0.004, using 6,567 sessions from Claude Code and Codex traces. The relationship is subquadratic but superlinear.

It then transfers this measured scaling relationship into a structural cost model that includes processing costs within agents and the communication overhead of delegation.

Under the pooled calibration, two-tier decomposition overtakes the flat alternative at approximately 403 findings when compared at equal modeled expenditure. Without the estimated briefing loss, the crossover occurs at 246 findings.

These numbers answer a different question from the fixed-workload retention theorem. The theorem asks how many original findings survive a given architecture. The budget comparison asks how many findings can survive when different architectures are allowed to process different amounts of material for the same expenditure.

The 403-finding threshold is therefore an economic prediction conditional on measured parameters and modeling assumptions. It is not an observed point where production task outcomes suddenly improve. The cost model also excludes output-token charges and latency, and the measured exponent relates input-token consumption to session rounds rather than directly identifying cost scaling with arbitrary task size.

Production agents rarely wait for context pressure before delegating

The paper’s production analysis provides an additional operational observation.

Across 7,244 sessions containing tool activity, 563 initiated at least one delegation, representing 7.8% of active sessions. Among spawning rounds, 74.5% launched exactly one subordinate agent, and the observed corpus contained no deeper nesting.

More revealing is the timing of delegation.

Using 502,718 session-round observations and information available before each decision, the paper estimates the hazard of first delegation. After controlling for elapsed rounds, each doubling of accumulated tool-result volume is associated with an odds ratio of 0.969 for delegation, with a 95% interval of [0.954, 0.985].

Rather than increasing as context accumulated, the conditional propensity to delegate declined slightly. The evidence is consistent with delegation being primarily an early-session architectural choice in these systems.

A cost-based version of the structural model predicts delegation-benefit shares ranging from 0.7% to 11.3% across sensitivity assumptions. The observed 7.8% lies within that range, but the match provides only broad calibration. It does not establish that production agents optimize the modeled objective.

Unobserved session differences can also influence the estimated delegation hazard.

Delegation should become a measured routing decision

The Cognaptus inference is that agent orchestration should treat delegation as a conditional resource-allocation policy, implemented at the workflow level rather than assumed to follow from agent specialization.

For teams deploying research, coding, or other tool-intensive agents, this suggests four measurements:

A flat workflow is a sensible baseline when context exposure is manageable and added handoffs mainly reduce retention. Temporary workers become more attractive when measured context-integrity risks or processing savings outweigh those losses.

The policy should be evaluated on representative local tasks, ideally through controlled comparisons of alternative topologies. Retained finding counts should be considered alongside relevance, correctness, completion quality, and total expenditure.

The primary uncertainty is transferability. The research-agent retention estimates come from a particular scaffold; the handoff parameter is weakly identified across frameworks; and the model assumes that retention parameters remain stable when inputs change from individual search results to entire worker reports. Correlated omissions and graded consequences of errors are not fully represented.

No randomized production comparison establishes that the predicted topology changes improve real task success.

The value of hierarchy depends on what the system is optimizing

The paper establishes a precise limit on the information-preservation argument for multi-agent decomposition: under its uniform-tree power-law assumptions, adding aggregation tiers compounds retention loss.

It also explains why this does not settle the architecture decision. Protecting persistent context and reducing the computational cost of processing a large workload are legitimate, separate reasons to introduce hierarchy.

For operators, the next step is not to adopt the calibrated 403-finding threshold as a universal routing rule. It is to estimate the relevant parameters within their own workflows and evaluate whether delegation improves the outcome they actually need.

Cognaptus: Automate the Present, Incubate the Future.