Menu

Research

One source, or all three.

How much information is enough when one of three sources may lie? In the specified model, a plan that reads either one source or all three attains the minimum worst-case expected cost of approximately 5.4293 units at a 5% failure limit.

Read more
Allowed failure probability against worst-case expected cost. A segment connects all three sources (about 0.2698546%, 6 model cost units) to one source chosen uniformly (about 33.4233456%, 2 units). It is both achievable and a lower bound for every strategy. At 5%, the optimum is about 5.4293 units.265%5.4293

Five observations, a different accuracy limit.

The same observation budget need not provide the same guaranteed accuracy. In a model with shared bias and bounded noise, we prove that five adaptive observations can attain the optimal worst-case accuracy of all nine. The error ratio between the best fixed five-observation strategy and the adaptive strategy can grow without bound.

Read more
As the noise bound epsilon approaches zero, the ratio of the best fixed five-observation error F to the optimal adaptive five-observation error A tends to infinity.limε → 0+F(ε)A(ε)=∞

FBest fixed five
Square-root error order

AOptimal adaptive five
Linear error order

F and A denote optimal worst-case absolute recovery errors. The noise bound ε tends to zero within the proved parameter region, with the other model conditions fixed.

From target accuracy to minimum observation cost.

What is the least we must spend to reach a required accuracy? We study minimum observation costs in known linear models, the unavoidable cost of checking learned predictions, and a bound on acquisition costs when learning and checking share the same batch.

Read more

We can stop.

{000, 100}one unknown dimension

The binary cube with candidate targets 000 and 100 highlighted. They differ in one bit. The output 000 is within one bit of both targets.000100010110001101011111

Choose 000.

The outputs 000 and 100 are each within one bit of both candidates.

We must continue.

{000, 111}one unknown dimension

The binary cube with candidate targets 000 and 111 highlighted. They differ in three bits. No output is within one bit of both targets, so zero failure requires further observation.000100010110001101011111

No output works for both.

The candidates are three bits apart. No output lies within one bit of both.

● Remaining candidates. Each edge changes one bit.At most one output bit may be wrong; failure probability is zero.

The cost of leaving information out.

Simplifying an observation interface changes the evidence available for verification. Within the studied models, we establish when optimal cost is preserved and derive an exact worst-case multiplier for the cost increase.

Read more
Conceptual geometric illustration of distinctions between observation outputs being merged.

Six-vertex minimality and optimal evidence design.

We establish six vertices as the smallest size at which the studied representation fails within the target class. The research combines independent verification of 8,675 instances with optimization of evidence configurations under fault-tolerance requirements.

Read more
Six-vertex construction

Carrying proofs forward.

Carry accumulated evidence into the next decision. Beyond sharing proof structure and using evidence across tasks, we establish conditions for completing execution after updates without reacquiring evidence, and determine the worst-case continuation cost in the model studied.

Read more
Conceptual modular structure showing multiple verifications sharing parts of a proof representation.