Wide Learning: Learning to Reach Evidence

Junzhou Chen

cs.LGAug 30, 2026

Wide Learning: Learning to Reach Evidence

Authors: Junzhou Chen

Organizations: School of Intelligent Systems Engineering, Sun Yat-sen University Shenzhen 518107, China

Abstract

Machine learning is usually evaluated after an evidence interface has been fixed. A dataset, sensor suite, query language, action set, or experimental protocol determines which observations can be obtained, and learning is judged by what it extracts from them. We study a complementary capability. A learner's state can determine which evidence-generating experiments it can reliably realise under bounded resources, even when primitive affordances remain fixed. We call this learner-relative experiment family its effective epistemic reach, and use Wide Learning for task-relevant learning-induced changes in that family.We formalise effective reach relative to learner state, deployment budget, reliability threshold, and evaluation distribution. In a controlled construction, two hidden worlds have exactly the same public observation law. An informative diagnostic exists in a fixed five-primitive substrate. Before calibration, one address attempt realises it with probability at most $2^{-10} = 1/1024$ , below a pre-specified 0.95 threshold; after calibration, held-out realisation is 1. Public-channel total variation is 0, whereas the realised diagnostic has total variation 1, and sealed binary risk moves from approximately 1/2 to 0. The construction establishes that learning can change effective epistemic reach even when primitive affordances and deployment resources are held fixed. It opens a complementary evaluation question for learning systems: not only what they infer from available evidence, but what informative evidence experience teaches them to bring within reach.

Figures & tables

Figure 1: Deep improves what can be extracted within current epistemic reach. Wide Learning changes what evidence enters that reach. In the controlled construction, the primitive substrate is fixed; learning changes the learner’s ability to realise the informative diagnostic under the same deployment budget. The dashed boundary in panel A denotes effective reach under the fixed reliability criterion, not logical impossibility. Calibration changes the learner state but adds no primitive affordance. Panel C shows a task-relevant split: the learned diagnostic enters effective reach, returns different outcomes in the paired worlds, and determines the sealed patch.

Condition	Diagnostic realisation probability	Valid-probe TV	Sealed error
Public only	0	N/A	0.5000
Pre-learning instrumentation	0.0015625 observed; $1/1024$ ensemble	1 if valid	0.49921875
Post-learning	1.0000	1	0.0000
Oracle	1.0000	1	0.0000

Table 2

Code	Failure interpretation	Status	Decisive check
F1	Public-channel leak	PASS	Exact public-law certificate, $TV=0$
F2	Deployment search sufficient	PASS	Analytic $1/1024<0.95$ bound
F3	Extra-affordance confusion	PASS	Identical five-primitive signature in every arm
F4	Test-specific lookup artefact	PASS	Fixed-repertoire valid rate $0$
F5	Compute-only explanation	PASS	A/B nominal compute exceeds C; public law remains insufficient
F6	Validator or label leak	PASS	Self-test is $\theta$ -independent; truth evaluator-only after patch

Table 3

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