Apoha is a classification model that defines concepts by exclusion — what they are NOT — rather than shared positive properties. This is a direct implementation of Buddhist Apoha theory (anyāpoha-vāda) from the pramāṇavāda (epistemology) tradition.

The key result: when an input fails to satisfy any concept's exclusion boundary, the model outputs UNCERTAIN instead of forcing a classification. OOD rejection is built into the classification mechanism, not added post-hoc.

On CLINC150 (30 intents, 5 seeds):

Apoha: 95.6% accuracy, 84.6% OOD rejection
Best contrastive baseline (InfoNCE): 97.7% accuracy, 15.1% OOD rejection
Apoha rejects 5.6× more OOD inputs with only a 2.1pp accuracy trade-off

Quick Start

python

from apoha_inference import ApohaClassifier, ConceptDefinition, Example, ExclusionExample

# 1. Initialise the classifier
clf = ApohaClassifier()  # loads fine-tuned encoder automatically

# 2. Define a concept with positives AND exclusions
cardiology = ConceptDefinition(
    concept_id="cardiology",
    concept_label="Cardiology",
    positive_examples=[
        Example(id="c1", input="chest pain radiating to left arm"),
        Example(id="c2", input="irregular heartbeat and palpitations"),
        Example(id="c3", input="elevated troponin levels suggest cardiac damage"),
    ],
    exclusion_set=[
        ExclusionExample(id="e1", input="chronic cough with phlegm", excludes_because="respiratory"),
        ExclusionExample(id="e2", input="stomach acid reflux after meals", excludes_because="gastroenterology"),
        ExclusionExample(id="e3", input="migraine headache with visual aura", excludes_because="neurology"),
    ],
)
clf.register_concept(cardiology)

# 3. Classify
result = clf.predict("patient presents with irregular heartbeat")
print(result.label)           # "cardiology"
print(result.uncertain)       # False
print(result.boundary_scores) # {"cardiology": 0.43}

# Out-of-distribution input
result = clf.predict("my stock portfolio crashed")
print(result.label)    # "UNCERTAIN"
print(result.uncertain) # True

How It Works

Concept Definition

A concept C is defined by:

Positive examples P = {p₁, ..., pₘ} — what C is
Exclusion set N = {n₁, ..., nₖ} — what C is not, with optional reasons
Margin γ (gamma) — the required separation between core and boundary

Boundary Score

At inference, for input x and concept C:

boundary_score(x, C) = min_{n ∈ N} d(x, n) - mean_{p ∈ P} d(x, p)

where d is cosine distance. The score measures how much further the nearest exclusion is than the average positive.

If the best score across all concepts exceeds γ → classified If no concept's score exceeds γ → UNCERTAIN

The min over exclusions is hard-negative mining: the closest counter-example defines the boundary, analogous to SVM support vectors. This is Dignāga's key insight: a concept boundary is challenged by the single nearest non-member.

Training (Apoha Boundary Loss)

L(x, C) = max(0, γ - [min_{n ∈ N} d(x, n) - mean_{p ∈ P} d(x, p)])

A hinge loss that pushes exclusions at least γ further from the query than the average positive. Fine-tunes the sentence encoder to create sharp exclusion boundaries in embedding space.

Benchmark Results

All results: 5 seeds (42–46), mean ± std Encoder: BAAI/bge-small-en-v1.5 (384d, 33M params) Hardware: NVIDIA L4 (24GB VRAM), CUDA 12.4

CLINC150-OOS (30 intents, 20 train/class)

Method	Accuracy	Macro-F1	AUROC	FPR@95	OOD Rejection
Apoha	0.956 ±0.011	0.970 ±0.009	0.980 ±0.004	0.070 ±0.029	0.846 ±0.032
InfoNCE	0.977 ±0.007	0.977 ±0.007	0.989 ±0.002	0.040 ±0.008	0.151 ±0.036
ProtoNet	0.979 ±0.006	0.979 ±0.006	0.985 ±0.003	0.072 ±0.018	0.005 ±0.003
Mahalanobis	0.660 ±0.027	0.769 ±0.026	0.991 ±0.001	0.040 ±0.014	0.999 ±0.001
Energy	0.977 ±0.007	0.977 ±0.007	0.383 ±0.062	0.969 ±0.020	0.000 ±0.000

Banking77-OOS (50 intents, near-OOD)

Method	Accuracy	AUROC	OOD Rejection
Apoha	0.822 ±0.021	0.829 ±0.021	0.291 ±0.036
InfoNCE	0.871 ±0.010	0.844 ±0.017	0.000 ±0.000
ProtoNet	0.899 ±0.012	0.851 ±0.019	0.000 ±0.000
Energy	0.871 ±0.010	0.406 ±0.059	0.000 ±0.000

HWU64-OOS (40 intents, near-OOD)

Method	Accuracy	AUROC	OOD Rejection
Apoha	0.813 ±0.019	0.816 ±0.053	0.249 ±0.077
InfoNCE	0.868 ±0.014	0.798 ±0.085	0.002 ±0.001
ProtoNet	0.895 ±0.015	0.801 ±0.031	0.000 ±0.000
Energy	0.868 ±0.014	0.401 ±0.117	0.000 ±0.000

Cybersecurity — MITRE ATT&CK (15 tactics)

Method	Accuracy	OOD Rejection	vs InfoNCE
Apoha	0.621 ±0.017	0.452 ±0.048	38×
InfoNCE	0.688 ±0.015	0.012 ±0.013	—

Summary: Apoha vs Best Baseline

Dataset	Accuracy Gap	Apoha OOD	InfoNCE OOD	OOD Ratio
CLINC150	−2.1pp	84.6%	15.1%	5.6×
Banking77	−4.9pp	29.1%	0.0%	∞
HWU64	−5.5pp	24.9%	0.2%	166×
Cybersecurity	−6.7pp	45.2%	1.2%	38×
Medical	−10.6pp	97.0%	86.0%	1.1×

Ablation Studies (CLINC150, 5 seeds)

Ablation	Finding
Fine-tuned vs raw encoder	10× accuracy gain (9.5% → 95.8%) — the loss reshapes embedding space
Min vs mean over exclusions	Min essential — mean destroys accuracy by 31pp
Gamma sweep (0.1–0.7)	Smooth accuracy/OOD trade-off — gamma is a tunable safety knob
Exclusion set size (5–50)	20+ exclusions needed; accuracy stable, OOD rejection scales 47%→89%
Loss variants (V1 vs V2 LSE)	V1 (hard-min) best accuracy; V2 LSE trades 4.6pp for 7.3pp more OOD rejection

When to Use Apoha

Use Apoha when:

You need the model to abstain on out-of-distribution inputs
You have 5–20 positive examples per concept (few-shot setting)
You can articulate what each concept is NOT (exclusion examples)
Silent misclassification has real costs (safety-critical domains)

Consider alternatives when:

All inputs are guaranteed in-distribution (closed world)
You need maximum accuracy and OOD rejection is not required
You have thousands of training examples per class (contrastive methods may be better)

Known Limitations

Accuracy trade-off: 2–7pp below contrastive baselines on in-distribution data
Exclusion set quality: Performance depends on choosing informative exclusions
Near-OOD: Banking77/HWU64 (semantically similar OOD) is harder (25–29% rejection vs 84% on CLINC150)
Binary classification: ADE drug safety dataset (binary, overlapping domains) is not a good fit — both classes' exclusion sets overlap with each other's positives
Scalability: Tested up to 50 concepts; behavior with hundreds is untested

Philosophical Grounding

Apoha is a direct implementation of anyāpoha-vāda — the exclusion theory of meaning developed by the Indian Buddhist logician Dignāga (c. 480–540 CE) and refined by Dharmakīrti (c. 600–660 CE) in the pramāṇavāda (valid cognition) tradition.

The core insight: concepts are not defined by shared positive properties ("cow" is not defined by what cows have in common) but by exclusion of non-members ("cow" is "not-non-cow" — everything that fails to be excluded by the concept's boundaries).

This maps directly onto machine learning:

Exclusion sets → hard-negative mining
Margin boundaries → SVM support vectors
The closest counter-example defines the boundary (Dignāga's key insight, validated by ablation)
UNCERTAIN output → Dignāga's epistemological principle that absence of sufficient evidence is itself informative

For a modern philosophical treatment, see:

Siderits, M., Tillemans, T., & Chakrabarti, A. (2011). Apoha: Buddhist Nominalism and Human Cognition. Columbia University Press.
Hattori, M. (1968). Dignāga, On Perception. Harvard University Press.
Dunne, J. D. (2004). Foundations of Dharmakīrti's Philosophy. Wisdom Publications.

EVAMLab/apoha-bge-small-en-v1.5

Apoha: Exclusion-Based Few-Shot Classification with Principled OOD Rejection

Overview