Research map / Label-efficient and robust learning / Zero-/few-shot and meta-learning
Discovering a Zero (Zero-Vector Class of Machine Learning)
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Proposes a vector-space framework for ML classes (addition = union, scalar multiplication = complement) with a zero vector called the Metta-Class, realized by training against uniform-noise data, and demonstrates applications on MNIST, CIFAR-10 and ImageNet-1k embeddings.
Problem
Classifiers learn decision boundaries that partition the whole feature space, which misrepresents the true class manifolds; there is no principled algebra for combining or complementing classes.
Approach
Represents each class as a vector of valid logit-function equivalence sets, with union as addition and complement as negative scalar multiplication; the zero vector corresponds to a uniform-distribution class (the Metta-Class), which is used as a negative/background class so networks learn only the data manifold.
Key results
- Zero-Inclusive networks learn clearer decision regions than Zero-Exclusive networks on synthetic 2D data, with empty space no longer classified as any class.
- Uni-class classifiers trained against Metta-Class data on MNIST digits can generate digit-like images via gradient ascent on the logit.
- The paper notes that the approach has scalability limitations on CIFAR-10.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add Metta-Class data and an output node (Zero-Inclusive-Network) | Neural network classifier · MNIST (Figure 6) | decision-region alignment | Helped |
| Train against Metta-Class data using BCE loss | Single-class neural network classifier · Single-class classification (Figure 7) | class learning | Helped |
| Use separate Metta-Class-trained classifiers together as a repository | Continual classification networks · MNIST and CIFAR10 (Figure 8) | classification accuracy | Mixed |
Surprising findings
- The paper reports that the approach does not scale well to higher-dimensional data such as CIFAR-10.
Limitations
- Scalability limited on CIFAR-10 and higher-dimensional data.
- Uniform PDF of the zero vector is an indication rather than rigorous proof, per the authors.
- Results are mainly on MNIST with limited larger-scale evaluation.
Experimental setup
Datasets: MNIST CIFAR-10 ImageNet-1k embeddings
Benchmarks: MNIST CIFAR-10 ImageNet-1k embeddings
Metrics: occupancy factor purity factor accuracy
Baselines: Zero-Exclusive Network
Builds on: Noise-Contrastive Estimation Energy-Based Models Langevin dynamics
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