Teacher Geometry Shapes Learnability in Teacher-Student Networks
Updated 2 h ago · first seen 11 Sept 2026
paper_01M294GMDR4HCZ4VFQ0G2JY8VH
- Published
- 11 Sept 2026
- T1 · 2 h ago
- arXiv
- 2609.09595
- T1 · 2 h ago
- Category
- cs.LG
- T1 · 2 h ago
Abstract
Teacher-student systems, in which a teacher neural network generates training labels so that a student neural network can learn to implement the same function, are widely used as an abstract setting to study learning. However, the structure of the teachers is often overlooked by assuming randomly-generated, normally-distributed parameters. This hides substantial variation in how learnable different teachers are. We formalize learnability as the success rate of converging to the global minimum, as a function of overparameterization, learning algorithm, student initialization distribution, and teacher geometry. We both identify an easy distribution that maximizes node dissimilarity and a hard distribution that minimizes it, and show that these two distributions induce markedly different success rates across a large range of settings and for different activation functions. To explain the gap, we study the loss landscape of small neural networks that contain two distinct kinds of suboptimal local minima, out-of-bounds (OOB) minima at the edge of the data distribution and interior minima within. Assuming infinite data and a fast readout layer, we analytically reduce the loss landscape of small networks to two dimensions, showing that the region of attraction of interior minima changes as a function of teacher structure. In larger networks, maximally dissimilar teachers induce more interior minima, while minimally dissimilar teachers induce more OOB minima. Motivated by these analyses, we show that differentially increasing the learning rate of the readout layer and decreasing the learning rate of the inner biases increases success rates. These findings provide an important step in narrowing the gap between the study of teacher-student networks and more structured functions that arise in practice.
Authors 5
Kai J. Sandbrink, Flavio Martinelli, Alexander van Meegen, Wulfram Gerstner, Johanni Brea
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Arxiv announce type
- cross
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- arXiv id
- 2609.09595
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Categories
- cs.LG, cs.AI, cs.NE
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Each value shows its source, tier and observation time. Conflicting claims are kept side by side and flagged — never averaged. How AI Atlas records facts →
Provenance
Attributed facts
9
Source tiers
T19
Freshest observation
2 h ago
Conflicts
None
No models linked to this paper yet.
As of
Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.
Claim history · Abstract
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| Teacher-student systems, in which a teacher neural network generates training labels so that a student neural network can learn to implement the same function, are widely used as an abstract setting to study learning. However, the structure of the teachers is often overlooked by assuming randomly-generated, normally-distributed parameters. This hides substantial variation in how learnable different teachers are. We formalize learnability as the success rate of converging to the global minimum, as a function of overparameterization, learning algorithm, student initialization distribution, and teacher geometry. We both identify an easy distribution that maximizes node dissimilarity and a hard distribution that minimizes it, and show that these two distributions induce markedly different success rates across a large range of settings and for different activation functions. To explain the gap, we study the loss landscape of small neural networks that contain two distinct kinds of suboptimal local minima, out-of-bounds (OOB) minima at the edge of the data distribution and interior minima within. Assuming infinite data and a fast readout layer, we analytically reduce the loss landscape of small networks to two dimensions, showing that the region of attraction of interior minima changes as a function of teacher structure. In larger networks, maximally dissimilar teachers induce more interior minima, while minimally dissimilar teachers induce more OOB minima. Motivated by these analyses, we show that differentially increasing the learning rate of the readout layer and decreasing the learning rate of the inner biases increases success rates. These findings provide an important step in narrowing the gap between the study of teacher-student networks and more structured functions that arise in practice. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
New paper: Teacher Geometry Shapes Learnability in Teacher-Student Networks
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.AI | feed | T1· Official | 3 min ago | 1 |
Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.