https://arxiv.org/abs/2503.02113
The core idea:
Deep learning does not work because neural nets somehow escape generalization theory. It works because very flexible models can still generalize when they have soft inductive biases — preferences for simple, compressible, structured solutions.
Key points:
- 🧠 Overparameterization is not automatically a problem.
Having more parameters than data points does not necessarily mean the learned function is complex. Parameter count is a bad proxy for the complexity of the actual solution.
- 📈 Benign overfitting is not unique to neural nets.
Models can perfectly fit training data, even noisy data, while still generalizing on structured data. Similar behavior appears in linear models, Gaussian processes, high-degree polynomials, and other classical model classes.
- 🔁 Double descent is not just a modern deep learning anomaly.
The pattern where test error falls, rises, then falls again as model size increases also appears outside neural networks. It can be understood through effective dimensionality, compression, and the geometry of learned solutions.
- 📦 Compression is central.
A huge model can generalize if the solution it finds is simple or compressible. The rough intuition is:
expected error ≈ training error + complexity/compressibility penalty.
- 📚 Some older theories already help explain this.
PAC-Bayes and countable hypothesis bounds are more useful here than raw VC dimension, Rademacher complexity, or parameter counting, because they focus on which solutions are likely/simple rather than just how large the hypothesis space is.
- 🎯 The paper’s recommended lens:
Don’t only restrict what a model can represent. Instead, allow a very rich hypothesis space, but bias the learner toward simpler solutions that fit the data.
- ✨ What is still distinctive about deep learning?
Not overparameterization or double descent by themselves, but things like representation learning, in-context learning, broad cross-domain usefulness, and mode connectivity in loss landscapes.
My takeaway:
Deep learning’s famous generalization puzzles may not require rewriting the textbooks from scratch. They may require reading the right parts of the textbooks more carefully — especially the parts about priors, compression, and soft preferences over solutions.
The core idea:
Deep learning does not work because neural nets somehow escape generalization theory. It works because very flexible models can still generalize when they have soft inductive biases — preferences for simple, compressible, structured solutions.
Key points:
- 🧠 Overparameterization is not automatically a problem.
Having more parameters than data points does not necessarily mean the learned function is complex. Parameter count is a bad proxy for the complexity of the actual solution.
- 📈 Benign overfitting is not unique to neural nets.
Models can perfectly fit training data, even noisy data, while still generalizing on structured data. Similar behavior appears in linear models, Gaussian processes, high-degree polynomials, and other classical model classes.
- 🔁 Double descent is not just a modern deep learning anomaly.
The pattern where test error falls, rises, then falls again as model size increases also appears outside neural networks. It can be understood through effective dimensionality, compression, and the geometry of learned solutions.
- 📦 Compression is central.
A huge model can generalize if the solution it finds is simple or compressible. The rough intuition is:
expected error ≈ training error + complexity/compressibility penalty.
- 📚 Some older theories already help explain this.
PAC-Bayes and countable hypothesis bounds are more useful here than raw VC dimension, Rademacher complexity, or parameter counting, because they focus on which solutions are likely/simple rather than just how large the hypothesis space is.
- 🎯 The paper’s recommended lens:
Don’t only restrict what a model can represent. Instead, allow a very rich hypothesis space, but bias the learner toward simpler solutions that fit the data.
- ✨ What is still distinctive about deep learning?
Not overparameterization or double descent by themselves, but things like representation learning, in-context learning, broad cross-domain usefulness, and mode connectivity in loss landscapes.
My takeaway:
Deep learning’s famous generalization puzzles may not require rewriting the textbooks from scratch. They may require reading the right parts of the textbooks more carefully — especially the parts about priors, compression, and soft preferences over solutions.
arXiv.org
Deep Learning is Not So Mysterious or Different
Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign...
关于层出不穷的各式 AI memory system 的一些思考：我们应该把更多的精力放在设计更好的 eval 上，从而让最强的 memory system 进化出来
https://linghao.io/posts/memory-systems-should-be-evolved
https://linghao.io/posts/memory-systems-should-be-evolved
linghao.io
Evolving Memory Systems: An Eval-First Approach
AI memory systems are often designed as architectural bets: vector stores, profiles, summaries, graphs, etc. This post argues for a different starting point: build longitudinal eval environments where systems without good memory cannot survive, then let better…
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https://linghao.io/posts/taxonomy-differences-matter
以前觉得 taxonomy 只是无聊的分类学，开始做 LLM quality 以后几乎每天都在思考和跟同事争论 loss taxonomy 的细枝末节。这几天放假闲下来仔细想想，taxonomy 无处不在，至关重要。
以前觉得 taxonomy 只是无聊的分类学，开始做 LLM quality 以后几乎每天都在思考和跟同事争论 loss taxonomy 的细枝末节。这几天放假闲下来仔细想想，taxonomy 无处不在，至关重要。
linghao.io
A Taxonomy Is a Theory of What Differences Matter
Taxonomies are not neutral filing systems. They predict, coordinate, allocate, and govern. The right way to judge one depends on the job it is doing.
https://alexzhang13.github.io/blog/2026/harness/
> A good harness is a harness that reduces unfamiliar problems to familiar ones and reduces complex problems to simple ones. In other words, even if the state s is out-of-distribution (OOD) to what any individual language model call was trained for, a good harness produces observations o that are locally in-distribution (LID), which we define as every individual LM call over this observation being in-distribution with respect to the training data.
> A good harness is a harness that reduces unfamiliar problems to familiar ones and reduces complex problems to simple ones. In other words, even if the state s is out-of-distribution (OOD) to what any individual language model call was trained for, a good harness produces observations o that are locally in-distribution (LID), which we define as every individual LM call over this observation being in-distribution with respect to the training data.
Alex L. Zhang
Language model harnesses are compositional generalizers
Modern post-training brute-forces ever more environments and ever longer horizons, because frontier Transformers are still poor at compositional generalization. A good harness makes every model call locally in-distribution, so what it learns carries across…
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