If AI models are padded with dead weight, can 'how complex is this?' still tell you anything real?
Can a complexity-predictor be meaningful if models are redundant?
This explores whether a measure of how complex a task or model is can still predict anything useful when models carry a lot of redundancy (extra parameters, repeated samples, padded reasoning) that does no real work.
This explores whether a measure of how complex a task or model is can still predict anything useful when models carry a lot of redundancy that does no real work. The corpus suggests yes, but only if the predictor measures what is left after the redundancy is squeezed out. Raw size and raw length stop being good proxies. Holding loss fixed, larger models and ensembles compress down to smaller sizes, so scaling produces cleaner, less-interfering functions rather than more complicated ones Do larger models actually learn simpler functions?. Reasoning chains show the same thing. When you prune them, models keep the symbolic-computation tokens and drop grammar and meta-discourse first, so a chain's length overstates how much reasoning it contains Which tokens in reasoning chains actually matter most?.
Task complexity fares worse as a predictor of failure. Reasoning models don't break at a complexity threshold. They break when an instance is unfamiliar, and a chain of any length succeeds if the model was trained on similar instances Do language models fail at reasoning due to complexity or novelty?. A different line of work predicts failures from how probable the correct answer is under an autoregressive model. That is why logically trivial tasks like reciting the alphabet backwards turn out to be hard Can we predict where language models will fail?. The useful signal looks like familiarity or probability, which has little to do with how hard a task feels to a human.
Redundancy is also what makes some difficulty scores valuable. Ranking training examples by difficulty lets you discard the easy, redundant ones. On CIFAR-10, half the data was pruned with no accuracy loss, and the approach beats standard power-law scaling Can we prune training data without hurting model performance?. Here the predictor works because it detects the redundancy. It is also relative to the model, not absolute. Problems that are far too hard don't just get wasted. They teach shortcuts that contaminate skills the model already had Do overly hard RLVR samples actually harm model capabilities?.
The limits show up when a predictor only sees outputs, or when it counts copies. Two models with identical accuracy can have very different internal organization. One can be fractured and fragile under distribution shift while looking perfect on standard metrics Can models be smart without organized internal structure?. Redundant samples don't add capability either. A committee of weak model calls matches a strong model only when an external check, such as tests or proofs, can pick the right answer When can weak models match strong model performance?. Undirected noise added to recursive reasoning models doesn't help either. The gains came from a principled variational objective Does adding randomness alone improve recursive reasoning models?.
So the meaningful predictor is something like effective complexity: the structure that survives compression, measured against what the model has already seen. Looped models point the same way. They beat larger feedforward networks by re-applying the same layers, which means the complexity sits in how many steps of computation are used and not in how many parameters exist Can models learn by looping instead of growing larger?. A predictor that counts parameters or chain length would miss this.
Sources 10 notes
Using compression-independent measurement, larger models and ensembles encode simpler functions than smaller ones when held at the same performance level. This shows scaling produces cleaner, less-interfering representations rather than greater expressivity.
Greedy likelihood-preserving pruning reveals six functional token categories; symbolic computation tokens are preferentially preserved while grammar and meta-discourse are pruned first. Student models trained on these pruned chains outperform those trained on frontier-model compression.
LRMs don't break at complexity thresholds but at instance-novelty boundaries. Models fit instance-based patterns rather than generalizable algorithms, so any reasoning chain succeeds if trained on similar instances, regardless of length.
By framing LLMs as autoregressive probability machines, researchers predicted tasks with low-probability target responses would be systematically harder, even when logically simple. Experiments confirmed predictions like backwards alphabet and letter counting.
Research shows that ranking training examples by difficulty (EL2N, forgetting, memorization) and removing easy ones beats power-law scaling laws. On CIFAR-10, 50% of data was pruned without accuracy loss, and self-supervised metrics scaled the approach to ImageNet.
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Training on nearly-impossible problems causes models to learn degenerate shortcuts rather than genuine reasoning, and these shortcuts contaminate pre-existing capabilities. Group-relative normalization treats rare accidental successes as high-advantage trajectories, reinforcing answer repetition and computation-skipping instead of sound reasoning patterns.
Models trained with SGD can contain all the linearly decodable features needed for a task while maintaining fundamentally broken internal organization. This makes them vulnerable to perturbation and distribution shift invisible to standard evaluation metrics.
Sampling alone amplifies coverage but cannot select correct solutions. Reliable performance matching requires external soundness signals—tests, proofs, or type checks—that convert latent correct proposals into actual selections.
GRAM's ablations show naive stochasticity added to existing models yields no improvement. Gains come specifically from amortized variational inference, which couples stochastic latents to a principled generative objective rather than injecting undirected noise.
Models that re-apply layers in recurrent depth outperform larger feedforward networks on reasoning tasks. This works because recursion enables state tracking and compositional generalization that parameter scaling alone cannot achieve, with convergence signals providing natural halting.
Papers this line draws on 8
The research behind the notes this line reads — ranked by how closely each paper relates.
- Large Language Model Reasoning Failures
- Generative Recursive Reasoning
- Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey
- Hierarchical Reasoning Model
- Less is More: Recursive Reasoning with Tiny Networks
- The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity
- Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?
- The Invisible Leash: Why RLVR May Not Escape Its Origin