The Illusion of Control: Why Bare Classifier Inversion Silently Fails in Concept-Bottleneck Text Generation
Organizations: Shanghai Jiao Tong University
Abstract
Concept-bottleneck controllable generation routes multi-attribute control through a low-dimensional concept code that, at deployment, must be synthesised from a target attribute configuration. We study this problem in concept-bottleneck text generation under multi-axis compositional generalisation, comparing three ways to obtain the inference-time code: classifier inversion against the encoder heads, reference-text encoding, and a post-hoc label-conditioned prior. Since a concept code admits no direct LM-fluency term, regularising inversion must instead constrain the code toward the encoder's training distribution. We therefore test bare inversion and three regularised variants: label-agnostic and label-conditioned Mahalanobis penalties, and a conditional normalising-flow density baseline. Every inversion variant we test underperforms a simple post-hoc prior fitted to per-combination encoder means on the same checkpoints, across three backbone families spanning M to B parameters. The bare form of classifier inversion also silently collapses to chance, traceable to a directly measured off-manifold code. We validate this diagnosis on real-world benchmarks and under external evaluators, enabling fair comparison with published baselines.
Figures & tables
| Method / z-source | Backbone | HO | ACD |
|---|---|---|---|
| CompMCTG-paper baselines, GPT-2-Medium 355M (quoted from Zhong et al. 2024 ) | |||
| PPLM ( Dathathri et al. 2020 ) | GPT-2-M 355M | 42.49 | 40.63 |
| Fudge ( Yang and Klein 2021 ) | GPT-2-M 355M | 41.71 | 40.42 |
| CatPrompt ( Yang et al. 2023 ) | GPT-2-M 355M | 64.57 | 54.77 |
| DCG ( Zeng et al. 2023 ) | GPT-2-M 355M | 66.39 | 64.71 |
| Con.Prefix ( Qian et al. 2022 ) | GPT-2-M 355M | 67.50 | 63.93 |
| Protocol | GPT-2-124M | LLaMA-1B |
|---|---|---|
| Cls-Inv bare | ||
| + Mahal. (agn.) | ||
| + Mahal. (cond.) | ||
| flow-prior (cond. NF) | ||
| Prior ( ) |
Appendix figures & tables20 assets
Supplementary material from the paper’s appendix.
Appendix
| z-source | DistilBERT-SST-2 | CB-LLMs RoBERTa |
|---|---|---|
| Ref-Enc | 0.846 / 0.850 | 0.895 / 0.891 |
| Prior | 0.915 / 0.921 | 0.964 / 0.964 |
| Cls-Inv | 0.500 / 0.500 | 0.916 / 0.918 |
| CB-LLMs (official ckpt, BOS) | — | 0.950 |
| z-source | split | sent. | topic | 2-axis |
|---|---|---|---|---|
| Cls-Inv † | seen | 72.8 | 20.2 | 46.5 |
| Ref-Enc | seen | 71.6 | 52.7 | 62.1 |
| Prior | seen | 78.7 | 74.3 | 76.5 |
| Cls-Inv † | unseen | 99.4 | 0 9.7 | 54.6 |
| Ref-Enc | unseen | 78.4 | 27.8 | 53.1 |
| Prior | unseen | 94.9 | 61.2 | 78.1 |
| Backbone | Scale | Task | Cls-Inv mean |
|---|---|---|---|
| GPT-2 | 124M | synthetic 4-axis | 0.239 |
| Qwen-0.5B | 500M | synthetic 4-axis | 0.276 |
| Qwen-1.5B | 1.5B | synthetic 4-axis | 0.239 |
| LLaMA-1B | 1B | synthetic 4-axis | 0.280 |
| LLaMA-3B | 3B | synthetic 4-axis | 0.224 |
| LLaMA-3 8B | 8B | YelpP binary | 0.500 |
| Backbone | Cls-Inv | Ref-Enc | Prior | pp |
|---|---|---|---|---|
| GPT-2 124M | 0.239 | 0.536 | 0.574 | |
| Qwen-0.5B | 0.276 | 0.603 | 0.679 | |
| Qwen-1.5B † | 0.239 | 0.360 | 0.379 | |
| LLaMA-1B ( ) | 0.280 | 0.791 0.021 | 0.840 0.026 | |
| LLaMA-3B | 0.224 | 0.857 | 0.907 |
| Method / z-source | Backbone | Acc | Acc | Acc | Acc |
|---|---|---|---|---|---|
| CompMCTG-paper baselines (GPT-2-Medium 355M) | |||||
| PPLM | GPT-2-M | 49.96 | 50.02 | 19.93 | 50.06 |
| Fudge | GPT-2-M | 49.61 | 48.80 | 20.91 | 47.50 |
| CatPrompt | GPT-2-M | 83.82 | 54.07 | 56.04 | 64.36 |
| DCG | GPT-2-M | 90.29 | 56.39 | 57.00 | 61.88 |
| Con.Prefix | GPT-2-M | 93.66 | 59.24 | 48.30 | 68.78 |
| z-source | Generated text (target: negative_female_bar_past ) |
|---|---|
| Cls-Inv | class class class Class Class Class Kids Class Class Sing Kid Class Kids Special Kids Special Children Class Kids Kids Special Special Kids Children … |
| Ref-Enc | adios everyone, this place is totally worth going back to. the owner, who was seated at the bar, told us he had come to check out and that he had some frien … |
| Prior | was so disappointed in this place. i ordered the last meal i had, which was a very small portion of the pizza. the waiter was so nice and attentive … |
| attr. match | fluency ( ) | ||
|---|---|---|---|
| z-source | (mean /3) | fluent | degraded / salad |
| Cls-Inv | 0.80 | 0 | 11 / 9 |
| Ref-Enc | 1.90 | 16 | 4 / 0 |
| Prior | 2.45 | 20 | 0 / 0 |
| Backbone | source | Mahalanobis | kNN-dist |
|---|---|---|---|
| GPT-2 124M | Cls-Inv | ||
| Ref-Enc | |||
| Prior | |||
| LLaMA-3.2 1B | Cls-Inv | ||
| Ref-Enc | |||
| Prior |
| GPT-2-124M | LLaMA-3.2 1B | |||
|---|---|---|---|---|
| Mahal. | shell | Mahal. | shell | |
| GPT-2-124M | LLaMA-3.2 1B | |
| Reference (from Tab. 11 , 3-seed mean): | ||
| Mahal., best (label-agnostic) | ||
| steps | |||
| lr | |||
| GPT-2-124M (paper default in bold): | |||
| LLaMA-3.2 1B at steps : | |||
| seen | unseen | |||
|---|---|---|---|---|
| Run | retr. | prior | retr. | prior |
| GPT-2 124M, HO | 68.8 | 67.7 | 46.6 | 55.2 |
| GPT-2 124M, ACD | 74.6 | 74.2 | 53.3 | 55.9 |
| LLaMA-3.2 1B, HO | 83.0 | 81.7 | 66.9 | 76.4 |
| LLaMA-3.2 1B, ACD | 87.0 | 86.9 | 64.0 | 69.5 |
| references | Hold-Out | ACD |
|---|---|---|
| prior |
| Additive decomposition (% variance explained) | Concept-code variance | ||||||||
| Backbone | Full | sent. | cuis. | tense | gend. | intra-std | inter-std | ratio | prior MSE |
| GPT-2 124M | 31.7 | 45 | 23 | 10 | 5 | 0.42 | 0.29 | 0.68 | 0.20 |
| GPT-2-Med. 355M | 38.3 | 54 | 38 | 13 | 6 | 0.43 | 0.33 | 0.76 | 0.20 |
| LLaMA-3.2 1B | 47.6 | 67 | 51 | 20 | 12 | 0.25 | 0.25 | 1.02 | 0.07 |
| Phase | Range | ||
|---|---|---|---|
| 1 (LM warm-up) | |||
| 2 (concept ramp) | |||
| 3 (orthogonality ramp) | |||
| 4 (full objective) |
| bf16-everywhere | bf16 + fp32 small | |
|---|---|---|
| Synthetic 4-axis Acc (mean) | ||
| LLaMA-3.2 1B (ref-enc) | ||
| LLaMA-3.2 1B (prior) | ||
| prior ref-enc | ||
| Qwen-2.5 0.5B (ref-enc) | ||
| Qwen-2.5 0.5B (prior) | ||
| Axis | target | seen-split prior | cls-inv unseen |
|---|---|---|---|
| sentiment | negative | ||
| gender | male | ||
| cuisine | american | ||
| tense | present | ||
| 4-axis mean | — | chance |
| Backbone | Cls-Inv | Prior | lift |
|---|---|---|---|
| GPT-2 124M | |||
| LLaMA-3.2 1B | |||
| Qwen-2.5 1.5B |
| Backbone | Mean joint | Grade |
|---|---|---|
| Synthetic 4-axis, marginal-independent attributes | ||
| GPT-2 (R4) | 0.028 | ENT |
| Qwen-0.5B (R5d) | 0.037 | ENT |
| Qwen-1.5B (R2) | 0.004 | ENT |
| LLaMA-1B ( ) | 0.145 0.019 | PARTIAL |
| LLaMA-3B (R7d) | 0.268 | PARTIAL |
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