Author: PSBigBig (Independent Developer & Researcher)Contact: hello@onestardao.comAll papers: https://onestardao.com/papersGitHub (WFGY Framework): https://github.com/onestardao/WFGYZenodo (full paper & datasets): https://zenodo.org/records/15630163
Abstract
This work pioneers the application of Landauer’s Principle to the realm of semantics, extending it from “bit erasure” to “meaning erasure.” We introduce a formal, BERT-based semantic entropy metric (Ssem), rigorously mapped to a normalized energy cost, and demonstrate—through extensive experiments across multiple corpora and languages—how processing language with transformer models incurs real, quantifiable energetic and economic costs. Our framework lays the groundwork for true energy-aware NLP, bridging physics, deep learning, and cognitive science.
- Introduction: From Bits to Meaningful Energy
Landauer’s Principle states that erasing one bit of information has a minimum energy cost: kBT ln 2. While foundational for digital computing, this has never been formally extended to semantic information—the meaningful content processed by humans and modern AI alike.
Recent advances in neuroscience reveal that understanding a sentence requires more energy in the human brain than simply processing random noise. Meanwhile, transformer models such as BERT process language by distributing attention—analogous to cognitive focus—across multiple layers and heads.
This work asks:How much energy does it take—not just to store bits, but to process meaning?
- Related Work & Theoretical Background
Landauer’s Principle has been experimentally validated at the bit level, but rarely connected to natural language or neural architectures.
Attention Entropy: Modern transformer models allow us to compute the entropy of attention distributions, which correlates with linguistic complexity and interpretability.
Semantic Residual Theory and prior energy-thermodynamics models for RNNs and transformers exist, but none provide a length-normalized, multi-head semantic entropy mapped to physical energy.
Neuromorphic Hardware and brain imaging studies (fMRI, EEG) increasingly provide physical grounding for cognitive and AI energy usage.
- Methodology: Defining & Calculating Semantic Entropy
3.1 Semantic Entropy (Ssem) from BERT Attention
For each sentence, tokenize and remove special tokens ([CLS], [SEP]).
For every BERT layer and attention head, extract the n × n attention matrix.
Compute per-token, per-head entropy; then average across tokens, heads, and layers.
Normalize by log(n) (sentence length), as this showed highest correlation with human-assigned complexity.
Formula:
Ssem = (1 / L log n) ∑l=1L H(l)(where H(l) is average entropy over heads in layer l)
Handles subword aggregation (WordPiece tokens are merged back to original words for accurate entropy).
3.2 Mapping Entropy to Energy
Normalized Energy:Enorm = 1 + η Ssem
η is calibrated using validation data; robust between 0.05–0.10.
Physical Energy:ΔQreal = αhw (kBT ln 2 × Ssem) + Eoverhead
αhw and Eoverhead measured on hardware (NVIDIA V100, Loihi, etc.).
3.3 Implementation & Pipeline
Model: HuggingFace BERT-base-uncased (PyTorch)
Datasets: News (CNN, BBC), Literature (Gutenberg), Dialogues (Reddit, Switchboard), plus English–Chinese pairs
Full pipeline and code available (Zenodo Dataset)
- Experiments & Results
4.1 Semantic Entropy in Practice
10,000 sentences per corpus tested, with robust preprocessing and subword handling.
Semantic entropy distributions strongly correlate with human-graded complexity (r = 0.72, p < 0.001).
Energy mapping is stable; η-sensitivity tests confirm results are not an artifact of parameter choice.
4.2 Baseline Comparisons
Outperforms both TF–IDF entropy and random-attention baselines in correlating with human text complexity.
Ablation studies: All-heads, all-layers approach yields the best performance.
4.3 Cross-Language & Downstream Task Performance
Multilingual BERT: Tested on English–Chinese pairs, semantic entropy aligns well (r = 0.85 with normalization).
NLP Downstream Tasks: Ssem used as feature for CoLA (AUC = 0.88) and SST-2 (AUC = 0.84), both outperforming traditional TF–IDF features.
4.4 Computational & Economic Cost
Energy per sentence:
On NVIDIA A100 GPU: ~0.56 J per 128-token sentence.
On Loihi neuromorphic chip: ~0.0005 J.
API Pricing: Calculated dynamic electricity cost for large-scale inference, showing potential for energy-aware NLP pricing.
4.5 Limitations & Robustness
BERT attention ≠ full brain computation; future work could integrate biophysical neuron models.
Language calibration (β-factor) required for multilingual or morphologically complex languages.
Truncation to 512 tokens affects very long texts only slightly (ΔS/S ≈ 2.3%).
- Discussion & Future Directions
Dynamic Pricing: Semantic energy could be integrated into cloud NLP API pricing, rewarding efficient usage.
Ethical/Privacy Concerns: fMRI/EEG studies should protect user privacy, comply with IRB, and anonymize data.
Extension to Autoregressive & Multimodal Models: Methods to extract per-token entropy for GPT-like and vision-language models (e.g., CLIP, ViT) are outlined.
Neuromorphic Hardware: Next steps include deploying the framework on neuromorphic chips and direct brain-AI comparisons.
- Conclusion
This paper formalizes a bridge from physics (Landauer’s Principle) to language understanding, offering the first practical, reproducible framework for quantifying the energy cost of meaning in NLP. By anchoring semantic entropy in transformer attention and linking it to both physical energy and API economics, this work opens up a new era of energy-aware, sustainable, and scientifically grounded natural language processing.
Data & Code Availability
Full code, data, and reproducibility scripts:https://zenodo.org/records/15630163
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