PrefixGPT: Tuning LMs & Optimizing Adders

• PrefixGPT is a dual-method framework that applies prefix tuning for controlled text generation and Transformer-based sequence generation for hardware adder synthesis.
• Focused prefix tuning employs both specific and general prefixes to suppress implicit attributes, achieving improved control accuracy and reduced perplexity compared to standard methods.
• For hardware, PrefixGPT transforms adder design through 2D-coordinate serialization and dynamic legality masking, delivering state-of-the-art area-delay performance with efficient generation.

PrefixGPT refers to two distinct technical methodologies, each situated within a different research domain under the umbrella of Transformer-based generative models: (1) the application of focused prefix tuning (FPT) to GPT-style LLMs for controllable text generation (Ma et al., 2023), and (2) the use of Transformer models to generate and optimize prefix adder circuits for hardware design (Ding et al., 22 Nov 2025). Both approaches leverage prefix-based sequence parameterizations and Transformer architectures, but in fundamentally different contexts—natural language control and hardware topology generation, respectively.

1. Prefix-Tuning and Focused Prefix Tuning in GPT Models

1.1 Standard Prefix-Tuning

Prefix-tuning is a parameter-efficient alternative to full fine-tuning for conditional text generation in large autoregressive LMs such as GPT-2. In prefix-tuning, all base model weights are frozen; instead, a small number of continuous “prefix” vectors are prepended as virtual tokens at each Transformer layer. Formally, for each layer $\ell$, learnable matrices $P^{(\ell)}_K \in \mathbb{R}^{m \times d_k}$ and $P^{(\ell)}_V \in \mathbb{R}^{m \times d_v}$ (where $m$ is the prefix length) are inserted into the key and value sequences, so that attention in layer $\ell$ operates over $[P^{(\ell)}_K; K^{(\ell)}]$ and $[P^{(\ell)}_V; V^{(\ell)}]$ (Li et al., 2021). Only these prefix parameters are trained, yielding per-task storage requirements as low as $0.1\%$ of the full model. Prefix-tuning matches or exceeds full fine-tuning in low-resource and out-of-domain settings, as shown in table-to-text and summarization benchmarks (Li et al., 2021).

1.2 Focused Prefix Tuning (FPT)

Focused Prefix Tuning addresses a critical limitation of vanilla prefix-tuning: unannotated (“implicit”) attributes in training corpora can leak into the generated text, undermining control accuracy. FPT trains both a “specific” prefix $H_{\text{attr}=val}$ (for the desired attribute) and a “general” prefix $H_{\text{gen}}$ (fitted over the whole dataset to capture latent biases). Inference proceeds by computing logit vectors for both prefixes:

$$z_t^{\text{spec}} = \text{logits from } H_{\text{attr}=val},\qquad z_t^{\text{gen}} = \text{logits from } H_{\text{gen}}$$

A recombined logit is then formed:

$$z'_t = \alpha z_t^{\text{spec}} - (\alpha-1) z_t^{\text{gen}}$$

where $\alpha>1$ controls suppression of implicit attributes. The final token distribution is $\mathrm{softmax}(z'_t)$. This subtraction removes confounding signals without degrading fluency. For multi-attribute control, the method generalizes to:

$$z'_t = \sum_{i=1}^K [\alpha z_t^{\text{spec},i} - (\alpha-1)z_t^{\text{gen}}]$$

Specific prefixes for new attributes can be trained and added with no retraining of the LLM or existing prefixes, preserving incremental extensibility (Ma et al., 2023).

2. Training, Optimization, and Inference

PrefixGPT for text control is instantiated on GPT-2 Medium, with all model parameters frozen and AdamW optimization applied only to the prefix parameters. Prefix length $m=10$ tokens per layer is used throughout. Prefix initialization is derived from real-token activations to enhance convergence. Inference employs a tuned $\alpha$ ($1.1$–$3.0$ depending on the control task), top-$p$ filtering ($p \approx 0.8$) to preserve fluency, and classifier-based metrics (relevance, perplexity, and bias) to measure attribute control and leakage.

Empirically, FPT achieves superior control accuracy and lower perplexity versus vanilla prefix-tuning, cutting implicit-bias in sentiment control from $40.6$ to $34.8$ and boosting topic-relevance to $86.5\%$ while also reducing perplexity from $36.4$ to $34.1$ (Table 2, (Ma et al., 2023)). Ablation without the general prefix significantly degrades performance, indicating the necessity of explicit bias separation.

3. Architectural and Methodological Innovations in Prefix Adder Design

In the context of hardware synthesis, PrefixGPT recasts prefix adder optimization—traditionally a graph search or refinement problem—as a pure sequence generation task (Ding et al., 22 Nov 2025). Each adder is encoded as a sequence of $(L_p^r, L_p^c)$ coordinates derived from a lower-triangular binary matrix representation of the prefix graph. The model features three central innovations:

• 2D-Coordinate Serialization: Every valid prefix adder corresponds to a unique sequence of 2D coordinates, enabling linearization of the design space.
• Dynamic Legality Mask: At each decoding step, a legality mask excludes any coordinate violating design rules, ensuring all outputs are valid by construction.
• Specialized GPT-Style Transformer: The decoder-only model employs per-row and per-column embeddings, fused by RoPE positional encodings, and separate row- and column-heads to predict next-step transitions.

4. Pretraining and Reinforcement Learning Fine-Tuning

PrefixGPT for hardware is pre-trained on $10^6$ randomly synthesized valid adders up to 48 bits, using a cross-entropy objective over sequence steps. Subsequent fine-tuning adopts Group Relative PPO (GRPO): a RL scheme maximizing expected negative area-delay product (ADP), with KL-regularization to a frozen reference policy and prioritized experience replay from a global top-k buffer (Ding et al., 22 Nov 2025). This enables robust, exploration-driven traversal of the exponentially large design space, leading to efficient discovery of new optimal circuits.

5. Comparative Evaluation and Empirical Performance

PrefixGPT outperforms state-of-the-art prefix adder optimizers, including PrefixRL (DQN), ArithTree (MCTS), and PrefixLLM (LLM-heuristic), across 16- to 48-bit benchmarks and all standard initializations. For 48 bits, PrefixGPT achieves a new best ADP of $121.3\,\mu\text{m}^2 \cdot \text{ns}$, surpassing ArithTree by $7.7\%$. Mean ADP improvement over ArithTree is $71.9\%$ (32b) and $79.1\%$ (48b). Robustness is also enhanced, with a $94\%$ reduction in ADP standard deviation at 48b relative to ArithTree (Ding et al., 22 Nov 2025).

Generation with legality masking is highly efficient ($\sim7$ms/sample on an RTX 4090 for $n=32$), outpacing heuristic LLM approaches by over two orders of magnitude.

6. Limitations, Extensions, and Future Directions

Focused Prefix Tuning in text generation is subject to increased sampling latency due to dual prefix forward passes, but remains computationally light compared to full retraining or large control modules. The ability to add new attribute controls without backpropagation through the base model or existing prefixes supports scalability for multi-attribute generation.

For prefix adder synthesis, further generalization is enabled by relaxing the more-significant-parent restriction in merges, scaling to larger bit-widths, or adapting methodology to broader classes of arithmetic circuits and hardware constraints such as power/wiring (Ding et al., 22 Nov 2025). Pre-training with large-scale random walks internalizes topology “grammar,” and ablations show significant drop in performance absent this phase or rotary pos-encodings.

7. Technical Synthesis and Contextual Significance

By leveraging prefix-parameterization and Transformer architectures in two distinct research problems—controllable generation in NLP and combinatorial hardware synthesis—PrefixGPT exemplifies the capacity of generative sequence models to adapt to both language and structural topology domains. In both settings, prefix-based representations, modular training, and principled architectural constraints (legality masks, bias separation) yield state-of-the-art efficiency, extensibility, and quality, demonstrating the utility of Transformer backbone plus prefix-parameter tuning as a general research paradigm (Ma et al., 2023, Ding et al., 22 Nov 2025, Li et al., 2021).