[Paper] Value-Aware Numerical Representations for Transformer Language Models

Source: arXiv - 2601.09706v1

Overview

Transformers have become the go‑to architecture for language tasks, yet they still stumble when asked to understand numbers—treating “42” as just another word token. The paper “Value‑Aware Numerical Representations for Transformer Language Models” proposes a simple, drop‑in modification that injects the actual numeric magnitude into the model’s input, dramatically improving arithmetic and number‑handling abilities without redesigning the whole architecture.

Key Contributions

• Value‑aware prefix token: Introduces a dedicated token placed before each numeric literal whose embedding is computed directly from the number’s value (e.g., via a small MLP over the float representation).
• Tokenizer‑agnostic design: Works with any existing sub‑word tokenizer; the numeric token is left untouched while the prefix supplies the missing magnitude information.
• Compatibility with decoder‑only Transformers: No changes to the model’s layers, attention heads, or training objectives are required.
• Comprehensive evaluation: Shows consistent gains on a suite of arithmetic benchmarks (addition, subtraction, multiplication, division) across decimal, scientific, and mixed‑format numbers, and for operand lengths up to 10 digits.
• Efficiency: The added prefix adds only a constant‑size embedding per number, keeping inference latency and memory overhead minimal.

Methodology

1. Detect numeric tokens during preprocessing (any token that matches a regex for integers, floats, or scientific notation).
2. Generate a value embedding:
   • Convert the literal to a floating‑point value.
   • Pass the value through a lightweight feed‑forward network (typically 2‑layer MLP) to obtain a dense vector.
3. Insert a prefix token (e.g., <NUM_VAL>) before the original numeric token in the token sequence. The embedding of this prefix is replaced by the value embedding computed in step 2.
4. Feed the augmented sequence to the unchanged Transformer model. Because the value embedding is part of the input, the self‑attention layers can directly attend to magnitude information when computing representations for downstream tokens.
5. Training / fine‑tuning: The authors fine‑tuned existing pretrained models (e.g., GPT‑2‑medium) on arithmetic datasets with the augmented inputs, allowing the model to learn how to combine symbolic and value‑aware cues.

Results & Findings

• Robustness to format: Works equally well for plain integers, floating‑point numbers, and scientific notation, indicating that the model learns a value concept rather than memorizing token patterns.
• Generalization: Gains persist when the model is tested on longer operands than seen during fine‑tuning, suggesting the prefix helps the model extrapolate arithmetic rules.
• Negligible overhead: Adding the prefix increased token count by ~0.5 % on average and added <0.2 ms per inference step on a V100 GPU.

Practical Implications

• Better data‑processing pipelines: Applications that rely on LLMs for spreadsheet‑style reasoning, financial report generation, or scientific data summarization can adopt the prefix trick to avoid glaring arithmetic errors.
• Plug‑and‑play upgrade: Since the method does not require architectural changes, existing production models can be retrofitted by updating the preprocessing layer only.
• Improved prompt engineering: Developers can explicitly request numeric precision (e.g., “<NUM_VAL> 3.14”) to guide the model, reducing the need for post‑hoc correction scripts.
• Foundation for hybrid AI: The value‑aware representation bridges symbolic numeric computation and neural language understanding, opening doors for tighter integration with external calculators or constraint solvers.

Limitations & Future Work

• Scope limited to scalar numbers: The current design does not handle complex structures like vectors, matrices, or units (e.g., “5 kg”). Extending the prefix to encode dimensional metadata is an open challenge.
• Dependence on fine‑tuning: Gains were demonstrated after fine‑tuning on arithmetic data; zero‑shot improvements on out‑of‑the‑box models were modest.
• Potential scaling issues: While the overhead is tiny for a few numbers, documents densely packed with numeric literals could see a noticeable token‑length increase.
• Future directions include:
  1. Learning the prefix embedding jointly with the main model in a multi‑task setting.
  2. Integrating unit‑aware embeddings.
  3. Exploring value‑aware representations for other modalities (e.g., dates, timestamps).

Authors

• Andreea Dutulescu
• Stefan Ruseti
• Mihai Dascalu

Paper Information

• arXiv ID: 2601.09706v1
• Categories: cs.CL, cs.AI, cs.LG
• Published: January 14, 2026
• PDF: Download PDF