The Shape of Addition: Geometric Structures of Arithmetic
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The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models
Announce Type: new Abstract: Large Language Models exhibit paradoxical fragility in fundamental arithmetic, implying a disconnect between internal computation and discrete output. By analyzing the residual stream geometry during multi-operand addition, we identify the Iso-Raw-Sum Trajectory (IRST), a geometric structure where representations are anchored by semantic digits and modulated by continuous carry fibers. We propose the Noisy Quantization Model to explain this geometry, framing...