LLM residual streams during addition form an Iso-Raw-Sum Trajectory anchored by digit semantics and modulated by continuous carry signals, with errors arising as geometric slippages across quantization thresholds in a noisy model.
arXiv:2402.02619 (2024)
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
years
2026 7verdicts
UNVERDICTED 7representative citing papers
Dynamic Latent Routing jointly learns discrete latent codes, routing policies, and model parameters via dynamic search to match or exceed supervised fine-tuning by 6.6 points on average in low-data settings across four datasets and six models.
Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
Llama-3.1-8B computes sums for cyclic concepts using base-10 addition via task-agnostic Fourier features with periods 2, 5, and 10 rather than modular arithmetic in the concept period.
LMs compare unit quantities via number-specific and unit-specific heuristics rather than unified scale conversion, evidenced by degraded accuracy near boundaries, linear surrogate predictions, and causal subspace interventions.
Transformer represents but does not causally transmit staged algorithmic intermediates for base-digit extraction, diverging from probe predictions.
LLMs show strong spatial generalization to unseen maps in shortest-path tasks but fail length scaling due to recursive instability, with data coverage setting hard limits.
citing papers explorer
-
The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models
LLM residual streams during addition form an Iso-Raw-Sum Trajectory anchored by digit semantics and modulated by continuous carry signals, with errors arising as geometric slippages across quantization thresholds in a noisy model.
-
Dynamic Latent Routing
Dynamic Latent Routing jointly learns discrete latent codes, routing policies, and model parameters via dynamic search to match or exceed supervised fine-tuning by 6.6 points on average in low-data settings across four datasets and six models.
-
Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior
Manifold steering along activation geometry induces behavioral trajectories matching the natural manifold of outputs, while linear steering produces off-manifold unnatural behaviors.
-
Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts
Llama-3.1-8B computes sums for cyclic concepts using base-10 addition via task-agnostic Fourier features with periods 2, 5, and 10 rather than modular arithmetic in the concept period.
-
Language Models Compare Quantities Using Number-specific and Unit-specific Heuristics
LMs compare unit quantities via number-specific and unit-specific heuristics rather than unified scale conversion, evidenced by degraded accuracy near boundaries, linear surrogate predictions, and causal subspace interventions.
-
Represented Is Not Computed: A Causal Test of Candidate Algorithmic Intermediates in a Transformer
Transformer represents but does not causally transmit staged algorithmic intermediates for base-digit extraction, diverging from probe predictions.
-
Generalization in LLM Problem Solving: The Case of the Shortest Path
LLMs show strong spatial generalization to unseen maps in shortest-path tasks but fail length scaling due to recursive instability, with data coverage setting hard limits.