REVIEW 7 cited by
Uncovering hidden geometry in Transformers via disentangling position and context
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Uncovering hidden geometry in Transformers via disentangling position and context
read the original abstract
Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor $\boldsymbol{h} \in \mathbb{R}^{C \times T \times d}$. Given embedding vector $\boldsymbol{h}_{c,t} \in \mathbb{R}^d$ at sequence position $t \le T$ in a sequence (or context) $c \le C$, extracting the mean effects yields the decomposition \[ \boldsymbol{h}_{c,t} = \boldsymbol{\mu} + \mathbf{pos}_t + \mathbf{ctx}_c + \mathbf{resid}_{c,t} \] where $\boldsymbol{\mu}$ is the global mean vector, $\mathbf{pos}_t$ and $\mathbf{ctx}_c$ are the mean vectors across contexts and across positions respectively, and $\mathbf{resid}_{c,t}$ is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) $(\mathbf{pos}_t)_{t}$ forms a low-dimensional, continuous, and often spiral shape across layers, (2) $(\mathbf{ctx}_c)_c$ shows clear cluster structure that falls into context topics, and (3) $(\mathbf{pos}_t)_{t}$ and $(\mathbf{ctx}_c)_c$ are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.
Forward citations
Cited by 7 Pith papers
-
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.
-
Task Vector Geometry Underlies Dual Modes of Task Inference in Transformers
In a controlled synthetic setting, transformers implement in-distribution task inference via convex combinations of task vectors and out-of-distribution inference via nearly orthogonal extrapolative representations.
-
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.
-
Give it Space! Explicit Disentangling of Positional and Semantic Representations in Encoders
Explicitly disentangling semantic and positional streams in a Transformer encoder reveals that absolute positional representations collapse to a 2D document-structure manifold, attention heads specialize by role, and ...
-
RDP LoRA: Geometry-Driven Identification for Parameter-Efficient Adaptation in Large Language Models
RDP-selected 13 layers for LoRA on Qwen3-8B-Base reach 81.67% on MMLU-Math, beating full 36-layer adaptation at 79.32% and random 13-layer selection at 75.56%.
-
High-Dimensional Statistics: Reflections on Progress and Open Problems
A survey synthesizing representative advances, common themes, and open problems in high-dimensional statistics while pointing to key entry-point works.
-
High-Dimensional Statistics: Reflections on Progress and Open Problems
This review synthesizes representative advances in high-dimensional statistics, highlights common themes and open problems, and points to key entry works.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.