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Jul 6

All Routes Lead to Collapse

Attention sinks, representation collapse, and norm stratification are treated as transformer-specific pathologies. We show they are not specific to attention: they are what content-based routing does under a fixed similarity metric. We give a reframing identity: softmax attention is Boltzmann-weighted aggregation over Euclidean distances with constant key norms, so its score omits a -|k|^2 term and is blind to key magnitude. This predicts that any router whose metric is ill-matched to its representations should compensate, by concentrating its routing and collapsing the routed representations. We test it on routers that score and aggregate over different axes: softmax attention over tokens (nine pretrained transformers), graph attention over nodes, a selective state-space model and a recurrent mixer over time, and learned residuals over depth. All develop the same signature, and two within-model ablations show it is caused by the routing mechanism rather than by incidental dynamics. The form is contingent, set by the strength of the positional brake each router carries alongside its content score; we sweep that brake and move the onset across its whole range. The mechanism is not contingent, and it does not require norm stratification: a router with norm-normalized keys concentrates just the same. We do not claim these models implement Riemannian geometry; the geometric view is a diagnostic that names the inadequacy of the flat, norm-blind metric.

  • 1 authors
·
Jun 20

How Alignment Routes: Localizing, Scaling, and Controlling Policy Circuits in Language Models

This paper localizes the policy routing mechanism in alignment-trained language models. An intermediate-layer attention gate reads detected content and triggers deeper amplifier heads that boost the signal toward refusal. In smaller models the gate and amplifier are single heads; at larger scale they become bands of heads across adjacent layers. The gate contributes under 1% of output DLA, but interchange testing (p<0.001) and knockout cascade confirm it is causally necessary. Interchange screening at n>=120 detects the same motif in twelve models from six labs (2B to 72B), though specific heads differ by lab. Per-head ablation weakens up to 58x at 72B and misses gates that interchange identifies; interchange is the only reliable audit at scale. Modulating the detection-layer signal continuously controls policy from hard refusal through evasion to factual answering. On safety prompts the same intervention turns refusal into harmful guidance, showing the safety-trained capability is gated by routing rather than removed. Thresholds vary by topic and by input language, and the circuit relocates across generations within a family while behavioral benchmarks register no change. Routing is early-commitment: the gate commits at its own layer before deeper layers finish processing the input. Under an in-context substitution cipher, gate interchange necessity collapses 70 to 99% across three models and the model switches to puzzle-solving. Injecting the plaintext gate activation into the cipher forward pass restores 48% of refusals in Phi-4-mini, localizing the bypass to the routing interface. A second method, cipher contrast analysis, uses plain/cipher DLA differences to map the full cipher-sensitive routing circuit in O(3n) forward passes. Any encoding that defeats detection-layer pattern matching bypasses the policy regardless of whether deeper layers reconstruct the content.

  • 1 authors
·
Apr 12 2

From Words to Routes: Applying Large Language Models to Vehicle Routing

LLMs have shown impressive progress in robotics (e.g., manipulation and navigation) with natural language task descriptions. The success of LLMs in these tasks leads us to wonder: What is the ability of LLMs to solve vehicle routing problems (VRPs) with natural language task descriptions? In this work, we study this question in three steps. First, we construct a dataset with 21 types of single- or multi-vehicle routing problems. Second, we evaluate the performance of LLMs across four basic prompt paradigms of text-to-code generation, each involving different types of text input. We find that the basic prompt paradigm, which generates code directly from natural language task descriptions, performs the best for GPT-4, achieving 56% feasibility, 40% optimality, and 53% efficiency. Third, based on the observation that LLMs may not be able to provide correct solutions at the initial attempt, we propose a framework that enables LLMs to refine solutions through self-reflection, including self-debugging and self-verification. With GPT-4, our proposed framework achieves a 16% increase in feasibility, a 7% increase in optimality, and a 15% increase in efficiency. Moreover, we examine the sensitivity of GPT-4 to task descriptions, specifically focusing on how its performance changes when certain details are omitted from the task descriptions, yet the core meaning is preserved. Our findings reveal that such omissions lead to a notable decrease in performance: 4% in feasibility, 4% in optimality, and 5% in efficiency. Website: https://sites.google.com/view/words-to-routes/

  • 3 authors
·
Mar 15, 2024

AlphaTransit: Learning to Design City-scale Transit Routes

Designing a transit network requires many sequential route extension decisions, but their quality is often visible only after the full network is assembled. This delayed-feedback challenge lies at the heart of the Transit Route Network Design Problem (TRNDP), where route interactions can be deceptive: an extension that appears useful locally can create transfer bottlenecks, produce redundant overlap, or reduce overall throughput. To guide route construction under delayed simulator feedback, we introduce AlphaTransit, a search-based planning framework for cityscale bus network design. AlphaTransit couples Monte Carlo Tree Search (MCTS) with a neural policy-value network: the policy proposes route extensions, the value estimates downstream design quality, and search uses these predictions to refine each decision. This provides decision-time lookahead during route construction without running simulator rollouts inside the search tree. We evaluate AlphaTransit on a new Bloomington TRNDP benchmark with realistic road topology and censusderived demand, under mixed and full transit demand settings. In the Bloomington network, AlphaTransit attains the highest service rate in both demand settings, reaching 54.6% and 82.1%, respectively. Relative to reinforcement learning without search, these correspond to 9.9% and 11.4% service rate gains; relative to MCTS without learned guidance, they correspond to 2.5% and 11.2% gains. These results suggest that coupling learned guidance with MCTS is more effective than using either approach alone for transit network design. Our code and data are publicly available in https://github.com/poudel-bibek/AlphaTransit.

  • 3 authors
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May 26 2