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Transformer architectures have been widely adopted for time series forecasting, yet whether the representational mechanisms that make them powerful in NLP actually engage on time series data remains unexplored. The persistent competitiveness of simple linear models such as DLinear has fueled ongoing debate, but no mechanistic explanation for this phenomenon has been offered. We address this gap by applying sparse autoencoders (SAEs), a tool from mechanistic interpretability, to probe the internal representations of PatchTST. We first establish that a single-layer, narrow-dimensional transformer matches the forecasting performance of deeper configurations across commonly used benchmarks. We then train SAEs on the post-GELU intermediate FFN activations with dictionary sizes ranging from 0.5x to 4.0x the native dimensionality. Expanding the dictionary yields negligible downstream performance change (average 0.214%), with large portions of overcomplete dictionaries remaining inactive. Targeted causal interventions on dominant latent features produce minimal forecast perturbation. Across all evaluated settings, we observe no empirical evidence that the analyzed FFN representations rely on strong superposition. Instead, the representations remain sparse, stable under aggressive dictionary expansion, and largely insensitive to latent interventions. These results demonstrate that superposition is not necessary for competitive performance on standard forecasting benchmarks, suggesting they may not demand the rich compositional representations that drive transformer success in language modeling, and helping explain the persistent competitiveness of simple linear models

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Mechanistic interpretability typically relies on post-hoc analysis of trained networks. We instead adopt an interventional approach: testing hypotheses a priori by modifying architectural topology to observe training dynamics. We study grokking - delayed generalization in Transformers trained on cyclic modular addition (Zp) - investigating if specific architectural degrees of freedom prolong the memorization phase. We identify two independent structural factors in standard Transformers: unbounded representational magnitude and data-dependent attention routing. First, we introduce a fully bounded spherical topology enforcing L2 normalization throughout the residual stream and an unembedding matrix with a fixed temperature scale. This removes magnitude-based degrees of freedom, reducing grokking onset time by over 20x without weight decay. Second, a Uniform Attention Ablation overrides data-dependent query-key routing with a uniform distribution, reducing the attention layer to a Continuous Bag-of-Words (CBOW) aggregator. Despite removing adaptive routing, these models achieve 100% generalization across all seeds and bypass the grokking delay entirely. To evaluate whether this acceleration is a task-specific geometric alignment rather than a generic optimization stabilizer, we use non-commutative S5 permutation composition as a negative control. Enforcing spherical constraints on S5 does not accelerate generalization. This suggests eliminating the memorization phase depends strongly on aligning architectural priors with the task's intrinsic symmetries. Together, these findings provide interventional evidence that architectural degrees of freedom substantially influence grokking, suggesting a predictive structural perspective on training dynamics.

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Standard Transformers suffer from a "Semantic Alignment Tax", a prohibitive optimization cost required to organize a chaotic initialization into a coherent geometric map via local gradient diffusion. We hypothesize that this reliance on diffusive learning creates "Catastrophic Rigidity", rendering models unable to adapt to novel concepts without destroying their pre-trained reasoning capabilities. To isolate this phenomenon, we introduce Iterative Semantic Map Refinement (ISMR), a diagnostic protocol revealing that alignment is a fixed geometric barrier that scaling cannot solve; a 20-layer model overcomes this barrier no faster than a 1-layer model. We introduce the Phase-Resonant Intelligent Spectral Model (PRISM). PRISM encodes semantic identity as resonant frequencies in the complex domain (C^d) and replaces quadratic self-attention with linearithmic O(N log N) Gated Harmonic Convolutions. We validate PRISM on the WMT14 translation task. While the Standard Transformer maintains a slight edge in general competence on static benchmarks (23.88 vs 21.40 BLEU), it fails the "Plasticity-Stability" stress test completely. When injected with novel concepts, the Transformer suffers Catastrophic Forgetting, degrading by -10.55 BLEU points while achieving only 60% acquisition. In contrast, PRISM demonstrates Lossless Plasticity, achieving 96% 5-shot acquisition with negligible degradation (-0.84 BLEU). These results suggest that harmonic representations effectively decouple memory from reasoning, offering a structural solution to the plasticity-stability dilemma in real-time knowledge adaptation.