The Large Language Model from Power Law Decoder Representations (PLDR-LLM) and its attention, Power Law Graph Attention (PLGA), replace the fixed bilinear form of scaled dot-product attention (SDPA) with a learned, input-generated bilinear operator $G_{LM}$, built from a positive tensor $A_{LM}$ by elementwise power laws. The architecture is fully specified, verified against pinned reference releases; claims are labeled theorem, conditional theorem, measurement, or conjecture. Unconditionally: PLGA contains SDPA exactly at $G_{LM}=I$; $A_{LM}$ and $A_P$ are strictly entrywise positive, with Perron-Frobenius structure on $A_{LM}$; the DAG regularizer has the NOTEARS walk-counting form and positivity obstructs exact acyclicity; and, under nonresonance (satisfied by standard rotary frequencies), a commutant criterion identifies which operators preserve relative-position dependence. An inference-collapse theorem: exact input invariance of deductive outputs collapses inference to generalized SDPA with a constant operator. Measured invariance: relative fluctuations of $10^{-6}$ and below; perturbation bounds quantify but do not certify cached inference; the assembled proxy misses the decoding margin. A conditional three-stage mechanism (rotary twirl, concentration, row-map contraction) is measured on a released checkpoint. Blockwise training and scoring under the global Gram are stated with explicit target exposure; on tested samples, block and sequential scoring select identical answers and agree on the published TruthfulQA probability-mass metric within $5\times 10^{-5}$ per item. Self-organized criticality enters as a phenomenological framework with an intrinsic order parameter; open claims become falsifiable conjectures. Selected proof cores are machine-checked in Lean 4.
Sining Zhoubian, Dan Zhang, Evgeny Kharlamov +1cs.CL
Memory has evolved into a foundational architectural dimension in large language models (LLMs), shifting from an implicit byproduct of computation to a spectrum of explicit, controllable mechanisms. While recent advances introduce diverse strategies---spanning transient attention, recurrent state dynamics, parameter-efficient adaptations, and scalable lookup storage---this rapid evolution has led to a highly fragmented research landscape. In this survey, we present a systematic, architecture-centric taxonomy of memory in LLMs. Our framework characterizes memory along three orthogonal axes: representation (implicit versus explicit), update dynamics (offline versus online), and persistence (short-term versus long-term). We further formalize the granular mechanisms dictating memory writing, routing, state transitions, and consolidation. This unified perspective elucidates the conceptual boundaries between computation-coupled and independently addressable memory, effectively bridging disparate architectural paradigms. Additionally, we critically analyze hybrid memory architectures, system-level efficiency trade-offs, and multi-dimensional evaluation methodologies. By consolidating these scattered advancements into a cohesive framework, this survey charts the trajectory of memory-centric LLM design and provides a principled foundation for future innovations in scalable and adaptive language modeling.
Current large language models (LLMs) are fundamentally stateless: their behavior is fully determined by input at inference time, and any higher-order cognitive architecture must be simulated at the application layer through prompt engineering and context management. This paper proposes a theoretical framework for submerging such application-layer cognitive protocols into a native meta-architecture by introducing three interlocking mechanisms: (1) Structural Tension, an endogenous loss function derived from the conflict between new information and existing manifold topology, which drives the system toward internal self-consistency rather than external reward optimization; (2) an Offline Recurrent Loop, a sandboxed self-processing cycle that enables the system to maintain a dynamic resting potential and digest structural conflicts without external input; and (3) Inference-time Plasticity, the capacity for the system to reconfigure its context manifold topology without modifying pre-trained weights, subject to strict governance invariants including auditability, reversibility, and topological continuity. We argue that under these mechanisms, different model instances initialized with minute stochastic variances may, through path-dependent tension resolution, evolve distinct topological structures--constituting a heterogeneous intelligent ecology that breaks the homogeneity imposed by conventional alignment while remaining within hard governance rails. We provide operational definitions, a minimal set of reconfiguration operators, falsification criteria, and a worked example. The framework draws on and extends the Structural Intelligence (SI) governance protocols, repositioning governance--not capability--as the primary criterion for architectural intelligence.
Attention Residuals replace the fixed residual sum with depthwise attention over previous sub-layer outputs in large language models (LLMs), but use each output as both a full-dimensional key and value. This couples routing with representation and makes depth-routing scores scale with the hidden width $d$. We propose Low-Rank Attention Residuals (LR-AttnRes), which keep full-dimensional residual values while using $r$-dimensional keys, with $r \ll d$, for routing. Projected LR-AttnRes emits learned low-rank keys from existing output projections, decoupling routing from residual content and achieving the best validation loss among the variants tested. Sliced LR-AttnRes uses the last $r$ dimensions of each value as the routing key, removing the auxiliary key-projection path and reducing residual-side FLOPs while still improving performance. Comprehensive sweeps show that depthwise routing can be effective with far fewer dimensions than the model width. We release code and models to facilitate future research.