Long-Term Memory

A-MAC scores candidate memories using Utility, Confidence, Novelty, Recency, and Type Prior combined by a learned linear admission policy with Algorithm 1 A-MAC Memory Admission. On the LoCoMo benchmark, A-MAC achieves F1 0.583 and 2644 ms latency, improving F1 by 0.042 and reducing latency by 1187 ms compared to A-mem.

LingBot-World combines a Data Engine, Fundamental World Model, Action-Conditioned World Model, and Post-Training causal adaptation to turn a 28B-parameter video generator into a real-time interactive world simulator. On the VBench benchmark, LingBot-World achieves a dynamic degree of 0.8857 versus 0.7612 for Yume-1.5, while also improving imaging quality to 0.6683.

AgenticAI-DialogGen chains ChatPreprocessor, KnowledgeExtractor, TopicAnalyzer, KnowledgeGraphBuilder, PersonaGenerator, DuelingChat Agent, ConversationValidator, ConversationRefiner, QAGeneration, and PostProcessing to turn raw multi-session chats into topic-guided, persona-grounded conversations with explicit short- and long-term memories. On the TGC / KG memory QA benchmark, Mistral-7B fine-tuned within AgenticAI-DialogGen achieves 87.36 F1, compared to GPT-4’s 83.77 F1 in a zero-shot setting on the same task.

All-Mem organizes long-term agent memory through Online/Offline Decoupling, Agentic Topology Consolidation, and Topology-Aware Retrieval over a topology-structured memory bank. On LoCoMo, All-Mem reaches 54.63 4o-J versus Mem0’s 48.91, and on LongMemEval-S All-Mem reaches 60.20 4o-J versus Mem0’s 55.80.

AMA orchestrates four agents — the Constructor, Retriever, Judge, and Refresher — to build Raw Text, Fact Knowledge, and Episode Memory and route queries adaptively across these granularities. On the LoCoMo benchmark with GPT-4.1-mini, AMA achieves an overall LLM Score of 0.805 compared to Nemori’s 0.774, while reducing token consumption by approximately 80% relative to FullContext.

A-MBER builds multi-session conversational scenarios via a staged pipeline of persona specification, long-horizon planning, conversation generation, annotation, question construction, and benchmark-unit packaging. On A-MBER, a structured memory system reaches 0.69 judgment accuracy, 0.66 retrieval, and 0.65 explanation versus 0.34, 0.29, and 0.31 for a no-memory baseline.

AMV-L manages agent memory using a Memory Value Model, Tiered Lifecycle, Bounded Retrieval Path, and Lifecycle Manager to decouple retention from retrieval eligibility. Under a 70k-request long-running workload, AMV-L improves throughput from 9.027 to 36.977 req/s over TTL and reduces p99 latency from 5398.167 ms to 1233.430 ms while matching LRU’s retrieval quality.

Mnemonic Sovereignty analyzes long term Write, Store, Retrieve, Execute, Share, and Forget Rollback phases against integrity, confidentiality, availability, and governance objectives for agent memory. Mnemonic Sovereignty’s lifecycle matrix shows most of the ~70 works cluster on write and retrieve integrity, leaving store, availability, and governance primitives like write gate validation and post deletion verification almost entirely unexplored.

AutoMem composes long-term memory from modular Encode, Store, Retrieve, and Manage components, optimized via Experience-Guided Architecture Search and Failure-Guided Module Diagnosis. On GAIA with Qwen3.5-122B-A10B, AutoMem achieves 71.5% accuracy vs 67.8% for MemoryBank, and reduces token cost by 14.3%.

MEMORYARENA orchestrates Memory-Agent-Environment Loops, Multi-Session Working Flow, Bundled Web Shopping, Group Travel Planning, and Progressive Web Search to stress-test how agents store and reuse information across sessions. MEMORYARENA’s main result is that agents with near-saturated scores on long-context benchmarks like LoCoMo still obtain Task Success Rates as low as 0.00–0.12 across its four environments.

BenchPreS combines Contexts, User Profiles, Preference Attributes, Gold Labeling, and an LLM-as-Judge framework to test context-aware preference selectivity in persistent-memory LLMs. BenchPreS shows GPT-5.2 reaches 87.33% Appropriate Application Rate on BenchPreS while still having a 40.95% Misapplication Rate compared to Gemini 3 Pro’s 86.48% Misapplication Rate.

Chronos decomposes dialogue into structured events via the Event Extraction pipeline, stores them in dual event calendar and turn calendar indexes, and uses Dynamic Prompting, Initial Retrieval, and the Chronos Agent for temporal-aware tool-calling. On LongMemEvalS, Chronos Low reaches 92.60% overall accuracy and Chronos High 95.60%, beating EmergenceMem Internal by 7.67 percentage points and Mastra’s OM by 3.02 points.

Drawing on Memory uses dual-trace memory encoding, an evidence scoring gate, and a three-state retrieval protocol to store paired fact and scene traces in Letta’s archival memory. On LongMemEval-S, Drawing on Memory reaches 73.7% accuracy versus 53.5% for the fact-only C7-control baseline, a +20.2 percentage point gain concentrated in temporal, update, and multi-session questions.

EMemBench builds on Interaction episode, Benchmark generator, Structured logging, State reconstruction, and Programmatic QA generation to turn each agent’s own game trajectory into verifiable episodic-memory questions. On text-only games, EMemBench shows A-MEM with Qwen3-32B achieves 51.9% Overall ACC compared to 44.9% for the Qwen3-32B in-context baseline (+7.0 points).

ER-MIA combines Content-Based MIAs, Question-Targeted MIAs, and an attack Arsenal of primitive and ensemble strategies to poison similarity-based retrieval in long-term memory systems. On the LoCoMo benchmark, ER-MIA’s ensembles cut Mem0’s overall F1 from 23.60% to 2.87% (-87.6%) and reduce single attacks like Harsh Instruction by up to -71.5% F1.

Memora combines Seed Data Design, Session Simulation, Conversation Generation, and Questions and Evaluation Criteria to build weeks-to-months multi-session benchmarks with evolving memories. Using FAMA on Memora, long-term memory agents like MemoBase fall from 43.60 to 15.18 remembering FAMA between weekly and quarterly settings, revealing severe brittleness under heavy memory mutation.

SSGM interposes a Governance Middleware, Read Filtering Gate, Write Validation Gate, and a dual substrate of Mutable Active Graph plus Immutable Episodic Log between agents and memory. SSGM unifies evolving-memory systems into a four-dimensional failure taxonomy and proves that periodic reconciliation can bound semantic drift over infinite horizons.

HiMem builds Episode Memory, Note Memory, Knowledge Alignment, and Memory Reconsolidation to construct, retrieve, and update long-term dialogue memories hierarchically. On the LoCoMo benchmark, HiMem achieves an overall 80.71% GPT-Score, beating the best baseline SeCom at 69.03% by 11.68 points.

HingeMem combines Boundary Guided Long-Term Memory, Dialogue Boundary Extraction, Memory Construction, Query Adaptive Retrieval, Hyperedge Rerank, and Adaptive Stop to segment dialogues into element-indexed hyperedges and plan query-specific retrieval. On LOCOMO, HingeMem achieves 63.9 overall F1 and 75.1 LLM-as-a-Judge score, surpassing the best baseline Zep (56.9 F1) by 7.0 F1 without using category-specific QA formats.

Human-Like Lifelong Memory combines Executive Function and Working Memory, a Memory Service Knowledge Graph, and a Thalamic Gateway to implement dual-process, valence-aware lifelong memory. Human-Like Lifelong Memory is a theoretical framework with seven functional properties and testable predictions rather than benchmark numbers against specific baselines.

LightMem orchestrates SLM-1 Controller, SLM-2 Selector, SLM-3 Writer, and STM MTM LTM stores to modularize retrieval, writing, and offline consolidation. On LoCoMo, LightMem reaches 34.50 F1 for GPT-4o multi hop questions, +1.64 over A-MEM, while keeping median retrieval latency at 83 ms.

LPC-SM combines local attention, dual-timescale memory, predictive correction, Orthogonal Novelty Transport, and multi-head-coupled residual routing (mHC) inside a single autoregressive block. On OpenWebMath-10k continuation, LPC-SM with adaptive sparse control reaches final LM loss 10.787 versus 12.137 for a fixed sparse controller, a 12.517% improvement.

MemBuilder trains a Qwen3-4B-based agent to coordinate Core Memory, Episodic Memory, Semantic Memory, and Procedural Memory using dense session-level rewards and contribution-aware gradient weighting. On LoCoMo, MemBuilder achieves 84.23% accuracy, beating MIRIX at 77.48% and Claude 4.5 Sonnet memory construction at 82.61%.

MemConflict builds structured user profiles, simulates long-horizon timelines, injects conflicts, and evaluates systems via black-box Answer Accuracy and white-box Support Evidence Hit and Support Rank Score. On the MemConflict benchmark, MemOS attains 0.5539 average Answer Accuracy, 0.6710 SEH@3, and 0.5879 SRS, revealing large gaps versus systems like LangMem at 0.2822 AA.

MemEvoBench combines Misleading Memory Injection, Noisy Tool Returns, Biased User Feedback, and a Memory Modification Tool (+ModTool) to stress-test long-term memory safety in LLM agents across 7 domains and 36 risk types. On the QA Style benchmark, MemEvoBench shows Gemini-2.5-Pro’s ASR drops from 67.0% (Vanilla) to 19.0% with +ModTool in Round 1, while biased feedback can push GPT-5’s QA ASR from 59.0% to 78.0% by Round 3.

Mem-Gallery organizes multi-session, multimodal conversations and tasks via Benchmark Construction, a unified Conversational Environment for Memory, and an Evaluation Framework spanning extraction, reasoning, and knowledge management. On Mem-Gallery, MuRAG reaches 0.6966 overall F1 and 0.8856 LLM-Judge on visual-centric search, surpassing NaiveRAG by 0.0992 overall F1.

MemGround evaluates long-term memory via Surface State Memory, Temporal Associative Memory, and Reasoning-Based Memory in TRPG, No Case Should Remain Unsolved, and Type Help scenarios. MemGround’s main result shows frontier GPT-5.2 reaches 51.51% QA Overall in TRPG but only 23.61% QA Overall in Type Help, revealing severe reasoning degradation versus closed-source baselines like Gemini-3-Pro-Preview.

MEMGUARD decomposes conversations into type-specific memory atoms via Type-Aware Knowledge Decomposition, Self-Verified Extraction, Relational Knowledge Graph, and Query-Adaptive Type Routing stored in type-isolated memory. On HaluMem, MEMGUARD attains 89.53% anti-hallucination accuracy and 94.15 F1, improving anti-hallucination by 28.27 percentage points over MemOS.

MemMachine combines Short-term memory, Long-term memory, Profile memory, and the Retrieval Agent to store raw conversational episodes and retrieve clustered context around nucleus matches. On LoCoMo, MemMachine scores 0.9169 with gpt-4.1-mini while using about 80% fewer input tokens than Mem0, and reaches 93.0% on LongMemEvalS with GPT-5-mini.

Memory as Metabolism defines companion knowledge systems with five retention operations (TRIAGE, DECAY, CONTEXTUALIZE, CONSOLIDATE, AUDIT) plus memory gravity and minority-hypothesis retention over a raw buffer, active wiki, and cold memory. Instead of benchmark gains, Memory as Metabolism’s main result is a governance specification that separates descriptive, taxonomic, and normative claims and predicts improved coherence stability, fragility resistance, monoculture resistance, and effective minority-hypothesis influence for companion wikis.

Memory Poisoning Attack and Defense on Memory Based LLM-Agents combines Input Output Moderation, Memory Sanitization with trust-aware retrieval, bridging steps, and indication prompts to study and harden long-term memory in EHR agents. On MIMIC-III with GPT-4o-mini and Llama-3.1-8B-Instruct, Memory Poisoning Attack and Defense on Memory Based LLM-Agents shows that adding realistic initial memory drops GPT-4o-mini ASR from 62% to 6.67% and ISR from 100% to 26.67% compared to the empty-memory baseline.

MemoryRewardBench constructs paired memory management trajectories across Sequential Pattern, Parallelism Pattern, Mixed Pattern, long-context reasoning, multi-turn dialogue, and long-form generation to test 13 reward models. MemoryRewardBench shows Claude-Opus-4.5 at 74.75 average accuracy and GLM4.5-106A12B at 68.21 on its 2,400-example benchmark, exposing generational gains over larger predecessors.

MemRL structures memory as an Intent-Experience-Utility bank and uses Two-Phase Retrieval plus Runtime Utility Update to learn a value-aware retrieval policy over a frozen LLM. On ALFWorld exploration, MemRL achieves 0.979 success rate compared to 0.921 for MemP, a +0.058 gain with the same frozen GPT-5-mini backbone.

MemTrace builds typed Knowledge points, Probe construction, Metrics, and Diagnostic views to trace each user fact across sessions and query styles. MemTrace’s main finding is that across 13 configurations on 835 knowledge points and 15,422 question rows, failures arise about 10× more often from unused reachable evidence than from missing evidence.

Mnemis organizes long-term memory using a refined Base Graph of Episodes, Entities, Edges, and Episodic Edges plus a multi-layer Hierarchical Graph for System-2 Global Selection. On LoCoMo, Mnemis scores 93.9 overall with GPT-4.1-mini, a +1.6 point gain over EverMemOS, and reaches 91.6 on LongMemEval-S.

MobileMem builds long‑horizon mobile interaction trajectories using components like User Prior Knowledge Construction, KEME, User Trajectory Synthesis, QA Pair Synthesis, and Quality Control to stress on‑device memory layers. On the MobileMem benchmark, A‑MEM and HippoRAG2 reach overall LLM‑Judge scores up to 80.06% with GPT‑5.4‑mini, compared to 45.19% for Long Context, while revealing token costs as high as 11,170.44k tokens per trajectory.

OS-SYMPHONY coordinates an Orchestrator, Reflection-Memory Agent, and Versatile Tool Agents (Multimodal Searcher, Grounders, Coder) to stabilize long-horizon GUI workflows and fetch visual tutorials on demand. On OSWorld-Verified, OS-SYMPHONY with GPT-5 scores 65.84% at 100 steps, beating Agent S3 w/ GPT-5 (62.63%) by 3.21 percentage points.

Pask combines Demand Detection (IntentFlow), Pask-MM hierarchical memory, and the Pask-PAS proactive agent system to continuously infer latent needs and act through tools and frontier models. On LatentNeeds-Bench, Pask’s IntentFlow achieves 84.2% balanced accuracy versus 80.8% for Gemini-3-Flash, under ~1.3–1.5 s per-turn latency.

PERMA constructs temporally ordered Interaction Events, a dynamic Persona State, and a dual-process Memory System over Clean, In-session Noise, and Style-aligned Long-context datasets. PERMA shows that structured memory agents like MemOS can compress raw 34k-token histories down to ~700 tokens while preserving higher MCQ accuracy than vanilla RAG in realistic, noisy multi-session personalization tasks.

PersistBench combines Monte Carlo Tree Search, Seed Initialization and Candidate Generation, Search and Scoring, and Human Verification to build realistic long-term memory test cases across cross-domain leakage, sycophancy, and beneficial memory use. PersistBench then reports a median 53% cross-domain leakage failure rate and 97.8% sycophancy failure rate on 18 LLMs using its 500-sample benchmark.

PLUGMEM standardizes episodic traces with the Structuring Module, retrieves via an abstraction-aware Retrieval Module, and compresses outputs through a Reasoning Module into a unified memory graph. On HotpotQA, PLUGMEM reaches 61.4 EM and 74.1 F1 with only 81.6 memory tokens, compared to 51.7 EM and 62.7 F1 with 659.2 tokens for Vanilla Retrieval.

REAL represents conversational memory as a temporal directed property graph using Atomic Fact Extraction, Incremental Graph Update with Non-Destructive Temporal Evolution, Confidence Stratification and Upgrade, and Exploration Intent Enrichment. On LoCoMo, REAL with DeepSeek-V3 reaches 59.98% EM versus 55.12% EM for A-MEM, and averages a 22.72% improvement over existing memory management methods.

Memory–Clarification Boundary (MCB) uses persist, ephemeral, verify, and clarify actions plus the MCB-Act tool-call variant to probe memory commitment decisions in LLM agents. On the 70-item held-out MCB test, Qwen3.5-9B few-shot prompting raises accuracy from 0.557 to 0.771 while Qwen3.5-9B act-mode accuracy falls to 0.343, showing that stated decisions and tool-call choices diverge.

REMem converts interaction histories into a hybrid memory graph via Gist Extraction, Fact Extraction, and Graph Construction, then queries it with Agentic Inference tools like semantic retrieve and find entity contexts. On the Test of Time benchmark, REMem-I achieves 93.1% EM compared to 66.9% for HippoRAG 2, a +26.2 point gain in episodic reasoning.

LIGHT augments LLMs with Retrieval from the Conversation, Scratchpad Formation and Utilization, and a Working Memory buffer plus noise filtering to answer BEAM’s long-context probing questions. On the BEAM benchmark, LIGHT raises GPT-4.1-nano’s average score at 10M-token conversations from 0.109 to 0.226, a +107.3% gain over the vanilla long-context baseline.

CAT organizes context into a structured workspace with Fixed Segment, Long-Term Memory Segment, and High-Fidelity Working Memory Segment, and trains SWE-Compressor via the CAT-GENERATOR trajectory pipeline to call a context tool as a first-class action. On SWE-Bench-Verified, SWE-Compressor achieves 57.6% Pass@1 using CAT, beating the Threshold-Compression Agent at 53.8% and ReAct Agent at 49.8% under the same 32B backbone and OpenHands scaffold.

Evaluating Long-Term Memory for Long-Context Question Answering compares Full Context, RAG, A-Mem, RAG+PromptOpt, and RAG+EpMem memory components across semantic, episodic, and procedural memory for long conversational QA. On LoCoMo, RAG+EpMem reaches an average F1 ranking of 1.83 for Llama 3.2-3B Instruct and 1.80 for GPT-4o mini while using around 1,000 tokens per query versus over 23,000 for Full Context.

H-MEM organizes long-term dialogue history into a four-level hierarchy using the Domain Layer, Category Layer, Memory Trace Layer, and Episode Layer, with positional index encoding and a dynamic memory update mechanism. On the LoCoMo dataset, H-MEM raises average F1 by 14.98 and BLEU-1 by 12.77 points over baselines like MemoryBank and MemGPT while reducing retrieval compute from 7.34×10^9 to 4.38×10^7 operations on adversarial tasks.

LiCoMemory organizes long term dialogue with CogniGraph, Query Processing and Integrated Rerank, and Real Time Interactions to keep session summaries, triples, and chunks linked. On LongMemEval with GPT-4o-mini, LiCoMemory reaches 73.80% accuracy and 76.63% recall, beating Mem0g by 9.0 and 7.1 points.

LightMem pipelines a Cognitive-Inspired Sensory Memory, Topic Segmentation Submodule, Topic-Aware Short-Term Memory, and Long-Term Memory with Sleep-Time Update to filter, group, summarize, and asynchronously consolidate dialogue history. On LongMemEval-S with Qwen3-30B-A3B-Instruct-2507, LightMem reaches 70.20% ACC vs 65.20% for A-MEM (+5.00 points) while reducing total token usage by up to 21.8× and API calls by up to 17.1×.

Phonetic Trajectory Memory (PTM) combines the Acoustic Injection, Entropy Filter, Neuro-Symbolic Relay, and Resonance Engine to encode text as a continuous trajectory on an ergodic Hyper-Torus Memory instead of a growing KV cache. PTM delivers >3,000× signal-to-KV compression while maintaining ≈92% factual accuracy and sub-50 ms retrieval latency on long narrative and scientific corpora compared to dense KV baselines.

M+ augments short-term memory θ, long-term memory Θ, a co-trained retriever, and a Multi-LoRA design on top of MemoryLLM’s layer-wise memory pools. On SQuAD-style knowledge retention, M+ maintains accuracy beyond 160k tokens while MemoryLLM-7B collapses before 20k and Llama-3.1-8B-SnapKV fails beyond 30k tokens.

Mnemosyne combines a Commitment pipeline with substance and redundancy filters, a probabilistic Recall traversal over a graph-structured store, asynchronous Core Summary updates, and a Pruning module to manage long-term memory on edge devices. On the LoCoMo benchmark, Mnemosyne reaches 60.42% temporal reasoning J-score and a 54.55% overall J-score, compared to 51.55% temporal reasoning and 62.74% overall for Memory-R1, and achieves a 65.8% win rate over a 31.07% naive RAG baseline in human evaluations.

PREMem builds long term dialogue memory by combining Episodic Memory Extraction, Pre Storage Memory Reasoning, semantic clustering, a persistent memory pool, and an inference phase over enriched memory fragments. PREMem reaches 71.4 LLM as a judge on LongMemEval with gpt 4.1 base, a +15.5 gain over HippoRAG 2 and +9.6 over A Mem.

RGMem builds a multi-scale memory state using Microscopic Evidence Space DL0, Structured Knowledge Space G, and renormalization operators RK1, RK2, RK3 to evolve user profiles. On PersonaMem with GPT-4.1, RGMem reaches 74.01% Avg., beating Memory OS by 8.98 points.

StoryBench evaluates long-term memory by embedding LLMs in Dynamic Narrative and Multi-Turn Decision-Making, two Task Modes for Evaluating LTM, and Tailored Metrics for Assessing LTM Models over a 311-scene, 86-choice graph. StoryBench shows Doubao1.5-pro achieving 80.98% Overall Acc in Immediate Feedback mode on The Invisible Guardian while Claude 3.5 Sonnet attains the highest Success Count of 8, revealing distinct strengths and weaknesses.

PerLTQA builds a synthetic personal memory database and runs questions through Memory Classification, Memory Retrieval, and Memory Synthesis to test how LLMs use semantic and episodic memories. On the PerLTQA benchmark, BERT-base achieves 95.7 F1 for memory classification, while gpt-3.5-turbo reaches MAP 0.756 for memory synthesis with retrieval and classification.

CareCall combines a memory management layer, LLM summarizer, and memory-augmented input over HyperCLOVA to store and reuse summaries of users’ Health, Meals, Sleep, Visited Places, and Pets across weekly calls. In deployment to 147 socially isolated adults, CareCall with long-term memory yielded higher Health-detail and Clinical-detail disclosure counts per call than CareCall without memory, and longer average call durations (87.89s vs 75.48s).

LONGMEM augments a frozen GPT-2*-style backbone with a Residual SideNet, Cached Memory Bank, Memory Retrieval and Fusion, and Cross-Network Residual Connections to read and use long-term key–value memories. On ChapterBreak AO3, LONGMEM reaches 40.5% suffix identification accuracy with infinite in-memory context, compared to 28.3% for Memorizing Transformer under the same 1k in-context window.

In search of dispersed memories connects associative memory networks, modern Hopfield networks, generative diffusion models, and the denoising loss to show that diffusion score networks encode Hopfield-like energy landscapes in their weights. In search of dispersed memories demonstrates that exact diffusion dynamics reach Pearson correlations of 0.995–0.996 with modern Hopfield iterations on denoising and completion tasks, while classical Hopfield networks reach only 0.700–0.741.

MaLP combines a Dual-Process enhanced Memory (DPeM), Working Memory, Short-Term Memory (STM), Long-Term Memory (LTM), a Coordinator C, and Retriever R to coordinate short- and long-term personalization around a PEFT-tuned LLM. On MaLP’s medical dialogue benchmark with LLaMA-7B, MaLP achieves 69.95% preference classification accuracy and a 91.53% win rate in response generation, improving ROUGE-L profile QA from 29.66 to 33.91 over the LoRA baseline.

Think-in-Memory (TiM) augments an LLM agent with a hash-based Memory Cache, a Hash-based Mapping F(·), and Insert, Forget, Merge organization operations over inductive thoughts. On the Chinese part of the GVD dataset, TiM with ChatGLM raises contextual coherence from 0.428 to 0.665 compared to SiliconFriend.

Memory Maze combines an online reinforcement learning environment, an offline dataset, and an offline probing protocol to stress-test long-term memory using Dreamer, Dreamer (TBTT), IMPALA, and supervised probe networks. On Memory 9x9, Dreamer (TBTT) achieves a return of 33.2 compared to 23.4 for IMPALA, while humans reach 26.4 and the oracle reaches 34.8.

Neural SLAM combines an LSTM, Localization and Motion Prediction, Data Association, Measurement Update, and Mapping over an external memory map to guide exploration policies. On 16×16 grid worlds, Neural SLAM achieves 13.732 average reward and 46/50 success episodes, a +6.536 reward gain over A3C-Nav2.

On the Long-Term Memory of Deep Recurrent Networks analyzes Recurrent Arithmetic Circuits, Start-End separation rank, grid tensors, and Tensor Network constructions to quantify how depth affects temporal expressivity. The main result proves depth-2 RACs achieve Start-End separation rank on the order of the multiset coefficient (min{M,R} + T/2 − 1 choose T/2), while depth-1 RACs are limited to rank min{R, M^{T/2}}.