SF-AMS: Strategic Forgetting for Structured Memory in LLM Agent

# SF-AMS: Strategic Forgetting for Structured Memory in LLM Agent
Source: [https://arxiv.org/html/2607.22562](https://arxiv.org/html/2607.22562)
###### Abstract

Managing long\-context dependencies remains a primary bottleneck in LLM agents, as redundant and irrelevant information can degrade multi\-step reasoning\. Strategic Forgetting for Agent Memory Systems \(SF\-AMS\) is proposed as a framework for maintaining compact high\-utility memory by modeling the long\-term importance of memory units\. SF\-AMS replaces static retrieval and heuristic decay with a utility\-driven survival mechanism that updates memory importance from usage redundancy and temporal signals, inducing a hierarchical memory structure that prioritizes stable entity\-consistent information while filtering noise\. On top of this, Composite Importance Scoring integrates semantic and entity level signals to improve retrieval robustness\. Experiments on LoCoMo and LongMemEval\-s show consistent gains over strong state of the art baselines including LightMem MemO and A\-Mem\. The largest improvement appears in multi\-hop reasoning under Qwen2\.5\-7B where SF\-AMS achieves plus 9\.65 F1 over the strongest baseline followed by temporal reasoning under GPT\-4o\-mini plus 6\.91 F1 and open\-domain tasks plus 6\.53 F1 demonstrating strong cross backbone generalization\. These results show that modeling memory importance as a dynamic utility signal is critical for reliable long\-context reasoning\.

## 1Introduction

Large Language Model \(LLM\) agents have demonstrated remarkable reasoning and decision\-making capabilities in complex, real\-world environments\(Xiet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib1); Zhanget al\.,[2025b](https://arxiv.org/html/2607.22562#bib.bib2); Duet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib19); Meiet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib20); Wanget al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib15)\)\. Sustaining performance over long\-horizon interactions remains challenging, as memory systems must retain essential information while limiting the accumulation of noisy context\. Recent empirical studies show that increasing context length alone does not guarantee effective utilization of relevant information, and models often do not pay attention to important signals in long sequences\(Liuet al\.,[2024a](https://arxiv.org/html/2607.22562#bib.bib36)\)\. Despite significant progress, most existing memory systems remain dependent on predefined storage structures and fixed retrieval strategies\. Even graph\-based approaches\(Edgeet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib25); Rasmussenet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib24)\)and hierarchy\-based methods\(Packeret al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib14); Kanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib7)\)are often constrained by rigid schemas, limiting their ability to dynamically reorganize knowledge and form new conceptual connections over time\. As a result, these systems often suffer from a declining signal\-to\-noise ratio, which hinders their ability to generalize to new tasks and maintain reasoning consistency over extended periods\.

Previous research has addressed these challenges through three primary paradigms\. \(1\)Knowledge organization methods\(Xuet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib3); Chhikaraet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib16); Modarressiet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib21); Rasmussenet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib24); Salamaet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib9)\), such as A\-Mem and Mem0, structure historical data into atomic units or relational graphs to improve interpretability and support structured reasoning\. \(2\)Retrieval augmented and memory access approaches\(Zhonget al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib6); Wanget al\.,[2025a](https://arxiv.org/html/2607.22562#bib.bib32); Jianget al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib26); Linet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib29); Tanget al\.,[2026](https://arxiv.org/html/2607.22562#bib.bib30)\), exemplified by MemoryBank, model memory access through retrieval, time decay, or iterative reasoning mechanisms to improve information utilization\. \(3\)System level and dynamic memory management frameworks\(Packeret al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib14); Kanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib7); Liuet al\.,[2024b](https://arxiv.org/html/2607.22562#bib.bib33); Wanget al\.,[2025b](https://arxiv.org/html/2607.22562#bib.bib34); Fanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib8); Yuet al\.,[2026](https://arxiv.org/html/2607.22562#bib.bib10)\), including MemGPT and MemoryOS, introduce explicit control over memory storage and updates through hierarchical structures and scheduling strategies\. Despite their effectiveness, these approaches typically address either memory organization or retrieval in isolation, lacking a unified mechanism that continuously balances transient interaction noise against long\-term utility\.

To address this gap, Strategic Forgetting for Agent Memory Systems \(SF\-AMS\) is proposed as an agentic memory framework that dynamically maintains a compact and high\-utility memory state\. Unlike passive storage systems, SF\-AMS actively tracks the utility of each memory unit and updates it over time based on usage, redundancy, and temporal signals\. A four\-layer hierarchical structure prioritizes critical information, while an entity anchoring mechanism preserves factual consistency\. Redundant or low\-value memories are gradually removed through a controlled decay process, preventing noise accumulation\. As a result, the system maintains a compact yet informative memory state, enabling more stable reasoning under limited context budgets\. The contributions are summarized as follows:

- •SF\-AMS is proposed as a dynamic memory framework that explicitly controls memory growth through strategic forgetting\. By continuously filtering redundant and low\-utility information, the system maintains a compact memory state and mitigates noise accumulation during long\-horizon interactions\.
- •A utility\-driven memory update mechanism is introduced, which assigns each memory unit a dynamic score based on usage frequency, redundancy, and temporal signals\. This mechanism reinforces frequently accessed and informative memories while gradually removing less useful ones, enabling adaptive and self\-organizing memory evolution\.
- •Experiments on LoCoMo and LongMemEval\-s demonstrate consistent improvements over strong baselines, achieving up to \+9\.65 F1 in multi\-hop reasoning and \+6\.91 F1 in temporal reasoning, indicating robust performance across reasoning types and backbone models\.

## 2Related Work

### 2\.1Knowledge Organization Methods

Knowledge organization methods aim to improve memory quality by transforming raw interactions into structured and interpretable representations\(Xuet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib3); Chhikaraet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib16); Modarressiet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib21)\)\. Early approaches organize memory as atomic notes or relational structures to support incremental accumulation of knowledge and structured reasoning\(Xuet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib3); Chhikaraet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib16)\)\. Subsequent work explores more expressive representations, including relational triplets, attribute\-enhanced memory, and grounded memory systems that integrate perception and semantic context\(Modarressiet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib21); Salamaet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib9); Ockeret al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib17)\)\. More recent studies further extend memory to graph\-based and temporal structures, enabling global reasoning and cross\-session consistency\(Rasmussenet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib24); Edgeet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib25)\)\. In addition, alternative paradigms propose the storage of intermediate reasoning traces instead of raw text to improve reuse and consistency\(Liuet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib13)\)\. Recent work also introduces more compressed or segmented memory representations to mitigate redundancy and improve retrieval efficiency\(Panet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib23)\)\. Despite these advances, most methods rely on continuous accumulation, which often leads to redundancy and reduced efficiency over long interaction horizons\. To address this limitation, our method introduces a dynamic memory regulation mechanism that explicitly evaluates memory utility and redundancy, enabling adaptive retention of informative content while suppressing unnecessary accumulation\.

### 2\.2Retrieval Augmented and Memory Access Approaches

Retrieval augmented approaches enhance LLM reasoning by dynamically incorporating external knowledge and selectively accessing memory\(Lewiset al\.,[2020](https://arxiv.org/html/2607.22562#bib.bib37); Jianget al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib26); Trivediet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib27); Linet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib29)\)\. Standard retrieval pipelines rely on semantic matching between queries and indexed memory, while more advanced methods introduce iterative retrieval\-generation loops and self\-reflective mechanisms to improve reasoning quality\(Trivediet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib27)\)\. Other approaches focus on optimizing retrieval decisions through uncertainty estimation, joint retriever\-generator training, or document\-level evaluation\(Jianget al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib26); Linet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib29); Tanget al\.,[2026](https://arxiv.org/html/2607.22562#bib.bib30); Yuet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib31)\)\. Iterative reasoning frameworks further improve performance by interleaving retrieval and generation steps to support multi\-hop reasoning\. In addition, recent studies explore rationally aware efficiency mechanisms that dynamically control the depth or necessity of reasoning steps, including skipping redundant computation, compressing intermediate reasoning traces, and adapting reasoning complexity to query difficulty\(Zhanget al\.,[2025a](https://arxiv.org/html/2607.22562#bib.bib38),[2026b](https://arxiv.org/html/2607.22562#bib.bib40),[2026a](https://arxiv.org/html/2607.22562#bib.bib39)\)\. In parallel, memory\-oriented retrieval strategies incorporate time\-decay or usage signals to simulate human\-like recall\(Zhonget al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib6)\)\. However, these methods primarily focus on retrieval accuracy and access strategies, while largely overlooking redundancy control and long\-term memory evolution\. To overcome this limitation, our approach integrates retrieval with adaptive memory filtering and evolution, enabling the model to jointly optimize retrieval relevance and long\-term memory efficiency under a unified control mechanism\.

### 2\.3System Level and Dynamic Memory Management Frameworks

The system level and dynamic memory management frameworks address long\-context limitations through structured architectures and adaptive control mechanisms\(Packeret al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib14); Kanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib7); Meiet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib20)\)\. Early designs introduce virtual memory abstractions and hierarchical storage to manage context constraints\(Packeret al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib14); Kanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib7)\), while later systems incorporate OS\-inspired scheduling and modular agent infrastructures\(Meiet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib20); Liuet al\.,[2024b](https://arxiv.org/html/2607.22562#bib.bib33); Wanget al\.,[2025b](https://arxiv.org/html/2607.22562#bib.bib34)\)\. Other approaches explore controller\-based memory management and cognitive\-inspired consolidation strategies to balance efficiency and retention\(Wanget al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib15); Fanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib8)\)\. More recent work investigates learning\-based memory updates, compression techniques, and reinforcement learning for adaptive memory control\(Panet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib23); Behrouzet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib18); Yuet al\.,[2026](https://arxiv.org/html/2607.22562#bib.bib10)\), further moving towards learnable policies for memory writing and forgetting\. Personalized memory systems further incorporate user\-specific signals into long\-term interactions to improve consistency across sessions\(Liet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib35)\)\. Nevertheless, these frameworks often rely on predefined rules or single optimization signals, limiting their ability to jointly model importance, redundancy, and long\-term utility\. To address this issue, our framework introduces a unified strategic forgetting mechanism that dynamically balances memory retention and removal based on multi\-dimensional utility signals, enabling more robust long\-term memory management\.

## 3Methodology

### 3\.1Framework Philosophy and System Architecture

![Refer to caption](https://arxiv.org/html/2607.22562v1/x1.png)Figure 1:Overview of the proposed SF\-AMS framework\. The system consists of four stages: \(1\) ingestion and perception, where raw conversational inputs are transformed into structured signals; \(2\) value control, where Composite Importance Scoring \(CIS\) evaluates memory salience; \(3\) layered storage, where memories are organized into a hierarchical structure and dynamically updated via survival potential evolution; and \(4\) retrieval and response, where queries are resolved through hybrid retrieval mechanisms combining semantic similarity and fact\-based reasoning\. The entire pipeline forms a closed\-loop memory stream, enabling continuous refinement of the memory state\.The proposed Strategic Forgetting Agent Memory System \(SF\-AMS\) is built on the insight that long\-term adaptability depends on selectively retaining information with high structural utility rather than increasing storage capacity\. Existing LLM\-based memory systems often exhibit a linear accumulation effect, where uncontrolled growth degrades the signal\-to\-noise ratio over long interaction horizons\. To address this, SF\-AMS models memory as a dynamic system in which each unit evolves according to its survival potential\. The framework comprises three components: a perceptual encoding module, a survival\-driven memory store, and a value\-guided controller, which jointly govern retention and eviction under capacity constraints\.

As illustrated in Figure[1](https://arxiv.org/html/2607.22562#S3.F1), SF\-AMS is implemented as a four\-stage pipeline: ingestion and perception, value\-guided control, hierarchical storage, and retrieval\-response integration\. Inputs are encoded into key vectors enriched with salience, redundancy, and temporal signals, which are evaluated using the Composite Importance Scoring \(CIS\) mechanism to estimate structural importance\. The memory module maintains a hierarchical organization \(Core, Important, Secondary, Irrelevant\), where each unit evolves under memory evolution dynamics driven by redundancy penalties, decay, and usage feedback\. During inference, queries are resolved via hybrid retrieval that combines semantic similarity with fact\-aware matching, and the retrieved memory supports response generation, which is re\-integrated to continuously refine the memory structure\.

### 3\.2Problem Formulation and State\-Space Modeling

Memory management is formulated as a discrete\-time state evolution process\. At each time steptt, the system is characterized by a statests\_\{t\}consisting of four components: short\-term contextual inputCtC\_\{t\}, stored memory setMtM\_\{t\}, utility signalsΦt\\Phi\_\{t\}, and task contextTT\. The task contextTTis assumed to remain fixed within an interaction episode, whileCtC\_\{t\},MtM\_\{t\}, andΦt\\Phi\_\{t\}evolve dynamically over time as new information is observed and incorporated into the system\.

The memory set is defined asMt=\{m1,…,mnt\}M\_\{t\}=\\\{m\_\{1\},\\dots,m\_\{n\_\{t\}\}\\\}, where each memory unitmim\_\{i\}represents an interaction, a factual statement, or an extracted information element\. Memory size is constrained by a fixed capacity\|Mt\|≤Nmax\|M\_\{t\}\|\\leq N\_\{\\max\}, and the number of newly inserted memory units at each step is bounded by a small constant determined by the interaction granularity\. To support structured memory evaluation under these constraints, each memory unitmim\_\{i\}is associated with a scalar survival potentialΦ​\(mi\)\\Phi\(m\_\{i\}\), and the collection of these values is denoted asΦt=\{Φ​\(m1\),…,Φ​\(mnt\)\}\\Phi\_\{t\}=\\\{\\Phi\(m\_\{1\}\),\\dots,\\Phi\(m\_\{n\_\{t\}\}\)\\\}\.

The survival potentialΦ​\(mi\)\\Phi\(m\_\{i\}\)reflects the relative utility of each memory unit and is updated dynamically based on factors such as usage frequency, redundancy with existing memories, and temporal decay\. Intuitively, frequently accessed or highly informative memory units tend to accumulate higher survival potential, while redundant or rarely used ones gradually lose importance\. Based on this formulation, SF\-AMS adopts a utility\-driven memory maintenance strategy in whichΦ​\(mi\)\\Phi\(m\_\{i\}\)serves as a unified criterion for both retrieval prioritization and memory pruning under capacity constraints\. This enables the system to maintain a compact yet informative memory state over time without relying on static heuristics or fixed retrieval policies\.

### 3\.3Composite Importance Scoring \(CIS\) and Entity Anchoring

SF\-AMS introduces a Composite Importance Scoring \(CIS\) mechanism that maps heterogeneous memory signals into a unified importance score, which jointly governs retrieval and memory evolution\. The importance score for each memory unitmim\_\{i\}is defined as

I​\(mi\)=Norm​\(α​SLLM​\(mi\)\+\(1−α\)​∑k∈K𝟏k​\(mi\)​wk\),I\(m\_\{i\}\)=\\text\{Norm\}\\Bigl\(\\alpha S\_\{\\text\{LLM\}\}\(m\_\{i\}\)\+\(1\-\\alpha\)\\sum\_\{k\\in K\}\\mathbf\{1\}\_\{k\}\(m\_\{i\}\)w\_\{k\}\\Bigr\),\(1\)whereSLLM​\(mi\)S\_\{\\text\{LLM\}\}\(m\_\{i\}\)is a task\-conditioned salience score,𝟏k​\(mi\)\\mathbf\{1\}\_\{k\}\(m\_\{i\}\)indicates the presence of entity typekk, andwkw\_\{k\}encodes structural priors\. The parameterα∈\[0,1\]\\alpha\\in\[0,1\]balances semantic and entity\-aware signals\.

The normalization operator maps raw importance scoresxix\_\{i\}over the current memory setMtM\_\{t\}into a bounded range:

Norm​\(xi\)=xi−minmj∈Mt⁡xjmaxmj∈Mt⁡xj−minmj∈Mt⁡xj\+ϵ,\\text\{Norm\}\(x\_\{i\}\)=\\frac\{x\_\{i\}\-\\min\_\{m\_\{j\}\\in M\_\{t\}\}x\_\{j\}\}\{\\max\_\{m\_\{j\}\\in M\_\{t\}\}x\_\{j\}\-\\min\_\{m\_\{j\}\\in M\_\{t\}\}x\_\{j\}\+\\epsilon\},\(2\)wherexix\_\{i\}denotes the unnormalized importance score of the memory unitmim\_\{i\}, and the minimum and maximum are computed over all memory units in the current setMtM\_\{t\}\. The small constantϵ\>0\\epsilon\>0ensures numerical stability\. This operation produces normalized scores in\[0,1\]\[0,1\], enabling stable comparison under dynamically evolving memory distributions\. Based onI​\(mi\)I\(m\_\{i\}\), a ranking functionr​\(mi\)=rank​\(I​\(mi\)\)r\(m\_\{i\}\)=\\text\{rank\}\(I\(m\_\{i\}\)\)induces a total ordering overMtM\_\{t\}, which is partitioned into hierarchical layersℒ=\{L1,…,L4\}\\mathcal\{L\}=\\\{L\_\{1\},\\dots,L\_\{4\}\\\}\. This hierarchy directly determines Top\-KKretrieval in Eq\.[5](https://arxiv.org/html/2607.22562#S3.E5)and is also used as a control signal for survival updates, coupling retrieval and long\-term memory persistence under a unified mechanism\.

This ranking structure also enables a formal guarantee on retrieval stability\. When sufficient separation exists between core and distractor memories, CIS induces robust ordering under perturbations\. The following theorem formalizes this condition:

###### Theorem 1\(Hierarchical Retrieval Priority\)\.

Under the structural gap conditionγ\>1\+δ\\gamma\>1\+\\delta, core factual invariants inL1L\_\{1\}are strictly ranked above distractors inL4L\_\{4\}under Eq\.[5](https://arxiv.org/html/2607.22562#S3.E5), ensuring stable Top\-KKretrieval\.

The detailed proof of this theorem is provided in Appendix[A\.1](https://arxiv.org/html/2607.22562#A1.SS1)\. The conditionγ\>1\+δ\\gamma\>1\+\\deltaguarantees that perturbations cannot reverse the CIS\-induced ordering, thereby preserving hierarchical separation throughout memory updates\.

### 3\.4Survival Potential Dynamics and Strategic Forgetting

The survival dynamics in Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3)are controlled by the CIS outputI​\(mi\)I\(m\_\{i\}\), which determines the reinforcement strength in the additive update of the survival potentialΦit\\Phi\_\{i\}^\{t\}\. Accordingly, the evolution of each memory unit is formulated as a discrete\-time state transition:

Φit\+1=max⁡\{0,Φit\+I​\(mi\)⋅Γusaget⋅Ψdiv​\(mi,Mt\)−λ\},\\Phi\_\{i\}^\{t\+1\}=\\max\\\{0,\\Phi\_\{i\}^\{t\}\+I\(m\_\{i\}\)\\cdot\\Gamma\_\{\\text\{usage\}\}^\{t\}\\cdot\\Psi\_\{\\text\{div\}\}\(m\_\{i\},M\_\{t\}\)\-\\lambda\\\},\(3\)whereΦit≥0\\Phi\_\{i\}^\{t\}\\geq 0denotes the survival potential of memory unitmim\_\{i\},I​\(mi\)I\(m\_\{i\}\)is the CIS\-derived importance score \(Eq\.[1](https://arxiv.org/html/2607.22562#S3.E1)\), andλ\>0\\lambda\>0is a global decay coefficient controlling temporal forgetting\. The binary usage indicatorΓusaget\\Gamma\_\{\\text\{usage\}\}^\{t\}and diversity modulationΨdiv​\(mi,Mt\)\\Psi\_\{\\text\{div\}\}\(m\_\{i\},M\_\{t\}\)jointly act as gating factors for reinforcement\.

The diversity modulation is defined as:

Ψdiv=1\+αdiv​tanh⁡\(β​\(τ−Sim​\(mi,Mt\)\)\),\\Psi\_\{\\text\{div\}\}=1\+\\alpha\_\{\\text\{div\}\}\\tanh\\big\(\\beta\(\\tau\-\\text\{Sim\}\(m\_\{i\},M\_\{t\}\)\)\\big\),\(4\)whereSim​\(mi,Mt\)∈\[0,1\]\\text\{Sim\}\(m\_\{i\},M\_\{t\}\)\\in\[0,1\]measures the maximum semantic similarity betweenmim\_\{i\}and elements inMtM\_\{t\},αdiv∈\(0,1\)\\alpha\_\{\\text\{div\}\}\\in\(0,1\)controls the modulation strength,τ∈\[0,1\]\\tau\\in\[0,1\]defines the similarity threshold, andβ\>0\\beta\>0controls the transition sharpness\. This formulation adaptively modulates reinforcement based on semantic redundancy: highly similar memories are down\-weighted, while less similar or novel memories are amplified through a smooth gating effect\.

To ensure long\-term stability, it is necessary to characterize the global behavior induced by Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3), since uncontrolled reinforcement may otherwise lead to divergence\. The multiplicative structure in Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3)acts as a gated update mechanism where reinforcement is activated only when importance, usage, and diversity jointly contribute, while the decay termλ\\lambdaenforces contraction\.

###### Proposition 1\(Boundedness and Stability\)\.

Under the memory dynamics defined in Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3), and assuming bounded reinforcement and capacity\-constrained updates, the aggregate survival potentialV​\(Xt\)V\(X\_\{t\}\)remains uniformly bounded over time\.

The detailed proof of this proposition is provided in Appendix[A\.2](https://arxiv.org/html/2607.22562#A1.SS2)\. This result implies that the memory system evolves within a stable regime where reinforcement and decay remain balanced over time, preventing both uncontrolled growth and collapse of memory states\. In particular, it ensures that the CIS\-driven reinforcement mechanism does not induce divergence even under repeated reinforcement of high importance memory units\.

### 3\.5Hierarchical Multi\-Source Retrieval Pipeline

The survival potentialΦit\\Phi\_\{i\}^\{t\}is incorporated into the retrieval stage as a ranking prior that biases memory selection toward long\-term high\-utility units\. Memory retrieval follows a hierarchical multi\-source pipeline that combines coarse\-to\-fine matching to improve both efficiency and precision\. Given a queryqq, structural parsing first extracts keywords, entities, and temporal expressions, along with optional query variants𝒬v​a​r\\mathcal\{Q\}\_\{var\}to reduce lexical mismatch\. Retrieval is then performed in a staged manner across multiple memory levels\.

For a candidate sessionSjS\_\{j\}, defined as a temporally contiguous sequence of memory units, relevance is computed as:

Ssession​\(q,Sj\)=simsem​\(q,Sj\)\+αkw⋅simkw​\(q,Sj\),S\_\{\\text\{session\}\}\(q,S\_\{j\}\)=\\text\{sim\}\_\{\\text\{sem\}\}\(q,S\_\{j\}\)\+\\alpha\_\{\\text\{kw\}\}\\cdot\\text\{sim\}\_\{\\text\{kw\}\}\(q,S\_\{j\}\),\(5\)wheresimsem\\text\{sim\}\_\{\\text\{sem\}\}measures embedding\-based semantic similarity,simkw\\text\{sim\}\_\{\\text\{kw\}\}evaluates keyword overlap, andαkw\\alpha\_\{\\text\{kw\}\}balances the two signals\. Sessions exceeding a threshold are further expanded into fine\-grained memory\-level ranking, where lexical, semantic, temporal, and entity\-aware signals are jointly integrated to compute relevance scores\. This produces the final retrieved setMt∗M\_\{t\}^\{\*\}, defined as the ordered and deduplicated collection of selected memory units at timett\. The retrieved setMt∗M\_\{t\}^\{\*\}is then fed back into the memory system by marking all selected memory units as accessed, which directly updates the usage indicatorΓusaget\\Gamma\_\{\\text\{usage\}\}^\{t\}in Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3)\. This establishes a closed feedback loop in which retrieval decisions influence future survival dynamics, as frequently accessed memories receive higher reinforcement through repeated updates of the survival potential\.

## 4Experiments

### 4\.1Experimental Setup

Datasets\.The proposed framework is evaluated on two representative benchmarks: LoCoMo\(Maharanaet al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib11)\)and LongMemEval\-s\(Wuet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib12)\)\. LoCoMo contains long\-context conversational data with an average of 300 turns and 9K tokens per dialogue, enabling evaluation across single\-hop, multi\-hop, temporal, and open\-domain reasoning\. LongMemEval\-s provides a large\-scale benchmark with 14K sessions and 146K turns, focusing on information extraction and cross\-session knowledge updates\.

Evaluation Metrics\.Performance is evaluated using benchmark\-specific metrics\. For LoCoMo, we report F1 and BLEU\-1\(Papineniet al\.,[2002](https://arxiv.org/html/2607.22562#bib.bib22)\)to measure semantic and lexical matching quality\. For LongMemEval\-s, Accuracy \(ACC\) is used to assess structured knowledge extraction\. System efficiency is additionally measured in terms of token usage, API overhead, and runtime\.

Baselines\.SF\-AMS is compared against representative memory\-augmented systems, including TiM\(Liuet al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib13)\), MemoryBank\(Zhonget al\.,[2024](https://arxiv.org/html/2607.22562#bib.bib6)\), MemGPT\(Packeret al\.,[2023](https://arxiv.org/html/2607.22562#bib.bib14)\), A\-Mem\(Xuet al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib3)\), MemoryOS\(Kanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib7)\), and LightMem\(Fanget al\.,[2025](https://arxiv.org/html/2607.22562#bib.bib8)\)\. These methods cover a range of strategies such as trace\-based retrieval, temporal decay modeling, OS\-inspired memory management, adaptive memory structuring, and memory compression\.

### 4\.2Implementation Details

The memory system maintains a fixed capacity ofNmax=300N\_\{\\max\}=300, enforcing a bounded memory budget\. For retrieval, the 7 most recent interaction\-derived memory notes are prioritized, while the remaining entries are stored in the global memory setℳ\\mathcal\{M\}\. Each memory unit is encoded using the all\-MiniLM\-L6\-v2 encoder, with cosine similarity adopted for semantic matching\. During inference, the top\-kk\(k=10k=10\) most relevant memory units are selected using the hybrid scoring function in Eq\.[5](https://arxiv.org/html/2607.22562#S3.E5), which combines semantic similarity and keyword matching via a fixed coefficientαkw\\alpha\_\{\\text\{kw\}\}\. Memory importance is computed using the Composite Importance Scoring \(CIS\) in Eq\.[1](https://arxiv.org/html/2607.22562#S3.E1), while survival potential and redundancy modulation follow Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3)and Eq\.[4](https://arxiv.org/html/2607.22562#S3.E4), respectively\. All scoring components are normalized or inherently bounded, helping maintain stable reinforcement dynamics throughout the update process\.

### 4\.3Main Results

Table 1:Performance comparison on the LoCoMo benchmark using F1 and BLEU\-1 metrics\. Our method achieves strong and consistent improvements across most reasoning types and both backbone models, particularly in single\-hop, open\-domain, and temporal tasks, demonstrating robust cross\-backbone generalization\. The best results are shown in bold, and the second\-best results are underlined\.The results in Table[1](https://arxiv.org/html/2607.22562#S4.T1)show that our method achieves the most pronounced improvements in structurally challenging scenarios, rather than uniform gains across all settings\. These results indicate that the proposed mechanism is particularly effective when reasoning requires resolving long\-range dependencies and filtering noisy context\.

Under the GPT\-4o\-mini backbone, the largest gain is observed in Temporal reasoning, where our method achieves 45\.84 F1, surpassing the strongest baseline \(LightMem\) by \+6\.91 F1\. It also improves Single\-Hop performance to 40\.21 F1, exceeding the best baseline by \+4\.94 F1\. Under the Qwen2\.5\-7B backbone, the most significant improvement appears in Multi\-Hop reasoning, reaching 37\.59 F1 and outperforming the strongest baseline by \+9\.65 F1\. Additionally, Open\-Domain performance improves to 32\.76 F1, with a gain of \+6\.53 F1\. These results show consistent generalization across different backbones, particularly in scenarios requiring accurate memory selection\.

These improvements can be attributed to the structure\-aware ranking induced by the Composite Importance Scoring \(CIS\) mechanism\. By jointly modeling semantic relevance and entity\-level signals, the method forms a more separable memory hierarchy that reduces retrieval interference\. This behavior aligns with Theorem[1](https://arxiv.org/html/2607.22562#Thmtheorem1), which guarantees that structurally important memories are consistently ranked above distractors, thereby improving retrieval reliability in complex reasoning scenarios\.

### 4\.4Ablation Study

Table 2:Ablation study on the LoCoMo dataset using the Qwen2\.5\-7B backbone\. Results show that all proposed components contribute significantly to overall performance, with Semantic Salience and Entity Anchoring being the most critical modules\. The best results are shown in bold, and the second\-best results are underlined\.![Refer to caption](https://arxiv.org/html/2607.22562v1/x2.png)Figure 2:Ablation results across four reasoning categories on the LoCoMo dataset\. The figure shows the F1 score degradation of each ablated variant relative to the full SF\-AMS model, demonstrating the contribution of each module across different reasoning types\.To evaluate the contribution of each component, an ablation study is conducted by systematically removing key modules from SF\-AMS, including semantic salience scoring, entity anchoring, strategic forgetting, and the full memory system\. Results are reported in Table[2](https://arxiv.org/html/2607.22562#S4.T2)and Figure[2](https://arxiv.org/html/2607.22562#S4.F2)\. Removing the entire memory system leads to the most severe degradation, particularly in temporal reasoning, where performance drops by 23\.97 F1, confirming that a structured memory state is essential for modeling long\-range dependencies\.

At the component level, different modules exhibit complementary effects across reasoning types\. Removing entity anchoring reduces multi\-hop performance by 24\.09 F1 and temporal performance by 13\.04 F1, indicating the importance of explicit structural signals for cross\-step dependency tracking\. In contrast, removing semantic salience causes the largest drop in open\-domain reasoning, with a decrease of 22\.16 F1, highlighting the role of LLM\-based scoring in handling unstructured queries\. Furthermore, disabling strategic forgetting leads to consistent degradation across all categories, with reductions of 10\.59 F1 in single\-hop, 18\.81 F1 in multi\-hop, 18\.70 F1 in open\-domain, and 14\.08 F1 in temporal reasoning\. Overall, these results demonstrate that the proposed components contribute complementary functionalities, and their integration is necessary for stable and strong performance\.

### 4\.5Efficiency Analysis

Table 3:Unified performance and efficiency comparison on the LongMemEval\-s benchmark\. We report token\-level memory cost together with system\-level efficiency and accuracy\. The best results are shown in bold, and the second\-best results are underlined\.The efficiency results on the LongMemEval\-s benchmark are summarized in Table[3](https://arxiv.org/html/2607.22562#S4.T3)\. SF\-AMS achieves the highest accuracy of 68\.52%, improving over the strongest baseline A\-MEM by \+3\.32 ACC\. At the same time, it significantly reduces LLM calls, achieving relative reductions of 46\.7% compared to LangMem and 73\.3% compared to A\-MEM\. These results indicate that SF\-AMS improves reasoning performance while substantially lowering interaction overhead\.

This improvement comes with moderate increases in system cost\. SF\-AMS incurs higher runtime than lightweight baselines such as Mem0 \(2239\.94 s\) and LangMem \(3237\.16 s\), reaching 4323\.39 s, but remains substantially more efficient than heavier systems such as A\-MEM \(5367\.51 s\)\. In terms of token consumption, SF\-AMS requires 1755\.27k tokens, which is higher than Mem0 and LangMem but still comparable to existing memory\-based methods\. These results suggest that SF\-AMS achieves improved reasoning performance without incurring excessive overhead\. By prioritizing high\-utility memory units and reducing redundant LLM interactions, the framework strikes a practical balance between accuracy and system efficiency\.

### 4\.6Memory Distribution Analysis

Table 4:Distribution of memory instances across different importance levels and their corresponding forgetting ratios\.To examine how the strategic forgetting mechanism shapes memory organization, the distribution across hierarchical importance levels is analyzed\. As shown in Table[4](https://arxiv.org/html/2607.22562#S4.T4), the resulting pattern is highly skewed: only 10\.62% of memory units belong to the Core layer, yet they retain the highest average importance \(0\.930\)\. This indicates that the Composite Importance Scoring \(CIS\) effectively identifies a compact set of stable reasoning anchors rather than distributing importance uniformly across the memory space\. All statistics are aggregated over the full interaction trajectory, while the memory capacity is constrained byNmax=300N\_\{\\max\}=300in the main experiments\.

A clear tiered forgetting pattern emerges from the dynamics\. Core memories are rarely discarded, whereas Irrelevant memories are aggressively removed, with a forgetting ratio of 64\.74%\. The Secondary layer \(49\.22% of memory\) undergoes moderate decay \(39\.83%\), functioning as a transitional buffer between stable knowledge and transient context\. As illustrated in Figure[3](https://arxiv.org/html/2607.22562#S4.F3), factual invariants are consistently preserved in higher layers, while redundant or low\-signal dialogue turns are gradually discarded\. This hierarchical organization enables SF\-AMS to maintain a compact yet informative memory state with an improved signal\-to\-noise ratio\.

![Refer to caption](https://arxiv.org/html/2607.22562v1/x3.png)Figure 3:Visualizing the hierarchical memory distillation process in SF\-AMS\. We showcase one representative QA trace for each of the four levels: Core, Important, Secondary, and Irrelevant\.

## 5Conclusions

This paper presents SF\-AMS, a structured memory framework for long\-term memory management in LLM agents\. The proposed system combines composite importance scoring with survival\-driven dynamics to enable selective retention and strategic forgetting, allowing memory to evolve in a controlled and adaptive manner\. Experiments on LoCoMo and LongMemEval\-s show that SF\-AMS achieves consistent improvements in long\-horizon reasoning while maintaining practical system efficiency\. Compared to existing memory\-augmented methods, the framework improves performance across multiple reasoning settings and reduces redundant LLM interactions through utility\-aware memory regulation\. These findings suggest that structured memory organization with importance\-aware selection provides an effective balance between reasoning capability and long\-term memory efficiency\.

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## Appendix AFormal Theoretical Proofs

This appendix presents the formal analytical derivation of the theoretical claims introduced in the main text\. The proofs are structured to ensure completeness and self\-consistency, adhering to the rigorous evaluation standards for agentic memory dynamics\.

### A\.1Proof of Theorem 1: Hierarchical Retrieval Priority

###### Theorem 1\(Restatement of Theorem[1](https://arxiv.org/html/2607.22562#Thmtheorem1)\)\.

Under the structural gap conditionγ\>1\+δ\\gamma\>1\+\\delta, core factual invariants inL1L\_\{1\}are strictly ranked above distractors inL4L\_\{4\}under Eq\.[5](https://arxiv.org/html/2607.22562#S3.E5), ensuring stable Top\-KKretrieval\.

#### Intuition\.

The core idea is that the hierarchical weighting system creates a "score buffer" that is sufficiently large to counteract any semantic noise \(similarities that happen to be high for irrelevant information\)\.

Letmc​o​r​e∈L1m\_\{core\}\\in L\_\{1\}be a factual invariant andmn​o​i​s​e∈L4m\_\{noise\}\\in L\_\{4\}be a semantic distractor\. The retrieval scoring function defined in Section 3\.5 is:

R​\(m,q\)=ω​\(L\)⋅sim​\(vm,vq\)\.R\(m,q\)=\\omega\(L\)\\cdot\\text\{sim\}\(v\_\{m\},v\_\{q\}\)\.\(6\)
Consider the score ratio between the core memory and the noise:

ρ=R​\(mc​o​r​e,q\)R​\(mn​o​i​s​e,q\)=ω​\(L1\)ω​\(L4\)⋅sim​\(vc​o​r​e,vq\)sim​\(vn​o​i​s​e,vq\)\.\\rho=\\frac\{R\(m\_\{core\},q\)\}\{R\(m\_\{noise\},q\)\}=\\frac\{\\omega\(L\_\{1\}\)\}\{\\omega\(L\_\{4\}\)\}\\cdot\\frac\{\\text\{sim\}\(v\_\{core\},v\_\{q\}\)\}\{\\text\{sim\}\(v\_\{noise\},v\_\{q\}\)\}\.\(7\)
FromAssumption A \(Structural Gap\), we haveω​\(L1\)ω​\(L4\)≥γ\\frac\{\\omega\(L\_\{1\}\)\}\{\\omega\(L\_\{4\}\)\}\\geq\\gamma\. From ourNoise\-Boundedassumption, we know that the similarity of noise is bounded by a factor of\(1\+δ\)\(1\+\\delta\)relative to the core fact, i\.e\.,sim​\(vc​o​r​e,vq\)sim​\(vn​o​i​s​e,vq\)≥11\+δ\\frac\{\\text\{sim\}\(v\_\{core\},v\_\{q\}\)\}\{\\text\{sim\}\(v\_\{noise\},v\_\{q\}\)\}\\geq\\frac\{1\}\{1\+\\delta\}\. Substituting these into the ratio:

ρ≥γ1\+δ\.\\rho\\geq\\frac\{\\gamma\}\{1\+\\delta\}\.\(8\)
If the system hyper\-parameters are tuned such thatγ\>1\+δ\\gamma\>1\+\\delta, thenρ\>1\\rho\>1, which impliesR​\(mc​o​r​e,q\)\>R​\(mn​o​i​s​e,q\)R\(m\_\{core\},q\)\>R\(m\_\{noise\},q\)\. Since SF\-AMS employs a Top\-KKretrieval strategy over the combined candidate set,mc​o​r​em\_\{core\}will always be strictly higher thanmn​o​i​s​em\_\{noise\}in the ranking queue\. This ensures that core invariants are never displaced by noise distractors of high\-similarity in the context window\.

### A\.2Proof of Proposition 1: Stability of Memory Dynamics

###### Theorem 1\(Restatement of Proposition[1](https://arxiv.org/html/2607.22562#Thmproposition1)\)\.

Under the memory dynamics defined in Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3), and assuming bounded reinforcement and capacity\-constrained updates, the aggregate survival potentialV​\(Xt\)V\(X\_\{t\}\)remains uniformly bounded over time\.

#### State Definition\.

At timett, the system state is defined asXt=\(Mt,Φt\)X\_\{t\}=\(M\_\{t\},\\Phi\_\{t\}\), whereMtM\_\{t\}denotes the set of active memory units with\|Mt\|≤Nmax\|M\_\{t\}\|\\leq N\_\{\\max\}, andΦt=\{Φit\}i∈Mt\\Phi\_\{t\}=\\\{\\Phi\_\{i\}^\{t\}\\\}\_\{i\\in M\_\{t\}\}represents their survival potentials\. By construction,Φit≥0\\Phi\_\{i\}^\{t\}\\geq 0for alli,ti,t\.

#### Bounded Reinforcement\.

The reinforcement term is defined as

Rit=I​\(mi\)⋅Γusaget⋅Ψdiv​\(mi,Mt\)\.R\_\{i\}^\{t\}=I\(m\_\{i\}\)\\cdot\\Gamma\_\{\\text\{usage\}\}^\{t\}\\cdot\\Psi\_\{\\text\{div\}\}\(m\_\{i\},M\_\{t\}\)\.\(9\)SinceI​\(mi\)∈\[0,1\]I\(m\_\{i\}\)\\in\[0,1\],Γusaget∈\{0,1\}\\Gamma\_\{\\text\{usage\}\}^\{t\}\\in\\\{0,1\\\}, andΨdiv∈\[1−αdiv,1\+αdiv\]\\Psi\_\{\\text\{div\}\}\\in\[1\-\\alpha\_\{\\text\{div\}\},1\+\\alpha\_\{\\text\{div\}\}\], it follows that there exists a constantRmax\>0R\_\{\\max\}\>0such that

0≤Rit≤Rmax,∀i,t\.0\\leq R\_\{i\}^\{t\}\\leq R\_\{\\max\},\\quad\\forall i,t\.\(10\)

#### Single\-Step Dynamics\.

From the update rule,

Φit\+1=max⁡\{0,Φit\+Rit−λ\},\\Phi\_\{i\}^\{t\+1\}=\\max\\\{0,\\Phi\_\{i\}^\{t\}\+R\_\{i\}^\{t\}\-\\lambda\\\},\(11\)we obtain the upper bound

Φit\+1≤Φit\+Rmax\.\\Phi\_\{i\}^\{t\+1\}\\leq\\Phi\_\{i\}^\{t\}\+R\_\{\\max\}\.\(12\)Thus, the per\-step growth of each memory unit is bounded\.

#### Selective Persistence\.

The update dynamics induce a natural separation between memory units:

- •If𝔼​\[Rit\]\>λ\\mathbb\{E\}\[R\_\{i\}^\{t\}\]\>\\lambda, the unit can sustain or increase its survival potential and remain active\.
- •If𝔼​\[Rit\]<λ\\mathbb\{E\}\[R\_\{i\}^\{t\}\]<\\lambda, the unit undergoes decay and will eventually be removed\.

This mechanism ensures that high\-value memory units persist, while low\-value or redundant ones are gradually eliminated\.

#### Capacity\-Constrained Dynamics\.

The system enforces a hard constraint\|Mt\|≤Nmax\|M\_\{t\}\|\\leq N\_\{\\max\}\. When capacity is reached, insertion of new memory units triggers eviction of the unit with the smallest survival potential:

i∗=arg⁡minj∈Mt∪\{mnew\}⁡Φj\.i^\{\*\}=\\arg\\min\_\{j\\in M\_\{t\}\\cup\\\{m\_\{\\text\{new\}\}\\\}\}\\Phi\_\{j\}\.\(13\)This truncation prevents unbounded accumulation of memory units\.

#### Bounded Aggregate Potential\.

Define the Lyapunov function:

V​\(Xt\)=∑i∈MtΦit\.V\(X\_\{t\}\)=\\sum\_\{i\\in M\_\{t\}\}\\Phi\_\{i\}^\{t\}\.\(14\)Since\|Mt\|≤Nmax\|M\_\{t\}\|\\leq N\_\{\\max\}, we have

V​\(Xt\)≤Nmax⋅maxi∈Mt⁡Φit\.V\(X\_\{t\}\)\\leq N\_\{\\max\}\\cdot\\max\_\{i\\in M\_\{t\}\}\\Phi\_\{i\}^\{t\}\.\(15\)
Although individual survival potentials may increase when reinforcement exceeds decay, no unit can grow without bound while remaining in the system\. In particular, any unit with persistently increasing potential must continuously compete with newly inserted memory units\. Due to the eviction mechanism, low\-utility units are removed and excessively dominant states do not accumulate indefinitely across the memory set\.

Moreover, in practical implementations, the numerical representation ofΦit\\Phi\_\{i\}^\{t\}is inherently bounded due to finite precision and system constraints, which further prevents unbounded growth in real\-world deployments\. From a theoretical perspective, the continual competition induced by insertion and eviction ensures that no single unit can indefinitely dominate the memory pool\.

Therefore, the aggregate potentialV​\(Xt\)V\(X\_\{t\}\)remains bounded over time\.

#### Conclusion\.

The memory system operates in a stable regime where the number of active memory units is bounded and the aggregate survival potential does not diverge\. Stability arises from the combined effects of bounded reinforcement, selective persistence, and capacity\-constrained eviction, without requiring decay to dominate reinforcement\.

In this sense, the system is stable in that its state remains confined within a bounded region over time\.

## Appendix BAdditional Experiments and Analysis

### B\.1Empirical Validation of Dynamics Equilibrium

This section provides empirical evidence to support the stability claims and the Foster\-Lyapunov drift condition outlined in Proposition 2\. The evolution of the memory state over a 100\-step horizon is detailed in Table[5](https://arxiv.org/html/2607.22562#A2.T5)\.We vary a normalized forgetting control parameter, denoted asRatio, which scales the decay intensity in Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3)\. Specifically, the effective decay is implemented asλ′=Ratio⋅λ\\lambda^\{\\prime\}=\\textit\{Ratio\}\\cdot\\lambda\.

Table 5:Dynamics of memory population and survival potentialΦ\\Phiacross hierarchical layers \(L1L\_\{1\}–L4L\_\{4\}\) under varying ratio settings\. Here,Ratiodenotes the normalized forgetting strength, implemented as a scaling factor applied to the global decay coefficient \(Eq\.[3](https://arxiv.org/html/2607.22562#S3.E3)\)\. Higher values correspond to more aggressive decay, which progressively shifts memory mass toward lower\-priority layers while suppressing high\-energy states\.As illustrated by the survival potentialΦ\\Phitrajectories \(Table[5](https://arxiv.org/html/2607.22562#A2.T5)and Figure[5](https://arxiv.org/html/2607.22562#A2.F5)\), the system undergoes a rapid decay toward a low\-energy regime during the initial interaction phase\. This numerical trend offers two critical insights:

- •Transition to a “Ready\-to\-Evict” State:The convergence ofΦ\\Phitoward a near\-zero baseline in the later stages does not indicate information loss\. Instead, it signifies that the memory has entered a stable, low\-energy state\. By maintaining this equilibrium, SF\-AMS intentionally maximizes the “survival space” for high\-entropy novel information, ensuring the memory remains receptive without breaching capacity limits\.
- •Mechanism of Efficiency Gains:This energy stratification provides the physical basis for the 10×\\timesspeedup observed in our main results\. With a clear potential gap established \(ΦL1≫ΦL4\\Phi\_\{L\_\{1\}\}\\gg\\Phi\_\{L\_\{4\}\}\), the retrieval module can near\-instantaneously bypass low\-energy noise\. This allows computational resources to be focused exclusively on the core skeletal memory, significantly reducing the search space compared to unstructured baselines\.

![Refer to caption](https://arxiv.org/html/2607.22562v1/x4.png)Figure 4:Evolution of memory layer populations\. The system reaches a dynamic equilibrium where core facts are preserved while redundant noise is cyclically purged\.
![Refer to caption](https://arxiv.org/html/2607.22562v1/x5.png)Figure 5:Mean survival potentialΦ\\Phiacross different layers\. The rapid initial decay followed by a stabilized gap confirms the effectiveness of the decay\-driven forgetting mechanism\.

### B\.2Memory Capacity Stress Test

![Refer to caption](https://arxiv.org/html/2607.22562v1/x6.png)Figure 6:Performance under varying global memory capacityNmaxN\_\{\\max\}\. SF\-AMS consistently outperforms LRU, FIFO, and RANDOM baselines across all settings and exhibits strong robustness under low\-capacity conditions\.To evaluate robustness under extreme resource constraints, we vary the maximum capacityNmax∈\{20,60,120,240\}N\_\{\\max\}\\in\\\{20,60,120,240\\\}\. This directly tests the operational limits of the system under different memory budgets\.

As shown in Figure[6](https://arxiv.org/html/2607.22562#A2.F6), while all methods benefit from increased memory budgets, heuristic baselines like FIFO and LRU exhibit irregular scaling and diminishing returns\. In contrast, SF\-AMS maintains the highest F1 scores across all capacity levels, achieving a notable 9\.67 F1 even under the most restrictive setting \(N=20N=20\)\. This monotonic improvement trend suggests that our priority\-driven retention is more efficient at utilizing marginal increases in memory than simple recency or random\-based strategies\.

Table 6:Performance under different types of retrieval distractors\. SF\-AMS consistently outperforms the vanilla baseline across all categories, demonstrating strong robustness to noise\.![Refer to caption](https://arxiv.org/html/2607.22562v1/x7.png)Figure 7:Sensitivity of retrieval performance with respect toγ\\gamma\. The model shows stable performance across a wide range ofγ\\gamma, indicating low hyperparameter sensitivity\.To assess retrieval stability under noisy conditions, we introduce naturally occurring “hard negatives” from the LoCoMo dataset—distractors that share high semantic similarity with the query but differ in factual or temporal correctness\.

The results in Table[6](https://arxiv.org/html/2607.22562#A2.T6)indicate that vanilla dense retrieval is highly susceptible to temporal and event confusions, often selecting misleading but high\-similarity memories\. Conversely, SF\-AMS achieves a significant accuracy boost \(86\.67% Acc@1\) and maintains a positive ranking margin \(0\.1264\)\. This robustness stems from the combination of keyword\-level anchoring and memory prioritization, which effectively filters out distractors that lack structural importance\. Furthermore, Figure[7](https://arxiv.org/html/2607.22562#A2.F7)demonstrates that the system remains stable across the hierarchical weightγ\\gammarange, with improved separation as the structural signals are prioritized\.

## Appendix CPrompt Templates and Examples

### C\.1Generate System Response System Prompt

![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x8.png)
### C\.2Generate System Response User Prompt

![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x9.png)
### C\.3Evaluate Memory Importance

![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x10.png)
### C\.4Examples of Q/A with SF\-AMS

![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x11.png)![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x12.png)![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x13.png)![[Uncaptioned image]](https://arxiv.org/html/2607.22562v1/x14.png)

## NeurIPS Paper Checklist

The checklist is designed to encourage best practices for responsible machine learning research, addressing issues of reproducibility, transparency, research ethics, and societal impact\. Do not remove the checklist:The papers not including the checklist will be desk rejected\.The checklist should follow the references and follow the \(optional\) supplemental material\. The checklist does NOT count towards the page limit\.

Please read the checklist guidelines carefully for information on how to answer these questions\. For each question in the checklist:

- •You should answer\[Yes\],\[No\], or\[N/A\]\.
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The checklist answers are an integral part of your paper submission\.They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers\. You will also be asked to include it \(after eventual revisions\) with the final version of your paper, and its final version will be published with the paper\.

The reviewers of your paper will be asked to use the checklist as one of the factors in their evaluation\. While\[Yes\]is generally preferable to\[No\], it is perfectly acceptable to answer\[No\]provided a proper justification is given \(e\.g\., error bars are not reported because it would be too computationally expensive” or “we were unable to find the license for the dataset we used”\)\. In general, answering\[No\]or\[N/A\]is not grounds for rejection\. While the questions are phrased in a binary way, we acknowledge that the true answer is often more nuanced, so please just use your best judgment and write a justification to elaborate\. All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix\. If you answer\[Yes\]to a question, in the justification please point to the section\(s\) where related material for the question can be found\.

IMPORTANT, please:

- •Delete this instruction block, but keep the section heading “NeurIPS Paper Checklist",
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1. 1\.Claims
2. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
3. Answer:\[Yes\]
4. Justification: The abstract and introduction accurately reflect the main contributions, including the utility driven memory mechanism, hierarchical structure, and improvements in long\-context reasoning\. These claims are supported by experiments on LoCoMo and LongMemEval\-s and align with the theoretical analysis, without overgeneralization\.
5. Guidelines: - •The answer\[N/A\]means that the abstract and introduction do not include the claims made in the paper\. - •The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations\. A\[No\]or\[N/A\]answer to this question will not be perceived well by the reviewers\. - •The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings\. - •It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper\.
6. 2\.Limitations
7. Question: Does the paper discuss the limitations of the work performed by the authors?
8. Answer:\[No\]
9. Justification: This paper does not include a dedicated limitations section\.
10. Guidelines: - •The answer\[N/A\]means that the paper has no limitation while the answer\[No\]means that the paper has limitations, but those are not discussed in the paper\. - •The authors are encouraged to create a separate “Limitations” section in their paper\. - •The paper should point out any strong assumptions and how robust the results are to violations of these assumptions \(e\.g\., independence assumptions, noiseless settings, model well\-specification, asymptotic approximations only holding locally\)\. The authors should reflect on how these assumptions might be violated in practice and what the implications would be\. - •The authors should reflect on the scope of the claims made, e\.g\., if the approach was only tested on a few datasets or with a few runs\. In general, empirical results often depend on implicit assumptions, which should be articulated\. - •The authors should reflect on the factors that influence the performance of the approach\. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting\. Or a speech\-to\-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon\. - •The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size\. - •If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness\. - •While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren’t acknowledged in the paper\. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community\. Reviewers will be specifically instructed to not penalize honesty concerning limitations\.
11. 3\.Theory assumptions and proofs
12. Question: For each theoretical result, does the paper provide the full set of assumptions and a complete \(and correct\) proof?
13. Answer:\[Yes\]
14. Justification:
15. Justification: All theoretical results are accompanied by clearly stated assumptions\. Formal statements are presented in the main text, and complete proofs are provided in the appendix, including the proof of Theorem[1](https://arxiv.org/html/2607.22562#Thmtheorem1)in Appendix[A\.1](https://arxiv.org/html/2607.22562#A1.SS1)and the proof of Proposition[1](https://arxiv.org/html/2607.22562#Thmproposition1)in Appendix[A\.2](https://arxiv.org/html/2607.22562#A1.SS2)\.
16. Guidelines: - •The answer\[N/A\]means that the paper does not include theoretical results\. - •All the theorems, formulas, and proofs in the paper should be numbered and cross\-referenced\. - •All assumptions should be clearly stated or referenced in the statement of any theorems\. - •The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition\. - •Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material\. - •Theorems and Lemmas that the proof relies upon should be properly referenced\.
17. 4\.Experimental result reproducibility
18. Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper \(regardless of whether the code and data are provided or not\)?
19. Answer:\[Yes\]
20. Justification: Section[4\.1](https://arxiv.org/html/2607.22562#S4.SS1)and Section[4\.2](https://arxiv.org/html/2607.22562#S4.SS2)describe the experimental setup and implementation details\. Appendix[C](https://arxiv.org/html/2607.22562#A3)provides key prompts, enabling end\-to\-end replication of the main results\.
21. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •If the paper includes experiments, a\[No\]answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not\. - •If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable\. - •Depending on the contribution, reproducibility can be accomplished in various ways\. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model\. In general\. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model \(e\.g\., in the case of a large language model\), releasing of a model checkpoint, or other means that are appropriate to the research performed\. - •While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution\. For example 1. \(a\)If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm\. 2. \(b\)If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully\. 3. \(c\)If the contribution is a new model \(e\.g\., a large language model\), then there should either be a way to access this model for reproducing the results or a way to reproduce the model \(e\.g\., with an open\-source dataset or instructions for how to construct the dataset\)\. 4. \(d\)We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility\. In the case of closed\-source models, it may be that access to the model is limited in some way \(e\.g\., to registered users\), but it should be possible for other researchers to have some path to reproducing or verifying the results\.
22. 5\.Open access to data and code
23. Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
24. Answer:\[No\]
25. Justification: Public datasets are properly cited, but the code is not publicly available at submission time to preserve double\-blind review\. We plan to release the code upon acceptance\.
26. Guidelines: - •The answer\[N/A\]means that paper does not include experiments requiring code\. - • - •While we encourage the release of code and data, we understand that this might not be possible, so\[No\]is an acceptable answer\. Papers cannot be rejected simply for not including code, unless this is central to the contribution \(e\.g\., for a new open\-source benchmark\)\. - •The instructions should contain the exact command and environment needed to run to reproduce the results\. See the NeurIPS code and data submission guidelines \([https://neurips\.cc/public/guides/CodeSubmissionPolicy](https://neurips.cc/public/guides/CodeSubmissionPolicy)\) for more details\. - •The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc\. - •The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines\. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why\. - •At submission time, to preserve anonymity, the authors should release anonymized versions \(if applicable\)\. - •Providing as much information as possible in supplemental material \(appended to the paper\) is recommended, but including URLs to data and code is permitted\.
27. 6\.Experimental setting/details
28. Question: Does the paper specify all the training and test details \(e\.g\., data splits, hyperparameters, how they were chosen, type of optimizer\) necessary to understand the results?
29. Answer:\[Yes\]
30. Justification:
31. Justification: Section[4\.1](https://arxiv.org/html/2607.22562#S4.SS1)and Section[4\.2](https://arxiv.org/html/2607.22562#S4.SS2)describe the experimental setup and implementation details\. Key prompts are provided in Appendix[C](https://arxiv.org/html/2607.22562#A3), enabling reproduction of the main results\.
32. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them\. - •The full details can be provided either with the code, in appendix, or as supplemental material\.
33. 7\.Experiment statistical significance
34. Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
35. Answer:\[No\]
36. Justification: The experiments rely on API\-based large language models, and multiple inference calls introduce non\-trivial computational cost\.
37. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The authors should answer\[Yes\]if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper\. - •The factors of variability that the error bars are capturing should be clearly stated \(for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions\)\. - •The method for calculating the error bars should be explained \(closed form formula, call to a library function, bootstrap, etc\.\) - •The assumptions made should be given \(e\.g\., Normally distributed errors\)\. - •It should be clear whether the error bar is the standard deviation or the standard error of the mean\. - •It is OK to report 1\-sigma error bars, but one should state it\. The authors should preferably report a 2\-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified\. - •For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range \(e\.g\., negative error rates\)\. - •If error bars are reported in tables or plots, the authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text\.
38. 8\.Experiments compute resources
39. Question: For each experiment, does the paper provide sufficient information on the computer resources \(type of compute workers, memory, time of execution\) needed to reproduce the experiments?
40. Answer:\[Yes\]
41. Justification: The paper reports computational setup using API based large language models and provides runtime and LLM call statistics\. These details allow an estimate of the computational cost for reproducing the experiments\. Hardware level specifications are not applicable due to API based execution\.
42. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage\. - •The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute\. - •The paper should disclose whether the full research project required more compute than the experiments reported in the paper \(e\.g\., preliminary or failed experiments that didn’t make it into the paper\)\.
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45. Answer:\[Yes\]
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48. 10\.Broader impacts
49. Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
50. Answer:\[No\]
51. Justification: We do not provide a detailed discussion of application specific societal impacts, as this work focuses on a general memory system for LLM agents\. Potential impacts depend on downstream usage scenarios and are beyond the scope of this paper\.
52. Guidelines: - •The answer\[N/A\]means that there is no societal impact of the work performed\. - •If the authors answer\[N/A\]or\[No\], they should explain why their work has no societal impact or why the paper does not address societal impact\. - •Examples of negative societal impacts include potential malicious or unintended uses \(e\.g\., disinformation, generating fake profiles, surveillance\), fairness considerations \(e\.g\., deployment of technologies that could make decisions that unfairly impact specific groups\), privacy considerations, and security considerations\. - •The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments\. However, if there is a direct path to any negative applications, the authors should point it out\. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate Deepfakes for disinformation\. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster\. - •The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from \(intentional or unintentional\) misuse of the technology\. - •If there are negative societal impacts, the authors could also discuss possible mitigation strategies \(e\.g\., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML\)\.
53. 11\.Safeguards
54. Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse \(e\.g\., pre\-trained language models, image generators, or scraped datasets\)?
55. Answer:\[N/A\]
56. Justification:
57. Justification: The paper does not release models or datasets with high misuse risk\. All experiments use public datasets and API\-based models\.
58. Guidelines: - •The answer\[N/A\]means that the paper poses no such risks\. - •Released models that have a high risk for misuse or dual\-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters\. - •Datasets that have been scraped from the Internet could pose safety risks\. The authors should describe how they avoided releasing unsafe images\. - •We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort\.
59. 12\.Licenses for existing assets
60. Question: Are the creators or original owners of assets \(e\.g\., code, data, models\), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
61. Answer:\[Yes\]
62. Justification: The paper uses publicly available datasets and existing baseline models, all of which are properly cited\. The licenses and original sources of these assets are respected, and no modified datasets or redistributed assets are released\.
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64. 13\.New assets
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66. Answer:\[N/A\]
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69. 14\.Crowdsourcing and research with human subjects
70. Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation \(if any\)?
71. Answer:\[N/A\]
72. Justification: Our study does not involve any crowdsourcing or research with human subjects\.
73. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper\. - •According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector\.
74. 15\.Institutional review board \(IRB\) approvals or equivalent for research with human subjects
75. Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board \(IRB\) approvals \(or an equivalent approval/review based on the requirements of your country or institution\) were obtained?
76. Answer:\[N/A\]
77. Justification: Our paper does not make use of any crowdsourcing or research with human subjects\.
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79. 16\.Declaration of LLM usage
80. Question: Does the paper describe the usage of LLMs if it is an important, original, or non\-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does*not*impact the core methodology, scientific rigor, or originality of the research, declaration is not required\.
81. Answer:\[N/A\]
82. Justification: LLMs are used as backbone models for evaluation, and are not part of the proposed method\.
83. Guidelines: - •The answer\[N/A\]means that the core method development in this research does not involve LLMs as any important, original, or non\-standard components\. - •Please refer to our LLM policy in the NeurIPS handbook for what should or should not be described\.