LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
Authors: Chen-Chia Chang
Wan-Hsuan Lin
Yikang Shen
Yiran Chen
Xin Zhang
Venue: ICML 2025 poster (2025)
Keywords: Analog Circuit Automation
Language Model
Primary area: applications->everything_else

Abstract: Automation of analog topology design is crucial due to customized requirements of modern applications with heavily manual engineering efforts. 
The state-of-the-art work applies a sequence-to-sequence approach and supervised finetuning on language models to generate topologies given user specifications.
However, its circuit formulation is inefficient due to $O(|V|^2)$ token length and suffers from low precision sensitivity to numeric inputs.
In this work, we introduce LaMAGIC2, a succinct float-input canonical formulation
with identifier (SFCI) for language model-based analog topology generation.
SFCI addresses these challenges by improving component-type recognition through identifier-based representations, reducing token length complexity to $O(|V|)$, and enhancing numeric precision sensitivity for better performance under tight tolerances.
Our experiments demonstrate that LaMAGIC2 achieves 34\% higher success rates under a tight tolerance 0.01 and 10X lower MSEs compared to a prior method. 
LaMAGIC2 also exhibits better transferability for circuits with more vertices with up to 58.5\% improvement.
These advancements establish LaMAGIC2 as a robust framework for analog topology generation.

LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
Chen-Chia Chang'
Wan-Hsuan Lin
Yikang Shen
Yiran Chen
Xin Zhang 34
Abstract
Analog topology generation
Specifications
Power converter
Automation of analog topology design is crucial due customized requirements of modern appli- cations with heavily manual engineering efforts. The state-of-the-art work applies a sequence-to- sequence approach and supervised finetuning on language models to generate topologies given user specifications. However, its circuit formulation is inefficient due to O(IV))) token length and suffers from low precision sensitivity to numeric inputs. In this work, we introduce LaMAGIC2, a succinct float-input canonical formulation with identifier (SFCI) for language model-based ana- log topology generation. SFCI addresses these challenges by improving component-type recog- nition through identifier-based representations, ducing token length complexity to ([VV)), and enhancing numeric precision sensitivity for bet- ter performance under tight tolerances. Our ex- periments demonstrate that LaMAGIC2 achieves 34% higher success rates under tight tolerance of 0.01 and 10X lower MSEs compared a prior method. LaMAGIC2 also exhibits better transfer- ability for circuits with more vertices with up 58.5% improvement. These advancements estab- lish LaMAGIC2 as a robust framework for analog topology generation. Code available at ht tps: / //github.. www/ttrtteeeeeeeeeeeoeecco LaMAGIC.
Available devices:
LM
VIN-+
two switches, capacitor, Voltage conversion ratio: 0.18887
VOUT Duty eycle:
Efficiency: 0.95544
LaMAGIC's analysis
Input with float embeddings: Duty cycle options 0.5 voltage ... 0.9554
Embedding (E) Linear layer (L)
Low success rates in strict tolerances
Adjacency-matrix circuit formulation:
Duty cycle: Connections: VIN <no <no_edge> <no VOUT GND Sa Sb C... L... <sep>
<no__dge edge>
Token lengths with complexity 0(IV13)
1.00
0.95
0.90
c 0.85
E 0.75
X 0.70
E 0.65
0.60
0.50
0.45
0.40
0.35
0.02
0.04
0.06
0.08
0.10
Tolerance
Finetune with 120k 3, 4, 5-comp circuits:
PM
FM
Then finetune with 1k 6-comp circuits:
FM
Figure I. Analog topology generation and the analysis of a state- of-the-art work LaMAGIC (Chang al., 2024).
1. Introduction
different power supply requirements, e.g., voltage conver- sion ratio and power efficiency, often requires varied topolo- gies. However, traditional topology design relies heavily on manual processes, which demand large engineering ef- forts and prolong the time-to-market period for new designs. Thus, automating analog topology design has become cru- cial accelerate circuit development.
With the rise of diverse electronic systems, the need for different analog circuit functionalities increases. Thus, the demand for analog topology customization has largely in- creased. For example, the power converter application with
'Duke University University of California, Los Angeles MIIT- IBM Watson Al Lab 'IBM J. Watson Research Center. Corre- spondence to: Chen-Chin Chang <chenchia.change @echechiacchang@duk..edee @du.eeeduuu.......... Xin Zhang <xzhang us. ibm.com?..
Early efforts (Fan et al., 2021; Zhao & Zhang, 2022; Lu et al., 2023) have focused on search-based approaches, which explore vast design spaces guided by simulation rewards. However, they are inefficient and are not suitable to gener- ate circuits for diverse specifications. The work (Fan et al.,
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
inputs by shrinking the LM inputs. In addition, we address the long token length problem by reducing the complexity from O(IVI²) to O(VVI) while incorporating component- type tokens. This reduction is particularly impactful for real-world circuits, whose node numbers are large. Thus, LaMAGIC2 can shorten the token length, as shown in Ta- ble I, to mitigate the long sequence challenge faced by transformer models.
Table 1. Average token lengths of LMM outputs from: SFCT in LaM- AGIC2 and FM in LaMAGIC (Chang et al., 2024).
Average token length
3.4, 5-comp circuits
6-comp circuits
LaMAGIC2-SFCI
36.40
41.41
LaMAGIC-FM
84.79
105.00
rein- forcement learning (RL) method for power converter design, which requires hundreds of simulation queries to generate a new topology. The other work (Zhao & Zhang, 2022) also develops an RL algorithm for operational amplifiers, which takes 73 simulation iterations for 4 hours per specification. Finally, the work (Lu et al., 2023) uses Bayesian optimiza- tion for topology search. However, 50 iterations are needed for one specification.
2021) designs a poppe--onfieence-buund-rreee
Our contributions are summarized as follows.
We propose succinct float-input canonical formulation with identifier (SFCT): A sparse and canonical represen- tation that uses identifiers to enhance learning of com- ponent types while maintaining linear token growth relative to circuit size.
LaMAGIC2 achieves a 122% and 34% higher success rate under a low tolerance 0.01 compared to an RL search method (Fan et al., 2021) and LaMAGIC, re- spectively.
Recent advances in generative modeling and large language models (LLMs) (Radford et al., 2019; Raffel et al., 2020; Chung et al., 2022; Nijkamp et al., 2023) offer an alterna- tive paradigm. Instead of exhaustively exploring the design space, generative models can learn direct mappings from performance requirements to circuit topologies. One such approach is LaMAGIC (Chang et al., 2024), which frames circuit generation as a sequence-to-sequene problem for transformer-basee autoregressive language models. LaM- AGIC proposes several circuit formulations to perform su- pervised finetuning (SFT) (Chung et al., 2022; Taori et al., 2023). The trained models can generate topology via one model inference, as shown in Figure 1, significantly ac- celerating the generation process compared to prior search methods.
Models trained with SFCI demonstrate superior per- formance in limited data scenarios for more complex circuits, achieving the highest success rates to outper- form other formulations.
Furthermore, our step-by-step analysis of formulations pro- vides valuable insights into graph generation with trans- former models, advancing the field of topology generation and beyond.
2. Preliminaries
2.1. Analog Topology Design
In this work, following LaMAGIC (Chang et al., 2024), we target on power converter topology generation, which aims to produce customized power converters that achieve specific design specifications, i.e., the voltage conversion ratio and the power conversion efficiency. The voltage con- version ratio is the ratio of output to input voltages. The power conversion efficiency is the ratio of output power to input power. Another design choice for power converter is the duty cycle with a range of 0 to 1, which controls the ON times of switches, influencing the output voltage and efficiency. In our framework, we consider five duty cycle options: {0.1, 0.3, 0.5, 0.7, 0.9}.
While LaMAGIC demonstrates great potential for analog topology generation, its circuit formulations pose notable limitations, as shown in Figure 1. First, its formulation re- duces the model's 's sensitivity to low precision difference of numeric inputs, resulting in low success rates under strict tolerance evaluations. Second, the token length of its for- mulations scales quadratically with the number of nodes ((VV2). The long output sequences pose significant chal- lenges to accuracy due to eтror accumulation and context window limitation for transformer-basee topology genera- tion. As generation progresses autoregressively. early errors propagate, compounding inaccuracies and reducing the reli- ability of generated circuit structures. Additionally, when output exceeds the model's fixed context window, critical early design elements may fall out of scope, leading to in- consistencies infeasible circuit configurations. These lim- itations are particularly problematic in topology generation, where precise structural relationships must be maintained.
We view the circuit topology as a hypergraph G with ver- tices V and hyperedges E. For each topology, the vertices V contain three terminal ports and several analog compo- nents. The three terminal ports are: a voltage input VIN, voltage output VOUT, and ground GND, each with an edge to connect to other vertices. User can pick four types of components: capacitors C, inductors L, phase-I switches Sa, and phase-Il switches Sb, each with two edges. Each hyperedge e E E is a set of vertices that represents connections between devices and ports. An example of the
In this work, we propose LaMAGIC2, an advanced circuit formulation designed for based topology generation. LaMAGIC2 improves low-precision sensitivity to numeric
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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
Switches
sources. AnalogCoder (Lai al., 2024) leverages prompt engineering in general-purpose LLMS to iteratively refine circuit designs based on simulation feedback. However, its methodology is fundamentally different from our work, as it does not involve SFT and tailor formulations for di- mapping. Our work builds
Phase-1
Phase-Il
VIN
Sa
VIN
Inductor
L
GND
VOUT
GND
VOUT
Capacitor
rect ppecification-tottoollle upon LaMAGIC (Chang al., 2024), which introduced cus- tom eircuit formulations enable precise specification to- topology generation. Given the drawbacks of LaMAGIC's formulations provided in our analysis in Section 3, we pro- pose novel formulations to address these limitations.
(a)
(b)
Figure 2. (a) An example power converter circuit and (b) its cor- responding hypergraph representation. Note that here use the same example in LaMAGIC (Chang et al., 2024).
power converter and its hypergraph representation is shown in Figure 2.
3. Analysis of Formulations in LaMAGIC
We utilize the same dataset in LaMAGIC (Chang et al., 2024). It contains 3, 4, 5-component circuits with 120k data points for training and 12k for evaluation. To assess the transferabilliyy of models to more complex circuits, the dataset has 76k unique 6-component circuits and split 9k data points for evaluation. In our experiments, we ran- domly select subsets of 500, Ik, and 2k 6-component cir-
LaMAGIC (Chang et al., 2024) introduces three formula- tions for circuit generation: (1) canonical formulation (CF), (2) pure-text sdlaccnnyy-matie formulation (PM), and (3) float-input adjacency-matre formulation (FM), as shown in Figure 3. In this section, we analyze advantages and disadvantages of each formulation.
cuits to fine-tune models initially trained on the 120k 3, 4, 5-component circuits.
3.1. Canonical Formulation (CF)
CF encodes circuit information with canonical representa- tion with output edges sorted based on predefined input vertex order.
Generating complex circuits is critical challenge for hu- man designers. Also, LaMAGIC does not perform well for transferability to larger circuits. Thus, our work focuses on improving this capability by leveraging input specifications that have performance targets and component requirements.
Advantage:
(1) Compact eircuit encoding: Since each edge is repre- sented by set of nodes, the length of CF is O([VI).
Based on these considerations, we define our problem: Problem. Given vertices V. voltage conversion ratio r, and an efficiency 77, the model generates connections E and determine the duty cycle 10.1, 0.3, 0.5, 0.7, 0.9) to build cireuit such that its simulation performance satisfies both and n7.
Disadvantage:
(1) Limited component type awareness: LaMAGIC's tok- enizer for CF encodes node-specific tokens (c.g., Sa0, Sal) into separate single embeddings (e.g., <Sa0>, <Sal>). This method make models difficult to learn relations be- tween different component types because models cannot easily recognize the component type of each node, e.g., SaO and Sal represent the same node type Sa. This drawback can be the reason of the bad generalizability of CF.
2.2. Autoregressive Language Modeling
Autoregressive language models (LMs) (Radford et al., 2019; Raffel et al., 2020; Chung et al., 2022; Nijkamp et al., 2023; Zhao et al., 2023) are widely used in sequence model- ing tasks. They predict the next token a sequence based on preceding tokens, optimizing the autoregressive loss: -=-En log P(xi|21, 22 ...; II-)) Building on LaM- AGIC (Chang al., 2024), this work also employs autore- gressive LMs to address analog topology generation. These models are well-suited for this task as they can sequentially generate the next component and connection in a circuit based on the evolving subgraph.
(2) Numeric tokenization: When numeric values (e.g.. 0 95544) are fed into the tokenizer, they are split into multiple subword tokens (e.g., "O". "g",, "5", di- luting their semantic meaning and making it harder for the model to learn numeric relationships.
Eim
3.2. Pure-Text Adjacency-Matris Formulation (PM)
PM represents circuit connections adjacency matrix for hypergraph, where rows and columns are indexed based on the vertex order given in the input.
2.3. Related Works on Topology Generation
Advantage:
Search-based methods (Fan et al., 2021; Zhao & Zhang, 2022; Lu et al., 2023) explore design spaces using simu- lation feedback but require significant computational re-
(I) Component type recognition: Because the matrix in- dexes are inherently ordered by the input vertex sequence, PM eliminates the need to assign identifiers to distinguish
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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
LaMAGIC
Canonical formulation (CF)
input:
Duty cycle options 0.1 0.5 0.7 0.9, voltage conversion rado 0,85973, e.8ceey, 0.93273, vertex order: <VIN> <VOUT> <GND> <Sa0> <Sal> <CO> <L0>
output:
<C0)),
<L0>). The duty cycle 0.3.
Pure-text adjaveenc--maatiii-bbssss formulation (PM)
Explore tabular formulation
input: Duty cycle options 0.1 0.5 <sep> voltage conversion ratio 0.85973 <sep> efficiency 0.93273 "sep>-ertees order: <VIN> <VOUT> <GND> <Sa> <Sa>
<sep?
LM output:
Duty cycle: <unselect> <unselect> <select> <unselect> <unselect> <sep> Connections:
<VIN> <no edge> <no_ edge> <no_ edge> <edge_ <no edge> <no edge> <no_ edge>
<VOUT> <no edge> <no edge> <no edge> <no edge> <no edge> <edgel> <edge 1>
<GND> <no edge> <no edge> <no edge> <no edge> <edge I> <edge_ 1> <no _dgee> <no_edge>>
<Sa> <edge_ 1> <no edge> <no edge> <no edge> <edge
<edge_ 2> <no_ edge?
<Sa> <no edge> <no
<no__dde edge> <edge <edge <no_ sro_edge> <edge_ <edge
<C <no edge> <edge_1> <edge <no_
<no_edge edge> <edge 2> <no edge> <edge_
edge> <edge_
edge> edge> <edge <edge_ <sep>
Float-input adjacceccy-matriv based formulation (FM)
Input numbers transformer
Duty cycle options 0.1 0.3 0.7 <sep? voltage conversion 0.85973 <sep? efficiency 0.93273 <sep>
Embedding (E)
Linear layer (L)
LaMAGIC2
Shrink redundant words in natural language
Succinet float-input adjaeencyy-matiii-bbnn formulation (SFM)
LM input:
0.1 0.3 0.5 0.7 0,9 0.85973 0.93273 <sep? <VIN> <VOUT> <GND> <Sa> <Sa>
<
< <sap?
output:
<duty_0.3. 0.3> <sep?
<VIN> <no_ <no__dooee edge> <no edge> <no edge> <edge_ <no edge> <no adge> <no <no_edge>
<VOUT> <no moo_eee>> <no edge> <no <no__dde moo_ede>> <no edge> <no edge> <edgel> <edge_ |>
<GND> <na moo_ddee>
edge> <no edge> <no edge> <edge <edge_ 1> <no edge>
<Sa> <edge_ 1> <na edge> <no edge> <no, edge> <edge 2> <edge 2> <no edge>
<$a> <no__dst _egee <no_edge pog_edge> <edge_ >> <edge_ >> <no_ mo_edee> <edge_ <edge_2>
<C> eno edge> <edge_ |> <edge 2> <no, edge> <edge 2> <no edge> <edge |>
<L> <no__de__s____ _dgeedee <edge_ <no <no_edge> <no sdgeedee> <edge <edge_ |> <sep>
Suceinet float-input canonical formulation with identifler (SFCI)
LM input:
0.1 0.5 0.7 0.9 0.85973 0.93273 <sep? <VIN> <VOUT> <GND> <S>> LM output:
<S>> <C> <L>> <sep?
<duty_ 0.1> <sep>
<VIN>
<Sa> <VOUT> <C> 2 24 < <C> <Sa> 0 <Sa>
<
<sep>
Figure circuit formulations proposed by LaMAGIC (Chang et al., 2024) and our work LaMAGIC2. Tokens enclosed within
denote those added to the tokenizer's dictionary, enabling distinct embeddings for each token.
nodes of the same component type. For example, instead of using <Sa0> and <Sal>, PM can simply use <Sa> to represent multiple nodes of the same type. Therefore, PM enhances the model's ability to recognize relationships be- tween nodes the same type, improving its understanding of circuit structures and generalizability.
attention complexity, which leads ineffectiveness in trans- former models.
(2) Numeric tokenization, the same as in CF.
3.3. Float-Input Majaccncy-Mattrt Formulation (FM)
FM addresses PM's numeric tokenization issues by incorpo- rating shared linear layer to encode numeric inputs directly into the transformer's embedding space.
(2) Graph difference detection:
This tabular formulation excels graph difference detection during training because enrors are localized to specific matrix entries. For example, missing or incorrect edge affects only the corresponding matrix entry, making it easier for the model to identify and correct isolated errors.
Advantage:
(1) Float-input numerical encoding: This method strength- ens the model's capacity to learn the relationship between input specifications and circuit structure. As result, FM demonstrates strong transferability, particularly when gener- ating circuits with six components.
Disadvantage:
(I) Long token length (3) Longer sequences increase

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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
Disadvantage:
2. Simplified representation for duty eycle selection: SFM simplifies duty cycle selection by replacing the five-token representation <unselect> <unselect> <select> <unselect> <unselect> in FM and PM with a single token <duty_0.3 . change better aligns with the classification nature of duty cycle selection, where the task involves choos- ing one option from five predefined choices <duty 0011>, <duty_0.. _0.3>, <duty_O., _0.5>, <duty_0.7>, or <duty_0.9>. Since autoregressive LMs inherently operate at the token level, treating this decision as a single-token classification task simplifies learning and prediction. We add these five to- kens into the dictionary of the tokenizer to let each one represented by a distinct embedding. ensuring clarity in the model's understanding. This formulation not only reduces sequence length but also leverages the natural behavior of LMs to enhance generation effectiveness.
(1) Low sensitivity to numeric precision: FM exhibits low success rates for 345-component circuits under strict tol- erance conditions, achieving only 0.67 compared to PM's 0.93 at a tolerance level of 0.01, as illustrated in Figure 1. This limitation could arise from FM's input formulation, which includes redundant natural language descriptions (e.g., duty cycle and voltage) that dilute the model's 's fo- cus numeric inputs. This reduces the model ability to capture fine-grained differences between numeric inputs.
3.4. Summary of Insights and Challenges
The formulations in LaMAGIC (Chang et al., 2024) high- light key insights: (I) the component-type token representa- tion is crucial for learning circuit structures, and (2) integrat- ing numerical inputs with a shared linear layer enhances gen- eralization for complex circuits. However, these approaches face challenges: (I) matrix-based formulations suffer from inefficient token lengths ((IV)), and (2) the float-input setting has low sensitivity to numeric input precision.
4.2. Succinet Float-Input Canonical Formulation with Identifier (SFCI)
As SFM shrinks the input and output by removing natural language descriptions and simplifying duty eycle representa- tion, matrix-related formulations still face challenges due to their long token length, ((1V)). Additionally, real circuits are often sparse, meaning that most entries in the adjacency matrix are <no_edge> tokens. This results in an inefficient representation, as the model expends capacity processing numerous tokens that carry minimal informational value. As [ increases, matrix- formulations could struggle to handle large circuit generation effectively.
To address these issues, our proposed formulations combine the strengths of FM and PM by enhancing numeric atten- tion, reducing token length to scale linearly with [V), and improving component type representation for better graph structure learning. These improvements enable more robust circuit generation.
4. Our Proposed Formulations
This work introduces two novel circuit representations: (1) succinet float-input adjacency-matrix-bann -baed formulation and (2) succinct float-input canonical formulation with identifier, as illustrated in Figure 3.
We observe that CF performs well for circuits with 3, 4, 5 components but lacks component-type tokens, which are important for distinguishing node types. We believe this limitation contributes to its lower performance in generating circuits with six components. In contrast, the matrix-based formulations (PM, FM), who has better transferability, all utilize node-type tokens (e.g., <Sa> and <Sb> as single to- kens). To address these limitations, we propose the succinct float-input canonical formulation with identifier (SFCI).
4.1. Succinet Float-Input Mdjacency-Matrix Formulation (SFM)
SFM improves upon the matrix-based and float-input set- tings of FM, by reducing unnecessary details in the represen- tation to better handle numeric inputs. Its key components are follows:
SFCI adopts the sparse graph representation of CF, where edges are represented as sets of nodes, and introduces the following design choices:
1. Succinet input: Because matrix formulation is deviated from natural language, the natural language descriptions, e.g.. "Duty cycle" and "voltage", cannot provide effective signal for topology generation. SFM removes these descrip- tions from the input, creating a representation that focuses on the essential numerical inputs. This representation re- duces attention dilution, enabling the model to concentrate on learning a direct mapping between numeric inputs and the adjacency matrix. As a result, SFM enhances the model's 's precision sensitivity and the performance under strict toler- ance conditions.
1. Identifiers for device nodes: SFCI separates each node token like SaO into two tokens: the device type (<Sa>) and an identifier (0). Identifiers are used only for device tokens, as circuits often contain similar devices. The identifiers are incremented from to V 3). where IV - 3| is the number of devices in the circuit. Three port nodes (<VIN>, <VOUT>, <GND>) do not use identifiers, as each port occurs only once in circuit. This approach allows SFCI to improve the component type recognition.
2. Simplified output format: SFCI removes bracket tokens
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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
SFCI without Componennt-ypee Tokens in Output (SFCI-NCT)
We observe that all formulations include duty-cycle prefix ranging from 0.1 to 0.9, common feature across all input- output pairs. To make formulations succinct, one might consider removing this redundancy, as shown in SFCI-NDP (Figure 4). However, this duty-cycle prefix has the following two benefits. First, the duty-cycle prefix serves as implicit regularization, helping the model stabilize its representa- tions. Second, it provides guidance for decision- making by acting valid set of duty cycle options the model can ref- erence throughout training. Without this prefix, the model must infer these duty-cycle values purely from other inputs. The effectiveness of the prefix is established in Section 6.1.
LM input:
(Same SFCI)
LM output:
<duty_ 0.1> <sep? <VIN> 0. 23, 22,0 1 <sep?
SFCI without Cytye Prefix (SFCI-NDP)
I.M input:
0.85973 0.93273 <sep? <VIN> <VOUT> <GND> <Sa> <Sa> I <C>
<<L>3 3 <sep>
L. output:
(Same as SFCI)
Figure 4. Two variants of SFCI: (1) without component-lype token
output (SFCI-NCT) and (2) without common feature duty- cycle prefix (SFCI-NDP).
5. Experimental Results
() and uses commas to separate the node set for each edge. For example, an edge is represented as <VIN> <Sa> rather than a verbose bracketed format. This reduces the token count to simplify the learning process.
5.1. Experiment Setup
Baselines. To evaluate the performance of our proposed formulations SFM and SFCI, compare them with three baseline formulations introduced in LaMAGIC (Chang et al., 2024): canonical formulation (CF), pure-text adjacency- matrix-based formulation (PM), and float-input adjacency- matrix-based formulation (FM), as introduced in Section 3.
3. Component-type tokens in the output: If we would like to ultimately shrink SFCI, we can eliminate the component- type tokens in the output to be SFCI-NCT in Figure 4. Al- though this method can reduce output lengths by nearly half, we retain component-type tokens (e.g., <Sa>, <Sb>, <C>, <L>) in the output of SFCI. Because SFCI's outputs are self-contained without relying on input-output fusion to understand the circuit, these tokens can provide explicit patterns that map identifiers to their component types in the circuit to facilitate model learning. The effectiveness of this design choice is validated in Section 6.2.
In addition to SFT methods that directly generate the cir- cuit in one-shot, we compare with a prior work (Fan et al., 2021) that uses RL search algorithm for power converter generation. They need to run simulator each query to give feedback to the RL engine. We set the total query budget to 100 per input specification. We also compare with an advanced reasoning model ol (Jacch et al., 2024) using a few-shot setup with 100 example circuits as context.
Token length complexity of SFCI: SFCI reduces the token length of the output to ([V)). Each hyperedge e, has k2 vertices. Thus, the total token length, representing the sum of vertex incidences across all e, is E/=0 ky. For our power converter devices, each vertex appears in at most two hyperedges: d(v) < 2. Thus, the total number of vertex incidences, which equals to the number of edges of all nodes, is _ A; = Evev d(vv= S 2.V) This upper bound implies the total token length is at most 2/V), which simplifies to O(VV)).
Training details. We follow LaMAGIC (Chang al., 2024), adopting the Flan-T5-base T5-base encoder-decoder trans- former (Chung et al., 2022) initialized with pretrained weights To handle numeric inputs, the standard word embedding layer is replaced by a shared linear projec- tion. Training employs conditional generation to map input-output pairs, with random vertex order permuta- tions applied as data augmentation (Chang et al., 2024). Customized tokens are added tokenizer's dictionary to represent component types and duty cycle options. For SFM. we add <sep>, <duty_0 1., <duty_0 3>, <duty_0 _0_ 5>, <duty_0. 7>, <duty_0. 9>, VIN, VOUT, GND, Sa, Sb, C, L, <no <no_edge>, <edge_1> <edge_28 2>>, <both edges,, For SFCI, we further add identifier to- kens 0 to 12.
This result indicates that the token length complexity of SFCI is independent of the number of edges [E) The O(VV) token length of SFCI demonstrates its compactness compared to O(VV?) lengths of matrix formulations. We compute the average token length of outputs from SFCI and FM in Table 1. Token length of SFCI only increases five when the dataset grows to 6-component circuits, while token length of FM grows quadratically from 73 to 105. By combining the strengths of CF's sparse representation with the use of component-typs tokens and identifiers, SFCI balances compactness and expressiveness, enabling robust generation of large circuits while addressing the limitations of canonical and matrix- based formulations.
Flan-T5- T5-base contains 248M parameters with 12 layers each in encoder and decoder, 64-diimensional key/value projec- tions, c048-dimensional feed serd-forward layers, and 12 atten- tion heads. Training runs on one NVIDIA V100 GPU using Adam W with the following hyperparameter: learning rate 10-4, cosine scheduler with 300 warm-up steps, batch size 128, L2 regularization 10-5, dropout 0. and epochs
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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
1.00
1.00
0.95
0.90
0.95
0.85
0.80
0.75
0..0
E0.70
0 0.665
0.85
5 5.335
8.660
0.50
Ours-SFCI
SFM
0.80
LaMAGIC-CF
LaMACIC-PM
6 0.45
0.40
0.75
LaMAGIC-FM FM
0.35
Su
0.30
0.25
0.70
SFCI
0.20
0.02
0.04
0.06
0.08
0.10
0.65
0.02
0.04
0.06
0.08
0.10
Tolerance
Tolerance
Figure Success rates an Re.-search method (Fan et al., 2021) and models trained with circuit formulations SFM and SFCI using 3, 4, 5-component circuits.
Figure 6. Success rates of models trained with different circuit formulations using 4, 5-component circuits.
Table MSEs of an RL-search method (Fan et al., 2021), ol with few-shot prompting, and models trained with circuit formula- tions SFM and SFCI using 3, 4, S-component circuits.
Table 3. MSEs of models trained with different circuit formulations
using 3, 4,54,,ccomm 5-component circuits.
MSE
RL
SFM
SFCI
MSE
Voltage
Efficiency
Voltage
0,313
0.602
0.0001
0.00008
CF
0.0160
0.0040
PM
0.0065
0,0023
FM
0.0061
0,0128
120.
SFM
0.0013
0.0003
Evaluation metrics. Our primary metrics for evaluation are (1) the success rate of the generated circuits within var- ied tolerances / ranging from 0.01 to 0.1 and (2) the mean squared error (MSE) between the input specifications and the simulated performance of the generated circuits. We run simulator NGSPICE (Nenzi P, 201 on each generated cir- cuit to get its actual voltage conversion ratio and efficiency for real-world applications.
0.0002
tolerance 0.01. In addition, ol does not perform well with few-shot prompting, indicating the need of SFT for analog tolopogy generation.
Comparison between different formulations. We per- form SFT under CF, PM, FM, SFM, and SFCI for 3,4,5- component circuits and evaluate them using the testing set containing 12k data points.
The success rate is the proportion of generated circuits whose simulated voltage conversion ratio u and efficiency e fell within a tolerance of the target input specifications v/ and e', i.e. and e are both within the range o' +t and e' t.. If a generated circuit is unsimulable (invalid), we mark it an unsuccessful one when calculating success rates. MSEs for voltage conversion ratio and efficiency are computed sep- arately. In addition, the invalid generated circuit is viewed as error in MSE calculation.
From LaMAGIC (Chang et al., 2024), FM does not per- forms well on 3,4.5-component circuits due to its float-input setting but it has better generalizability to more complex circuits. As shown Figure 6, our SFM and SFCI success- fully improve the success rates under tight tolerance ranges compared to FM (from rates 0.67 to 0.9 under tolerance of 0.01). In addition, both SFM and SFCI become comparable to PM that uses the all-text-input setting. Specifically, our success rates are 0.99 when tolerances are larger than 0.04 and 1.00 when the tolerance is 0.1.
5.2. Generation Results on 3, 4, 5-Component Circuit
Comparison with RL-search method and ol. We run RL-search method (Fan et al., 2021) for 5 days to complete generation of 350 specifications from our testing set. Thus, we will compare this work (named RL) and ol with our formulations under the same 350 specifications. Since RL only constrains voltage conversion ratio in topology generation, we evaluate the performance
Under MSE in Table 3, SFM and SFCI significantly out- perform all baseline formulations, especially for SFCI that shows 10X lower MSE compared to FM and PM. SFM's result shows that our succinct formulation benefits the float input setting to let models better learn the mapping between numerical numbers and edges. Additionally, comparison between SFCI and CF shows that component-tyl type tokens can improve CF's sparse formulation in circuit generation.
success rates and MSE calculated only on voltage conversion ratios. As shown Figure 5 and Table 2, our SFT methods under SFM and SFCI largely outperform RL (Fan et al., 2021), with success rates 0.41 (RI.) and 0.91 (SFM and SFCT) on a tight

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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
Training with 500 6-component circuits
Training with 1000 6-component circuits
Training with 2000 6-component circuits
0.90
0.85
0.50
0,75
E0.65
00.00
5..55
LANAGIC
LAMAGIC-CF
LaMAGIC-PM
LAMAGIC-M
LaMAGIC-PM
0.48
LaMACIC-FM
FM
LMMACIC.MM
0.40
Ours-SPM
Ours-SFM
0.35
SFCI
Our-SFCI
SFrt
0.30
Tolezation
Tulersnne
Telerance
Figure 7. Success rates of models finetuned with different circuit formulations using 500, 1000, and 2000 6-component circuits.
1.00
Table 4. MSEs of voltage conversion ratio and efficiency evaluated
0.95
models finetuned with 500, Ik, and 2k 6 component circuits.
0.90
0.85
500
1000
2000
0.80
0.75
MSB
Voltage
Eff
Voltage
Eff
Voltage
Eff
0.70
CF
0.1843
0.1970
0.1684
0.1844
0.1459
0.1661
0.66
0.66
PM
0,1661
0.1705
0.1494
0.1565
0.1334
0.1315
0.55
SFCI-NDP
FM
0,1324
0.1156
0.1341
0.1325
0.1014
0.0865
0.50
SFCI-NCT
0.45
SFCI
SFM
0,1570
0.1543
081
0.1109
0.0941
0.1009
0.40
0.02
0.04
0.06
0.08
0.10
SECI
0,1102
0.0899
0,0475
0.0719
0,0580
0.0418
Tolerance
Figure 8. Success rates of models trained with SFCI and its two
variants using 3, 4, 5-component circuits: (1) SFCI-NDP and (2)
SFCI-NCT, as in Figure 4.
5.3. Transferability Evaluation on 6- 6-Component Circuit
In real world scenario, large amount of data for circuits with a large node number could be hard to collect. A six- component circuit requires 30 seconds of simulation to ob- tain the voltage and efficiency. Similar to LaMAGIC, we extend models trained with 3, 4, 5-components circuits to be finetuned with only 500, 1k, and 2k 6-component circuits randomly selected from our dataset. Then, we evaluate each model on the testing set (9k data points) and run simulation on each generated circuit to get its real performance.
Table 5. MSEs of voltage conversion ratio and efficiency evaluated on SFCI and its two variants using 3, 4, 5-component circuits: (1)
SFCI-NDP and (2) SFCI-NCT, as in Figure 4.
MSE
Vollage
FN
SFCI-NDP
0.0033
0.0028
SECI-NCT
0.0022
SFCI
0.0006
0.0002
The results are shown in Figure 7 and Table 4. Similar to the results of 3, 4, 5-component circuits, SFM has higher suc- cess rates in low tolerance ranges (0.01 to 0.03) compared to FM. This shows that our succinet formulation also enhances low precision sensitivity in transferability evaluation.
6. Ablation Study & Discussion
6.1. SFCI without Duty-Cycle Prefix
When shrinking formulations, the prefix containing five duty cycle numbers is common feature across data points and might be removed, stated the end of Section 4.2. Thus, we evaluate how omitting this prefix affects model performance by training variant SFCI-NDP without the duty-cycle prefix, as in Figure 4. The results in Figure 8 and Table 5 show that SFCI-NDP suffers a performance drop compared to SFCI, showing that this prefix provides an effective guidance for model's decision making.
Models trained with SFCI demonstrate best transferability. Notably, the success rate of the model finetund with 2000 6-component circuits improves to 0.84 compared to FM's 0.76 under tolerance 0. In MSE, SFCI also performs the best compared to all other formulations with up to 58.5% improvement. This result shows that the sparse graph rep- resentation is more suitable for complex circuits due to its short token length. Additionally, our component-type tokens let model to better learn different component's 's representa- tions to boost the generalizability. In summary, these results suggest that our proposed SFCI is the best formulation to perform the topology generation.
6.2. SFCI without Component-Type Tokens in Output
To validate the design choice of keeping component-type tokens the output of SFCI, we compare SFCI against a variant SFCI-NCT that removes them from the output as
8

---

LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
VDD
PMOS
LMiput
(Performance specification) <sep> <VDD> <VIN> <GND> <PMOS> S <PMOS> 0 <PMOS> O <PMOS> O B <NMOS> <NMOS> <NMOS> D <NMOS> B <sep>
VIN
VOUT
LMoutut:
B
(parameters to be set) <sep> <VDD> <PMOS> 05 <PMOS> 0B. <VIN> <PMOS> O <NMOS>
NMOS
G.<GND> <NMOS> S <NMOS> B, <VOUT> <PMOS> 0 <NMOS> D <sep>
GND
Figure 9. The example of extending SFCI into transistor-based inverter that contains NMOS device and PMOS device, each has four distinct device pins: drain (D), gate (G), source (S), and body (B). We view an NMOS with the identifier O as four nodes; <NMOS> 0
D, <NMOS> G, <NMOS> and <NMOS> 0 B. In addition, PMOS device with the identifier is viewed four nodes: <PMOS>
0 10, <PMOS> 0 G, <PMOS>
C S and <PMOS> 0 B. Then, we base on all nodes to construct our inverter.
shown in Figure 4. SFCI-NCT yields worse performance according to both Figure 8 and Table 5. These results con- firm that including component-type tokens helps the model better capture the circuit structure, leading to more accurate generation despite slightly longer output.
tal results show that SFCI achieves a 34% higher success rate under a stringent tolerance condition 0.01 compared to LaMAGIC's FM formulation, along with 10X lower MSEs. Moreover, SFCI excels transferability evaluations, achiev- ing up to 37.5% higher success rates and 58.5% lower MSEs when finetumed on limited datasets of more complex circuits. LaMAGIC2 paves the way for more efficient and scalable automated analog design methodologies.
6.3. Computation Efficiency Analysis
We analyze the computational efficiency of our SFCI by comparing with the SFM. Specifically, the training for SFM saturates at 8,943 steps, whereas SFCI converges sig- nificantly faster at 6,886 steps, representing 23.0% re- duction in required training steps. Moreover, as the token length complexity decreases to O(VV)), SFCI also achieves shorter inference times compared to SFM. These results demonstrate that SFCI substantially enhances computational efficiency in both training and inference phases.
For future works, first, we can integrate search-based decod- ing methods with our models to generate optimized circuits for even larger and more diverse design spaces. This inte- gration can balance the strengths of generative and search- based approaches, enhancing the quality and practicality of automated analog circuit design solutions. Second, we can extend our formulations to transistor- circuits to sup- port wide range semiconductor circuit design applications that has precise numeric specifications from users. LaM- AGIC2 presents great potential for complex circuit designs.
6.4. Extend SFCT into Transistor based Circuits
Future developments can extend SFCI to handle transistor- based circuits, enabling support for a wider range of applica- tions. In this context, transistors, e.g., NMOS devices (ND), have four distinct pins: drain (D), gate (G), source (S), and body (B). To represent these circuits, nodes need to be de- fined at the pin level. Thus, we can view an NMOS with the identifier 0 as four nodes: <NMOS> 0 D, <NMOS> 0 G,
A ckknowledgment
This work is partially supported by SRC 3104.001 and NSF 216228 Special thanks to Prof. Jason Cong from UCLA for paper writing suggestion.
Impact Statement
<NMOS> 0 s, <NMOS> 0 B. We construct an example of cansistor-based inverter in the Figure 9.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
7. Conclusion
In this paper, we introduced LaMAGIC2, an advanced cir- cuit formulation designed to enhance language model-based topology generation for analog circuit design. LaMAGIC2 addresses key limitations of prior approach by introduc- ing the Succinct Float-input Canonical Formulation with Identifiers (SFCI). SFCI improves component-type recogni- tion through the use of unique identifiers, simplifies input specifications to enhance numeric precision sensitivity, and reduces circuit representation length to O(V)). Experimen-
References
Chang, C.-C., Shen, Y., Fan, S., Li, Zhang, S., Cao, N., Chen, Y., and Zhang, X. LaMAGIC: Language-moded based topology generation for analog integrated eircuits. In Proceedings of the 41st International Conference on Machine Learning, pp. 6253 6262. PMLR, 21-27 Jul 2024.

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LaMAGIC2: Advanced Circuit Formulations for Language Model-Based Analog Topology Generation
Chung, H. W., Hou, L., Longpre, S., Zoph, B., Tay, Y., Fedus, W., Li, Y., Wang, X., Dehghani, M., Brahma, S., et al. Scaling instructionn-finetuned language models. arXiv preprint arXiv:2210. 1416, 2022.
Zhao, Z. and Zhang, L. Analog integrated circuit topology synthesis with deep reinforcement learning. IEEE Trans- actions Computer-Aided Design of Integrated Circuits and Systems, (1(12):5138-5155 2022.
Fan, S., Cao, N., Zhang. S., Li J., Guo, X., and Zhang, X. From specification to topology: Automatic power converter design via reinforcement learning. In 2021 IEEE/ACM International Conference On Computer Aided
Design (ICCAD), pp. 1-9. IEEE, 2021.
Jaech, A., Kalai, A., Lerer, A., Richardson, A., El-Kishky,
A., Low, A., Helyar, A., Madry, A., Beutel, A., Car- ney, A., et al. Openai system card. arXiv preprint arXiv:2412.16720, 2024.
Lai, Y., Lee, S., Chen, G., Poddar, S., Hu, M., Pan, D. Z., and Luo, P. Analogcoder: Analog circuit design via training- free code generation. arXiv preprint arXiv:2405. 14911 2024.
Lu, J., Lei, L., Huang, J., Yang. F., Shang, L., and Zeng, X. Automatic op-amp generation from specification to layout. IEEE Transactions Computer-Aided Design of Integrated Circuits and Systems, 2023.
Nenzi P, V. H. Ngspice users manual version 23., 2011. URL http::://pkgs..feoorrpppp/
org/ happ///erra//ggppceeeegggllaaaaa
ptf//8bb66ee63331111111777533553 ngspice23-manuale
Nijkamp, E., Hayashi. H., Xiong, C., Savarese, S., and Zhou, Y. Codegen2: Lessons for training lims on programming and natural languages. arXiv preprint arXiv:2305.02330 2023.
Radford, A., Wu, J., Child, R., Luan, D., Amodei, D., Sutskever, I., et al. Language models are unsupervised multitask learners. OpenAl blog, 1(8):9, 2019.
Raffel, C., Shazeer, N., Roberts, A., Lee, K., Narang, S., Matena, M., Zhou, Y., Li. W., and Liu, P. J. Exploring the limits of transfer learning with a unified text-to-text transformer. The Journal of Machine Learning Research, 21(1):5485-5511, 2020..
Taori, R.,
Gulrajani, I., Zhang, T., Dubois, Y., Li, X., Guestrin, C., Liang, P., and Hashimoto, B. Stanford alpaca: An instraction-following llama model. https: wtt.bb...h.ucg///g///ooo/.b.. www/tatsutleaaaaeaa stanford_ alpaca, 2023.
Zhao, W. X., Zhou, K., J., Tang. T., Wang, X., Hou, Y., Min, Y., Zhang, B., Zhang, J., Dong, Z., et al. survey of large language models. arXiv preprint arXiv:2303.1822. 2023.
10


Reviews:
[{"review_id": "Pszew2oMvG", "reviewer": "Reviewer_bUno", "summary": "This paper proposes LaMAGIC2, introducing succinct formulations (SFM and SFCI) for language-model-based analog circuit topology generation. Compared to the previous LaMAGIC approach, these formulations effectively reduce output sequence length and improve component-type recognition. Experiments demonstrate that LaMAGIC2 achieves higher success rates and lower MSE under strict tolerance conditions.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Q1: Choice of Model Architecture\nWe appreciate the suggestion to evaluate our proposed formulations using other model architectures. In this work, we adopted T5 to maintain architectural consistency with previous work LaMAGIC, enabling a fair comparison focused on the impact of new formulations.\n\nWe have considered extending to encoder-only models (e.g., GPT-2), which are often more suitable for scaling up the parameter count compared to encoder-decoder models. However, due to the limited rebuttal timeline, we were unable to complete the experiments. \n\n\nOur proposed float-input setting and SFCI formulation are architecture-agnostic and can be applied by any transformer models with sequential inputs. Specifically, the float-input directly feeds numerical specifications into the model without discretization by transitional tokenizers to improve numerical representation. Also, the SFCI formulation further provides a compact representation of circuit topologies, which improves the learning for larger circuits. \n\nAnother reason we chose T5 is its smaller model size comparing to more general models, which makes it more suitable for application-specific use cases like this work while also being more energy-efficient and low-cost.\n\n### Q2: Comparison with commercial LLMs\n\nBased on your suggestion, we evaluate o1 using a few-shot setup. We provide 100 example circuits as context and evaluate performance on the same 350 specifications used in our main experiments (Figure 5 in the paper). Below are the results:\n\nSuccess rates at thresholds from 0.01 to 0.1:\n\n|Threshold| 0.01| 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.1|\n| -------- | ------- | ------- | ------- | ------- | ------- | ------- | ------- | ------- | ------- | ------- |\n|Success rate of o1 | 0.27 | 0.32 | 0.36 |  0.39 |  0.40 |  0.41 |  0.42 |  0.43 |  0.44 | 0.46 |\n|Success rate of SFCI | 0.90 | 0.96 | 0.98 | 0.99 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |\n\nMSE of voltage conversion ratio: \n| Metric | SFCI | o1 |\n|:------:|:-------------:|:--:|\n|  MSE   |     8e-5      | 0.602 |\n\nThis result shows that our model significantly outperforms o1, indicating our supervised fine-tuning is needed to tackle the analog circuit design, which demand high precision and the interaction of custom SPICE simulators.", "claims_and_evidence": "The claims made in the submission are well-supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "The methods and evaluation criteria are well-aligned with the problem, effectively measuring improvements in circuit topology generation.", "theoretical_claims": "No theoretical claims were involved.", "experimental_designs_or_analyses": "The experimental design is sound, using benchmark datasets and appropriate metrics.", "relation_to_broader_scientific_literature": "The paper builds on prior work in language-model-based analog circuit topology generation, particularly LaMAGIC. It improves upon previous formulations by reducing output sequence length and enhancing component-type recognition. These contributions align with broader trends in applying machine learning, especially transformer-based models, to circuit design automation. However, expanding comparisons to other ML-based circuit design approaches could further contextualize its impact.", "essential_references_not_discussed": "The paper provides a sufficient discussion of prior work, particularly LaMAGIC, and appropriately cites relevant literature. No essential references appear to be missing.", "other_strengths_and_weaknesses": "The paper presents a well-structured study with clear contributions to refining analog circuit topology generation using language models. The proposed formulations effectively improve efficiency and component-type recognition. While the methodological novelty is somewhat incremental, the improvements in output sequence length and numerical precision make it a valuable contribution.", "other_comments_or_suggestions": "1. The paper focuses primarily on power converter circuits. Expanding experiments to other types of analog integrated circuits or evaluating the method’s transferability to new circuit types would strengthen its generalizability.\n\n2. The proposed approach is tested on circuits with up to six components, which is only a slight scalability improvement over previous work (five components). Evaluating larger-scale circuits would better demonstrate the method’s scalability.", "questions_for_authors": "1. The paper uses T5 as the underlying model. Have the authors tried or considered extending their formulations to other language models (e.g., GPT variants)? How generalizable is the proposed approach across different model architectures?\n\n2. Have the authors conducted comparative experiments with advanced commercial LLMs (e.g., GPT-o1, Claude 3.7, etc.) in circuit topology generation tasks?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yBoiB74Sae", "reviewer": "Reviewer_B3t1", "summary": "This paper addresses the automation of analog topology design, which aims to determine the optimal connections between given nodes while satisfying various constraints. Existing methods, including search-based and reinforcement learning-based approaches, are often inefficient. This paper analyzes the structure of a large language model-based approach, LaMAGIC. To tackle the challenges of low-precision sensitivity and long token lengths, the paper introduces two circuite representations:SFM and SFCI. SFM simplifies numerical input representation, while SFCI preserves a sparse graph structure with improved component-type recognition, leading to more efficient and accurate circuit generation. The proposed method, LaMAGIC2, outperforms baseline approaches by achieving higher success rates under strict tolerances, reducing mean squared errors by up to 10×, and demonstrating superior transferability to more complex circuits, with improvements of up to 58.5%.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Clarification on previous work and our methodology\nWe thank the reviewer for this important comment. Our paper focuses on developing supervised fine-tuning (SFT) methods for language models in analog topology generation task. Our SFCI formulation contributes these key innovations:\n1. It proposes a compact canonical form with component-type tokens to enhance the learning of different circuit devices.\n2. It increases the attention on the float-valued inputs of circuit specifications, thus effectively capturing the relations between numerical circuit specifications and circuit topologies.\n\n\nLaMAGIC was selected as the primary baseline because, to the best of our knowledge at submission time, it is the only prior work using SFT with transformer-based LMs for analog topology generation. Additionally, we compare with a RL search method for power converter to comprehensively demonstrate the benefits of our generative approach over conventional search techniques. These two methods (LaMAGIC and RL) cover well the previous works for power converter topology generation, and we have thoroughly discussed other related methods in Section 2.3 of our paper.\n\n## Question for complexity\nWe appreciate the reviewer’s question and apologize for any confusion caused by our initial complexity characterization. In our original submission, we described the token length complexity as $O(|V| + |E|)$, assuming a simple graph scenario where the SFCI representation is a vertex-to-edge adjacency list for a graph with $|V|$ vertices and $|E|$ edges. \nUpon careful re-examination, we realized this characterization was inaccurate, as our formulation is actually a hypergraph represented by an edge-to-vertex adjacency list.\n\n### Correct Hypergraph Complexity Analysis\nEach hyperedge $e_i$ has $k_i$ vertices. Therefore, the total token length, representing the sum of vertex incidences across all hyperedges, is:\n$$\n\\sum_{i=1}^{|E|} k_i\n$$\nFor our power converter devices, each vertex appears in at most two hyperedges: $d(v)≤2$.\n\n\nThus, the total number of vertex incidences , which equals to the number of edges of all nodes, is:\n$$\n\\sum_{i=1}^{|E|} k_i = \\sum_{v \\in V} d(v) \\leq 2|V|\n$$\nThis upper bound implies the total token length is at most $2|V|$, which simplifies to $O(|V|)$. This result indicates that the token length complexity of SFCI is independent of the number of edges $|E|$.\nThe $O(|V)$ token length of SFCI demonstrates its compactness compared to $O(|V|^2)$ lengths of matrix formulations.\n\nWe will revise the token length complexity to $O(|V|)$ and include the above proof in our manuscript accordingly, to improve clarity and readability for the readers.", "claims_and_evidence": "The proposed methods, SFM and SFCI, are well supported by Figure 3, which also effectively illustrates the disadvantages of previous methods.", "methods_and_evaluation_criteria": "The proposed method is reasonable, but it primarily involves prompt engineering, which is a relatively naive mechanism. The approach presented by the author is an extension of the previous method, but a more advanced algorithm is needed for further improvement. Nevertheless, the evaluation criteria are appropriately set.", "theoretical_claims": "There is no theoretical validation required, but it would be beneficial to analyze or establish a connection to the LLM structure to explain why the proposed method achieves a higher success rate. Additionally, providing a reference that supports the main idea would further strengthen the argument.", "experimental_designs_or_analyses": "The author adhered to the experimental design of previous studies, ensuring the validity of the results. Additionally, while the ablation studies are appropriately conducted, it would be necessary to perform experiments using a different LLM model architecture, given that this paper is primarily experimental.", "relation_to_broader_scientific_literature": "The author discusses search-based and RL-based methods; however, to provide a comprehensive understanding of the automation of analog topology design, more related work should be included. Additionally, sufficient information on analog topology design using LLMs is needed. The author refers to \"one such approach\" for the direct mapping from performance requirements to circuit topologies, but a brief explanation of why LaMAGIC was chosen for this study would further clarify the rationale behind the selected method.", "essential_references_not_discussed": "All essential references are covered; however, additional related works should be included to provide a more comprehensive background and context for the study.", "other_strengths_and_weaknesses": "This paper presents an effective method that integrates large language models (LLMs) to automate analog topology design. The proposed approach is practical and has a significant impact on automation system design. However, the method is somewhat naive, as it primarily relies on prompt engineering.", "other_comments_or_suggestions": "There are no further comments for the author.", "questions_for_authors": "1. Why the author specify 'LaMAGIC' for the baseline algorithm? Is there no other similar research to handle the limitation of the LaMAGIC?\n2. Can the author give a more detailed explanation of how the author changed the tocken length complexity to O(|V|+E|)? It is quite confusing.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ky6c3j8Pmx", "reviewer": "Reviewer_2sgz", "summary": "This paper introduces LaMAGIC2, an improved approach for language model-based analog topology generation. It proposes SFCI, which enhances component recognition, reduces token complexity from $O(|V|^2)$ to $O(|V| + |E|)$, and improves numerical precision sensitivity. The method achieves a 34% higher success rate under strict tolerance and 10X lower MSE compared to prior work. It also generalizes better to complex circuits, improving MSE by up to 58.5%. Future work includes extending SFCI to transistor-based circuits and integrating search-based techniques.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Question for computational efficiency\n\nBased on the question, we further record the training steps that required for matrix formulation (SFM) and the succinct canonical formulation with identifier (SFCI). Specifically, SFM saturates at 8943 steps, and SFCI converges at 6886 steps. This shows that our SFCI reduces 23.0% of training steps compared to SFM, thus enhancing the computational efficiency.\n\n\nWe will include this experimental results if we get accepted!", "claims_and_evidence": "The paper claims that LaMAGIC2 reduces token complexity, improves component recognition, enhances numerical precision, and increases transferability through a sparse representation. These claims are well-supported, as the method effectively streamlines circuit encoding, improves model learning, and aligns with real-world circuit sparsity.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria align well with language model-based analog topology generation. SFCI effectively reduces token complexity, improves component recognition, and enhances numerical precision, all essential for accurate circuit generation. Success rate and MSE metrics appropriately measure performance, while the benchmark dataset from LaMAGIC provides a diverse set of 3–6 component circuits for evaluation.", "theoretical_claims": "The paper does not present formal proofs for its theoretical claims but instead supports its methodology through empirical results. The key theoretical claim is that reducing token complexity from $O(|V|^2)$ to $O(|V| + |E|)$ improves efficiency and model performance. While this claim is reasonable given the sparsity of real-world circuits, it is not formally proven. The paper demonstrates the impact of this reduction through token length statistics (Table 1) and empirical success rate/MSE comparisons (Tables 2–5), but it does not provide a mathematical proof showing how this complexity reduction affects training dynamics or inference efficiency.", "experimental_designs_or_analyses": "The experimental design is generally sound, with well-defined metrics, meaningful comparisons, and ablation studies. Success rate and MSE effectively assess circuit generation, and the LaMAGIC dataset provides a reasonable benchmark. Comparisons with prior methods, including RL-based search and different formulations, demonstrate performance gains, while ablation studies on SFCI variants validate key design choices.", "relation_to_broader_scientific_literature": "The paper builds on LaMAGIC and related work in language model-based circuit generation, improving token efficiency, numerical precision, and transferability by incorporating structured tokenization, float-input formulations, and efficient graph encoding, aligning with broader trends in transformer-based design automation.", "essential_references_not_discussed": "As far as I am concerned, the references are sufficient.", "other_strengths_and_weaknesses": "The paper is clearly written, effectively identifying the limitations of previous methods and explaining how each issue is addressed. The structured presentation makes it easy to follow the improvements and their impact on circuit generation.\n\nWeaknesses are shown in other parts.", "other_comments_or_suggestions": "The claim that reducing token complexity from $O(|V|^2)$ to $O(|V| + |E|)$ improves efficiency is intuitive, as shorter sequences generally lead to faster inference and reduced memory usage in transformer models. However, the paper lacks explicit empirical analysis to substantiate this impact. A more detailed discussion on how token reduction influences training time, convergence speed, and inference efficiency would strengthen the argument.", "questions_for_authors": "Can you provide some results in terms of computational efficiency, e.g., training time or convergence speed compared to previous methods?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "oCbZZys3Tc", "reviewer": "Reviewer_F8r4", "summary": "This paper introduces LaMAGIC2, a circuit formulation approach analog topology generation. The authors identify limitations in previous methods, particularly LaMAGIC, which used inefficient circuit representations with quadratic token length complexity and showed low sensitivity to numeric input precision. Experimental results show that LaMAGIC2 achieves 34% higher success rates under tight tolerance conditions (0.01) and 10X lower MSEs compared to LaMAGIC.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Addressing limitations\nThanks for your advice on discussing the weakness of our methods. This is a helpful idea to contribute more to the community. \n\n\nThe circuit space will grow exponentially with number of nodes increases. In addition, the simulation time for larger circuits will also increase, causing the scarcity of training data and limiting the model generalizability. Thus, this one-shot generation approach may become less effective for significantly larger circuit designs.\n\n\nTo address these challenges, for future works, we are developing search-based decoding methods with our models to generate optimized circuits for larger and more diverse design spaces. For example, Monte-Carlo tree search (MCTS) is a promising method to expand the language model capability in test-time computation. This integration can balance the strengths of generative and search-based approaches, enhancing the quality and practicality of automated analog circuit design solutions.\n\n### Response to Question on Architecture Impact\n\nIn our experiments, all circuit representations (both SFCI and matrix-based) fit within a single 1024-token context window, and no context-window shifting is necessary during generation. Under this setting, we observed that our SFCI consistently outperformed matrix-based formulations. The reduced token length and the use of component-type token of SFCI can improve the model performance and has faster convergence (23.0% fewer training steps compared to SFM, as mentioned in our response to Reviewer 2sgz).\n\n\nGiven that our experimental setup does not require multiple context windows, increasing the window size (e.g., from 1024 to 2048 tokens) would not directly influence the relative benefits of SFCI. However, we expect that as circuit size scales up (e.g., larger circuits exceeding one context window), SFCI would provide greater advantages. Specifically, when matrix-based formulations need context-window shifting, this will lead to degraded performance, since the model cannot see the entire circuit during generation. In contrast, SFCI would be more suitable for generating larger circuits without context-window shifting due to its compact token length.", "claims_and_evidence": "Claim: LaMAGIC2 achieves higher success rates under tight tolerance conditions.\nEvidence: The authors provide comprehensive experiments comparing success rates across different tolerance levels (0.01-0.1), showing LaMAGIC2 outperforming baselines.\n\nClaim: SFCI reduces token length complexity to O(|V| + |E|).\nEvidence: The authors provide theoretical analysis and empirical measurements of token lengths (Table 1), showing significant reduction compared to matrix-based formulations.\n\nClaim: Component-type tokens improve circuit structure learning.\nEvidence: The ablation study comparing SFCI with SFCI-NCT (without component-type tokens) provides clear evidence supporting this claim.", "methods_and_evaluation_criteria": "- Circuit formulations: The authors provide clear descriptions and analyses of different formulations, highlighting their advantages and disadvantages.\n- Comparison with baselines: The authors compare with both previous formulations from LaMAGIC and an RL-search method, providing a comprehensive evaluation.\n- Transferability evaluation: Testing on more complex 6-component circuits with limited training data is a practical approach to evaluate generalization capabilities.", "theoretical_claims": "The paper does not present formal mathematical proofs but makes theoretical claims about computational complexity.", "experimental_designs_or_analyses": "The experimental design is generally sound: The authors use the same dataset as LaMAGIC for fair comparison, with appropriate splits for training and evaluation. Model architecture: Using the same Flan-T5-base architecture as LaMAGIC ensures fair comparison. The simulation-based evaluation using NGSPICE provides realistic performance metrics. The approach of training on 3,4,5-component circuits and fine-tuning on limited 6-component circuits is a reasonable test of transferability.", "relation_to_broader_scientific_literature": "It builds upon prior work in search-based approaches for analog topology design.", "essential_references_not_discussed": "Recent work on graph generation using language models beyond circuit design, which could provide additional context for the token-based graph representation approach.", "other_strengths_and_weaknesses": "Strengths:\n\nThe paper presents a clear analysis of the limitations of existing formulations before proposing improvements.\nThe proposed SFCI formulation is elegant and addresses multiple issues simultaneously.\nThe experimental results are comprehensive and convincingly demonstrate the advantages of the proposed methods.\n\nWeaknesses:\n\nThe paper could benefit from more discussion of failure cases or limitations of the proposed formulations.\nWhile the paper shows improved performance on 6-component circuits, it's unclear how well the approach would scale to even larger circuits.", "other_comments_or_suggestions": "NA", "questions_for_authors": "Have you investigated how the choice of language model architecture influences the performance of various formulations? For instance, do models with longer context windows alter the relative benefits of SFCI compared to matrix-based formulations?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a novel method for large-language-model-based automatic circuit analog topology design. The method builds on a previous method, LaMAGIC, and proposes nontrivial technical improvements including supervised finetuning, compact and better token representations for the output, etc. Issues regarding contribution, evaluation, and lack of details were raised by reviewers, but were addressed satisfactorily. The complexity claim was questioned by several reviewers, but was revised by authors during rebuttal. Empirical results were solid and strong, as agreed by all reviewers.
Decision: Accept (poster)